PHOTOPRODUCTION OF po0 IESONS ON COCPLEX NUCLEI
by
GARY HILTON SANDERS
A.B., Columbia University
(1967)
SUM1ITTED IN
PARTIAL FULFILUEI\l'
OF THlE RETQUIIRiENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPIHY
at the
MASSACHUSETTS INSTITUTE OF TEC2HNOLOGY
June, 1971
Signature
of
Author.,
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/
Certified by ............
..................
.........................
Department of Physics,
.......
.. .... ....
......
.. .....
"'" "'
June, 1971
Thesis Suervisor.
..........
*e
' * *e **o*"
Chairman, Department Ccmnmittee on Graduate Students
Archives
APSS. INST.
APR 28 1971
eA
R I F-
-2-
ABSTRACT
PHOTOPRODUCTION OF p0 MESONS ON COMPLEX NUCLEI
GARY HILTON SANDERS
Submitted to the Department of Physics, March,
1971, in partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
An experiment was performed on the reaction
y + A + A + pO + A + irt++ f-
at the DESY 7.5 GeV electron synchrotron. Using a
double arm magnetic spectrometer, approximately 106
dipion events were detected on thirteen complex nuclei
covering a range from Beryllium to Uranium. The events
were in a kinematic region defined by 20 intervals
in dipion mass from 400 to 1000 MeV/c 2 , 10 intervals
in the po resonance momentum from 3.5 to 7 GeV/c, and
20 intervals in the ;ransverse momentum transfer from
0.0 to -0.04 (GeV/c) .
The data were corrected for systematic effects
and differential cross-sections da/dndm(A,m,p,t)
were extracted, revealing the predominant dynamical
features of the data. Further analysis was carried
out using current models for photoproduction and
scattering on complex nuclei. The aim of this
analysis ,was to:
1) study nuclear density distributions by
fitting the t-dependence of the crosssections for each A to determine the
nuclear radii seen by the po meson.
2) extract the absolute and relative
forward po production cross-sections
by fixing A, p, and t and studying
the dipion spectrum as a function of
-3invariant mass. This gives a
determination of the po line-shape
and background.
3) extract the po-nucleon cross-section apN
and the y-p coupling constant y 2 /4r.
pN
By studying the nuclear density p
distributions and the A-dependence of
the production cross-sections, one
determines the rate of reabsorption of
po by nuclear matter and the effective
single-nucleon forward production cross-
section Ifo12
and the two quantities
above in a self-consistent manner.
Results of the analysis are:
a) Woods-Saxon radii R(A) = (1.12+0.02)A1 '3
b) apN = 26.7 ± 2.0 mb
c) y2 /4f = 0.57 ± 0.10
Cross-sections and resonance parameters are detailed
in the text.
Thesis supervisor:
S.C.C. Ting
Title: Professor of Physics
-4-
THE AUTHOR
Gary Hilton Sanders was born in New York City
on August 27, 1946. His early education was in the
New York public school system. He received his high
school diploma from Stuyvesant High School in June,
1963.
At Columbia University, majoring in physics,
working as an assistant in the Columbia Radiation Labs,
and being caught up in the social and political milieu
of Morningside Heights, combined to make four very
rich and rewarding years. He received his A.B. in
June, 1967.
As a graduate student, research assistant and
New York State Regents Fellow at M.I.T., he did course
work for one year and in June, 1968 went to the
Deutsches Elektronen Synchrotron in Hamburg to join
the M.I.T.-DESY collaboration, where he spent the
next two and one half years participating in photoproduction experiments listed in the bibliography
below, and writing this thesis.
-5-
PUBLICATIONS
1. H. Alvensleben et al,"Validity of Quantum
Electrodynamics at Extremely Small Distances",
Physical Review Letters 21, 1501 (1968).
2. H. Alvensleben et al,"Validity of Quantum
Electrodynamics at Extremely Small Distances",
Proceedings of XIV International Conference on High
Energy Physics, Vienna, September 1968, paper 958.
3. H. Alvensleben et al,"Photoproduction of Charged
Pion Pairs on Protons", Physical Review Letters 23,
1058 (1969).
4. H. Alvensleben et al, Abstract No. 163, Fourth
International Symposium on Electron and Photon
Interactions at High Energies, Liverpool, September,
1969.
5. H. Alvensleben et al,"Photoproduction of Charged
Pion Pairs on Protons", Proceedings of the International Seminar, Dubna, U.S.S.R., September 1969.
6. H. Alvensleben et al,"Leptonic Decays of Vector
Mesons: The Observation of Coherent Interference
Pattern Between p-w Decays", Proceedings of the
International Seminar, Dubna, U.S.S.R.,September 1969.
7. H. Alvensleben et al,"On the Photoproduction of
-6-
Neutral Rho Mesons from Complex Nuclei",Proceedings
of the International Seminar, Dubna, U.S.S.R.
September, 1969.
8. H. Alvensleben et al,"Photoproduction of Neutral Rho
Mesons", Nuclear Physics B18, 333 (1970).
9. H. Alvensleben et al,!!Photoproduction of Neutral Rho
Mesons from Complex Nuclei", Physical Review Letters
24, 786 (1970).
10. H. Alvensleben et al,"Determination of Strong Interaction Nuclear Radii", Physical Review Letters 24,
792 (1970).
11. G. Sanders,"Photoproduction of p0 Mesons on Complex
Nuclei", Talk presented at the Herbstschule fur
Hochenergiephysik, Maria Laach, Germany, September
1970.
12. H. Alvensleben et al,"p-w Interference in 7iiT
Photoproduction", XV International Conference on
High Energy Physics, Kiev, September 1970.
13. H. Alvensleben et al,"Photoproduction of Massive
Pion Pairs", XV International Conference on High
Energy Physics, Kiev, September 1970.
14. H. Alvensleben et al,"Determination of the Photoproduction Phase of p0 Mesons", Physical Review
Letters 25, 1377 (1970).
-7-
15. H. Alvensleben et al,"Observation of Coherent
Interference Pattern Between p-w Decays", Physical
Review Letters 25, 1373 (1970).
16. H. Alvensleben et al,"Observation of Coherent
Interference Pattern Between p-w Decays", Nuclear
Physics B25, 333 (1971).
17. H. Alvensleben et al,"Determination of the Photoproduction Phase of po Mesons", Nuclear Physics
B25,
342 (1971).
18. H. Alvensleben et al,"Photoproduction of Pion Pairs
With High Invariant Mass", Physical Review Letters
26,
273 (1971).
-8-
ACKNOWLEDGEMENTS
I must first acknowledge my supervisor Professor
S. Ting for the example he has set me over the past
few years. I have learned from him how research can
be
pursued in a vigorous and accurate manner. He has
provided me with opportunities to test myself and to
learn, and with many sleepless nights. He has stacked
lead bricks beside me and counseled me and was quick
to tell me when I was wrong. To have been his student
was a strenuous experience, but one which will, I'm
sure, stand me in good stead throughout my career.
My colleagues also deserve my thanks. I appreciate
the direct help of H. Alvensleben, M. Chen, K.J. Cohen,
M. Rohde and H. Schubel. Two in particular, Robin
Marshall and Ulrich Becker have my special thanks for
the many useful discussions by which they taught me
what this experiment was all about. I would also like
to thank Wit Busza for discussions of the SLAC
experiment, and Jim Trefil for helping me understand
the theory.
The scientists who made our collaboration possible
-9-
deserve special mention. They include Professors W.
Jentschke, V.F. Weisskopf, P. Demos, A.G. Hill and
H. Joos. Interesting comments came from Professors
S.D. Drell, B. Margolis, A. Dar, R. Wilson, E.
Lohrmann, and others.
I thank the people at DESY who always treated
me as a guest and provided a photon beam, computer
time and auxiliary services in generous quantities.
I recall particularly H.O. WUster, D. Lublow,
H. Kumpfert and G. Hochweller. DESY is an excellent
laboratory.
I must not forget those at M.I.T. who tried to
make Hamburg and Cambridge seem closer together. They
made the repeated ordeal of airplanes and suitcases
and shipping crates much easier and kept a steady
stream of communication open.
The drawing of FraUlein Ingrid Schulz and the
typing of Frau Hannelore Feind were indispensable in
producing this dissertation. Mrs. K. Ting must be
thanked for the skill and effort she put into Fig. 15.
Herr Peter Berges' technical assistance must be noted.
-10-
I would like to thank Hartmut F.W. Sadrozinski
for all sorts of things and also because he promised
me if I acknowledged him in my thesis, he would
acknowledge me in his.
I must also express my appreciation for the city
of Hamburg (especially the region known as St. Pauli),
the continent of Europe, and Alfa Romeos for always
providing an alternative to high energy physics.
To my parents and family who set me on my feet
and gave me a start and always got me from the airport,
my warmest thanks.
Funds for this work were in part provided from M.I.T.
and also from the U.S. Atomic Energy Commission through
its contract AT(30-1)-2098 with the Laboratory for Nuclear
Science, M.I.T.
-11-
CONTENTS
I.
Introduction
II. Review of Theoretical Models
III. Problems of the Analysis
IV.
Instrumentation
A. The Beam
B. The Double-Arm Magnetic Spectrometer
C. The Electronics
D. The Data-Handling System
E. Systematic Effects and Corrections
V. Analysis
A. Preliminary Steps
B. Dynamical Dependencies of the Data
C. Model-Dependent Analysis
D. Fitting
E. Nuclear Radii Determination
F. Resonance Parameters, Differential Cross-
Sections, Total Cross-Sections and
Coupling Constant
VI. Comparison With Other Experiments
Bibliography
Figures
-12-
I. Introduction
The study of high energy phenomena generally
involves some sort of scattering process. The internal
structure of nuclear matter, interaction dynamics and
the properties of the particles used as projectiles or
produced in the interaction can be investigated.
In the realm of electromagnetic interactions one
is particularly interested in the scattering of photons,
the quanta of the electromagnetic interaction. The photon
and the vector mesons p0 ,w and
*
have the same quantum
numbers J = 1, C = -1, P = -1. This suggests that the
study of vector meson scattering may provide information
on the nature of photon interactions with nuclear matter.
In this thesis I shall describe a detailed
examination of the photoproduction of po mesons on a
variety of nuclear targets. A simple diagram for this
process is shown in Fig. 1. The relationship between
the photon and the vector inesons is commonly embodied
in the vector-dominance model (VDM)1 . In terms of this
model, the incoming photon dissociates into its vector
meson components. This dissociation is facilitated by
the similarity in quantum numbers, requiring only a
-13-
mass change in going from the photon to the vector
mesons. The decomposition of the photon in terms of
the known vector mesons is usually expressed as
(1)
-j (x)
(m2 o/2Y
vo)
v
vP 0,w,-
)
(x)
v(
where j (x) is the total hadronic electromagnetic
current, Vo is an index indicating summation over
Po ,, and
*, mvo is the mass of the respective vector
meson, yvo its coupling constant to the photon and
v0 (x) its phenomenological field operator. Using
this
model, the diagram for p0 photoproduction can
be drawn as in Fig. 2. Here, the transformation of the
photon into the vector meson is depicted as outside
the nucleus. The precise question as to whether this
transformation occurs before scattering in the nucleus
begins or somewhere inside has been discussed by others 2 ,
with the result that in terms of the vector dominance
model, the theoretical results are equivalent.
In addition to gaining understanding of the photonvector meson couplingi the study of vector meson photoproduction on nuclei can afford us a
way of measuring
vector meson-nucleus scattering. Since the vector mesons
-14-
are short-lived objects one cannot produce beams of
them for use in direct scattering experiments. However,
using current models3 for scattering inside nuclei,
one can interpret the production of vector mesons in
the nucleus and their subsequent rescattering in
traversing nuclear matter in such a way as to provide
information about the vector meson-nucleon scattering
amplitude.
Since the models for scattering from complex
nuclei involve assumptions about nuclear structure
(density distributions, radii, etc.) comparison of data
on vector meson photoproduction with these models can
yield information about these nuclear parameters.
That coherent photoproduction takes place without
a change in the nucleus' quantum numbers also suggests
the process may exhibit an energy and momentum
dependence similar to elastic pion and proton diffraction
scattering.
II.
Review of Theoretical Models
Since we are dealing with targets consisting of a
widely varying number of nuclear constituents, the
photoproduction problem is complicated by a whole
range of nuclear physics effects. We require a
description of the scattering process that takes into
account these effects.
High energy hadron production is well treated by
the Glauber theory' and derivatives of it. Light
nuclei can be treated using this model and good nuclear
wave functions. Less sophisticated descriptions of the
nucleus, when combined with the Glauber theory,
provide an adequate description of heavier nuclei.
Such nuclei are commonly described by optical models.
In the Glauber theory one considers the nucleus to
be a collection of discrete scattering centers. An
incoming hadron with an impact parameter b and
momentum t traverses the nucleus and undergoes a series
of scatterings, emerging with momentum t'(see Fig. 3a).
In developing the theory a number of physical assumptions
-16-
are made, and these assumptions define the range of
validity of the theory.
All momentum transfer to the nucleus is assumed
to be transverse. This restricts the theory to
scattering at small angles. In the particular case
of photoproduction of p0 mesons, this assumption is
strictly valid only at infinite energies, since the
mass difference between the photon and the vector
meson implies that there is some minimum longitudinal
momentum transfer. However, even in this instance,
parallel assumptions can be made preserving the main
features of the theory'.
Individual particle-nucleon scatterings are
described by phase shifts Xi.
It is further assumed
that the total phase shift for the complete scattering
process off the nucleus is the sum of these individual
phase shifts. In optics the analogous assumption
(2)
XT
=
Xi
would be to consider refraction through a medium as
consisting of successive refractions through thin
-17-
plates of the medium. This requires that successive
nucleons be close to each other and lie in each other's
shadow.
The model also assumes that the incident energy
is much greater than the Fermi energy of the nucleons,
or conversely, that the interaction time with an
individual nucleon is short compared to its
relaxation time. Thus the constituents are stationary
during the interaction.
These assumptions restrict the model to high energy,
small angle scattering, implying it is particularly well
suited for coherent production. The additive phase shift
assumption introduces optical features to the theory.
Glauber writes the total scattering amplitude as
(3)
Ffi()
k
<ff
A
id2b{e
j
11
2ni
where A =
-
- %', E is the impact parameter, the s
are the individual nucleon displacements .from the
central axis (see Fig. 3) of the nucleus chosen in the
-18-
z direction (along t), the Xj are the phase shifts,
and the indices f and i refer to the final and initial
states. The profile function (the bracketed term
containing the phase shifts) is expanded into a
series resembling the common multiple scattering
series, where each term represents scattering of
different order. Thus
A
A
izx×-1
(4)
rT = e j
= 1- 1[ (1-rk)
k=1
A
A
3 )
= E rk- E rkr 1 + 0(r
k=1
k=1
k l
O(r)
Note the alternation of signs. The first minus sign
has the simple physical interpretation as the effect
of nucleons lying in the shadow of other nucleons.
Many authors have used the general Glauber theory
as a starting point for application to more specific
and useful models. These models differ mainly in
their assumptions about the nuclear physics. I shall
review some of these models, showing the assumptions
built into them and make some comparisons with data.
+***
-19-
In an optical model, Drell and Trefil s have used
a simplified eikonal approximation to first calculate
the total cross-section, comparing it to pion-nucleon
and proton-nucleus cross-sections as a function of A.
Assuming the nucleus to be a purely absorbing medium
of density p(r) they write
(5)
Ta = 4r lfb db (1-exp{-U .:p(z,b)dz})
where U is the projectile-nucleon total cross-section
2
2
averaged over protons and neutrons and r = (b +z )1"
2
Using the hard sphere model for the nuclear density
(Fig. 3b)
(6)
p(r)
r<roA" 3s
{RR(6)0 r<roA''
otherwise
and a modified Gaussian distribution (Fig. 3c)
(7)
p(r) =
1+exp(r 2 -c2 )/ B
;
B = (c/2.2)s
with s representing the skin depth, they find good
agreement with the pion-nucleus and proton-nucleus
data if 5N is taken to be 25±10 mb and -NN is
-20-
45±5 mb. They also take into account, in the comparison,
the change resulting from neglecting the real part of
the scattering amplitude.
For the coherent po production process, letting
A be the momentum transfer, and <f>e i d z be the forward
amplitude for po production by a single nucleon at
r = (z,b), they write the forward amplitude as
(8)
fT = 2w<f>•o bdbf'dz exp{-
Izop(y,b)dy}p(r)e
The integral over p(r) represents the effect of nuclear
shape, the term exp..***} is the absorption of p0 mesons
produced in the nucleus but absorbed before getting out
of it, and the mass change between the photon and p0 is
included by the eiAz with Amin = m/2k. They evaluate
this expression for the two choices of nuclear density
listed above and make a comparison with the early p0
data of ,Lanzerotti et
a16 to obtain values for pN'
--- --pN
albeit large errors, consistent with 30 mb. Finally
they indicate the validity of their neglect of the po
instability, showing that its mean free path in nuclear
matter is much smaller than its decay length. This
has also been discussed by Julius' who shows that this
-21-
is negligible on light nuclei and introduces a maximum
error of only 15% on heavier nuclei at the relatively
low resonance momentum of 2.7 GeV/c.
In a more recent work 2 , Trefil describes a model
in which the Glauber multiple scattering series is
summed and use is made of the closure approximation to
write a single expression which should be valid for all
A and in both the coherent and incoherent regions. If
one wished to interpret data in which the final nuclear
state is known (for example, if one's resolution is
such that coherent production can be separated from
other processes), then the amplitude can be written
(9)
F = < oIFI o>
where F is the multiple scattering series. A reasonable
choice for the ground state wave function To, or Il012
enables ,one to extract information from the data.
However, in the more general case of data including
events in the quasi-coherent or incoherent regions,
all nuclear states contribute, and one can use closure
to separate the coherent contribution from all other
processes. Thus, writing
(10)
EIFfil
2 =
f
2 = Z<ilFtlf><flFli>
I<fIFl i>1
f
and applying closure
(11)
E If><f
f
- 1
the ground state to ground state transition is isolated.
Trefil uses simple nuclear wave functions
A
(12)
p(r) = Iol 2 -
2/2
e-rj/R
R22
;
2
<r
j=1
where <r 2>1 ' 2 is the experimental rms nuclear radius.
He expects this to obscure some of the nuclear physics,
and indeed, in comparing his theory with the 19.3 GeV/c
data of Bellettini et al',for proton-nucleus scattering
he finds good agreement at low momentum transfer (the
coherent diffraction region), good agreement in the
incoherent region, but the model fails in the intermediate region where the differential cross-section
displays structure. In this region it is sensitive to
the details of nuclear shape. The nuclear radius
information in the wave function is sufficient to
predict the behavior of the cross-section at high and
low momentum transfer, even if the shape has been
approximated. Trefil also points out that the inclusion
of closure is essential for the agreement in the
incoherent region, as might be expected. The coherent
region is easily treated by Glauber theories or optical
absorption models, with or without closure.
Trefil also discusses the distortion of the po
line shape as a result of the minimum longitudinal
momentum transfer, pointing out that this transfer
is distributed over the entire nucleus, bringing the
nuclear form factor and all other parameters into the
problem. In addition, the distortion favors low masses
at low momentum transfers, but due to threshold effects,
high masses are favored at high momentum transfer,
where the nucleon Fermi momentum is small compared to
the momentum transfer, and processes like nucleon
ejection take place.
The analysis of the measurements presented in this
thesis was based on a model due to K1lbig and Margolis 8 .
These authors sum the Glauber series and use closure to
extend the formalism to the incoherent region. This
model is intended to treat coherent and incoherent
-24-
production on medium and heavy nuclei. In performing
the summation they have ignored higher order terms
in A- 1 and the t-dependence of the particle-nucleon
differential cross-section. They treat the problem of
the non-vanishing longitudinal momentum transfer (at
finite energies). Since the production process is
sensitive to the individual nucleon contributions,
they present tables of the "effective" number of
nucleons involved in the process. The effect of the
finite po width (po instability) is not included,
although we have already indicated this is a small
effect.
The formula, as used in this thesis, for the
coherent part of the scattering amplitude, includes
also the Woods-Saxon density distribution p (see
Fig. 3d) as incorporated by Kblbig and Margolis.
(13)
f=
(-0)2
27 fofbdbfoodzJo (b/=te
p(z,b)exp(-
-I=
Q(b)
)exp(izvTt_)x
.
o'(1-ia)/fp~z'
,b)d
2
2
exp(-b 2 /4a)g(z,b)d bdz
_0= p 2 (z,b)dz
T(b)
fp(z,b)
0=
dz
-25-
d(a)
= lexp(- OT(b))Q(b)d2b/fexp(-
a = 8 (GeV/c) 2
T(b))T(b)d2b
s = .545 fm
p = po/(1+exp(r-R(A)/s))
This density function gives a more accurate treatment
of the nuclear physics effects. Formula (13) includes
the modifications to the amplitude due to nuclear
correlations as well as its real part. The four
unknowns in this equation are:
a) fo, the effective forward production
amplitude on a nucleus
b) 8, the ratio of the real to the
imaginary part of the scattering
amplitude
c) apN, the total p0 -nucleon cross-section
d) R(A), the nuclear radius for each A
The determination of fo, apN and R(A) can be visualized
simply in the following way. For a set of measurements
of po production on complex nuclei, the relative
normalization determines opN, the absolute normalization
determines Ifo 2, and for each nucleus the variation of
the production cross-section as a function of momentum
transfer determines R(A).
mination of 8 later.
We will discuss the deter-
-26-
It is important to note that the value of Ifo1
2
determined from equation (13) should agree with the
direct measurement from the process y + p -+ p
+ p0 .
We shall return to equation (13) in our discussion of
the analysis.
-27-
III. Problems of the Analysis
Having reviewed some of the models relevant to
photoproduction of p0 mesons on complex nuclei, we
wish to discuss some of the concepts useful in
formulating a method of analysing experimental data.
The aim of such an analysis is the extraction
2
of opN, the total po-nucleon cross-section, Ifo
0 ,
the differential cross-section in the forward direction
as a function of A, the shape of the nuclear density
distribution, the nuclear radii, and using vector
dominance, the photon-po coupling constant y 2 /4r.
The problems involved in the analysis of po data
are numerous. We are first presented with the uncertainties in the spectral shape. This is generally
parametrized by some sort of Breit-Wigner form, but
no theory to date can be used confidently for a
resonance as wide as the pO. In addition, the shift
of the po mass and the skewing of the line shape
further complicates the model. In analysing data
which includes non-resonant background one must have
a scheme for subtracting this portion of the data to
-28-
isolate the pure p0 contribution. The two most commonly
used schemes for calculating the background contribution
are both somewhat arbitrary, neither being on a firm
theoretical ground. The first, suggested by S6ding 9 ,
describes the departure from a simple resonance shape
as the interference between the pure po amplitude and
the amplitude for non-resonant pion pair production
in which one member of the p-wave pair scatters
diffractively off the nucleus (Fig. 4).
The other method involves the use of a term
(mP/m
)4 to modify the Breit-Wigner shape chosen.
Due to Ross and Stodolsky'o this modification then
involves fitting the background with an arbitrary
function which of course introduces additional
uncertainty in the extraction of the cross-section.
Nevertheless, both schemes have been used by
different groups with success in fitting their data.
Julius4 points out some of the problems
associated with doing the analysis as a function of
A. He comments that from a theoretical point of view,
light nuclei are the most suitable for use in
determining the po-nucleon interaction parameters.
-29-
This would be done by studying the dependence of the
forward da/d~dm or da/dt on A. However, the contribution
from incoherent processes is larger on light nuclei,
introducing a large uncertainty in the absolute
normalisation. Thus the confrontation between theory
and experiment should be made by measurements on
heavy nuclei.
If one uses heavy nuclei and a model appropriate
for high A, such as that of K5lbig and Margolis, one
is faced with the extreme sensitivity of the tdependence to the nuclear radius (,R'). Thus, the
value of the po-nucleon cross-section depends
critically on the set of nuclear radii used.
Therefore, in the determination of apN one should
study the relative po yields for a set of nuclei,
emphasizing higher A, in the region of the pO peak.
This minimizes the effects of background, the inability
to parametrize the shape of a wide resonance, and
normalization uncertainties. The nuclear radii used
should ideally be measured at the same time.
The vector meson-photon coupling constant can
-30-
then be determined using
(14)
2
2
47r
647r
2
[fo0
from vector dominance.
t
Another common notation for the coupling constant is
gp =P
p
P
1
P2
-31-
IV. Instrumentation
A. The Beam
The experiment was performed at the DESY 7.5 GeV
electron synchrotron. A bremsstrahlung beam of average
intensity 1011 equivalent quanta per second and duty
factor 2-4% was produced in an internal rotating
tungsten target and passed through a series of lead
collimators and sweeping magnets.
The experimental target was mounted downstream
on a calibrated optical bench. The beam spot at the
target position was approximately 2x2 cm. and square
in shape. The photon beam then passed through a
vacuum pipe shielded from the spectrometer by concrete
and lead, ending in a Wilson-type quantameter''. The
quantameter had a calibration constant of 1.65x10'
MeV/Asec and was filled with 90% He and 10% N2.
9 +2%
The
number of equivalent quanta counted in the quantameter
can be calculated from the formula
(15)
Q = (Quantameter Sweeps) x (Integrator Scale
Factor) x 10 x 1.65 x 1019 x (I/kmax)
-32-
where kma
x
is
the peak photon energy in the bremsstrahlung
spectrum.
The bremsstrahlung spectrum for the tungsten target
can be
(16)
expressed as
f(k,kmax) = T(k,kma x ) a t dk
giving the probability a photon has momentum in the
range k to k+dk. T(k,kmax)
is the spectrum for an
infinitesimally thin target i2 and a t is an empirical
correction for multiple scattering and absorption in
a target of finite thickness. These factors are
expressed explicitly as
(17)
T(k,kmax) = (R-0.925(Z/137)
x{
2 +0.0555)-'
(1+(1-v) 2 )x(R-0.91y-0.925(Z/137) 2 )
-(2/3)(1-v)(R-0.1667-0.925(Z/137)
at = -(1+30/kmax){0.00082278(1
- v) -
2 -0.647y)}
+1.0540
-0.42189v+1 .0953v 2 -0.8049v3 }
v = k(kmax+me)
Y = 100me Z -
1 3
R = ln(183Z - 1'3 )
(k ma x +me ') -
l
1-v) - '
where me is the electron mass. The spectrum is shown(Fig. 5).
-33-
B. The Double Arm Magnetic Spectrometer
Pion pairs produced from pO decay in the target
were counted by a double arm symmetric magnetic
spectrometer shown in Fig. 6. It consists of dipole
magnets (MD, MA, MB), scintillation counters (L2, L3,
L4, R2, R3, R4, SLC, SRC), Cerenkov counters (LC, RC,
HL,
HR) and hodoscopes (TL, TR, QL, QR, VL, VR).
The
pairs first enter the magnet MD which bends them away
from the photon beam and sweeps out low energy background. Pions produced with a central spectrometer
momentum po at an angle 8 from the photon beam are bent
outwards by 15'-0. Within the effective volume of the
magnet (1.0x1.5x0.3 m 3 ), but always at least 5 cm away
from the extreme particle trajectories, considerable
shielding was placed to reduce the effect of the photon
beam line and associated low energy particles as a
source of background in the spectrometer. Because of
its separation from the extreme particle trajectories
the shielding itself was not a source of scattered
background. After the MD magnet, the central momentum
particles are bent inwards by -8o
in the magnet MB
(1.029x0.303x0.106 m') which is 2.18 meters downstream
from the center of MD. Note that this bending angle is
-34-
independent of the spectrometer setting (po,Oo) as is
the bending of the last magnet MA. This points to one
of the spectrometer's properties as listed below. The
MA magnets, located 5.39 meters downstream from the
MB's, bend the central trajectory particles by -12.930
and have an effective field volume of 1.30x0.488x0.166 m 3 .
Three important properties of the spectrometer are:
(1) Since the spectrometer setting is changed
by adjusting the target position on the optical bench
and the MD magnet field in such a way that the bending
of the magnets MB and MA are constant, the trajectory
of the central momentum particles is nearly identical
for all settings. Thus, the spread in position and angle
of all particles as they pass through the counters does
not depend strongly on the spectrometer setting. Therefore, there is no change in counter efficiencies at
different pa and Go.
(2) The acceptance of the spectrometer is
limited only by the scintillation trigger counters
L2, L3, L4, and R2, R3, R4 and not by the magnet
apertures or shielding. This eliminates the possibility
of accepting particles scattered from the magnet walls
or shielding. In order to reduce the rates in the
-35-
hottest counters so as not to increase corrections for
dead-time or decreased efficiency, the counters are
placed so that they are not exposed directly to the
target.
(3) The spectrometer focuses trajectories
of constant pem, preserving good mass resolution and
large acceptance. Sample acceptance limits are shown
in Fig. 7. Typical limits are Ap/po=±0.18, A68/80o-.14,
Am/m-+0.10, and A=+±10 mrad, where ý is the projected
vertical production angle.
In each arm, the two V hodoscope counters, five
T hodoscope counters and fifteen Q hodoscope counters,
giving 22,500 double arm combinations, provided a
resolution in the resonance kinematic quantities of
Amp = ±15
MeV/c 2, App
= +150 MeV/c, and At
=
+.001
(GeV/c) 2 .
C. The Counters
The counters L2, L3, L4,
R2, R3, R4 were used as
trigger counters. All were tested in an external beam
and found to be >99.9% efficient. Made of Pilot Y
scintillator, only .3 cm thick to minimize the effects
-36-
of multiple scattering, they were connected to RCA 7746
phototubes by twisted lucite strips. The tubes were
chosen for high gain and low noise and the counters
were uniformly efficient over their entire areas, a
requirement for fast timing. The dimensions of the
trigger counters were L2, R2 (13.47x33.04 cm), L3, R3
(14.91x33.04 cm), and L4, R4 (18.04x43.06
cm).
The Cerenkov counters, normally used to provide a
veto against pion events during electron runs, were
not in the master trigger logic. Since they were
physically present, their effects on the measurement
(multiple scattering and absorption of pions) were
included in the corrections to the data. Scalers
recording the coincidence rates between the Cerenkov
counters and the pion trigger indicated the electron
contamination of the data was always less than 1 part
in
10 4 ,
as might be expected.
D. The Electronics
The logic, shown in Fig. 8, consisted of circuits
capable of operating at 160 MHz, minimizing dead-time
and accidental coincidences. The resolving times and
-37-
pulse widths of each circuit are indicated in the
diagram.
In each arm, a coincidence was formed between the
trigger counters L2,L3,L4 and R2,R3,R4 (the counters
SLC and SRC were inserted in coincidence with L2 and
R2
to reduce the singles rates in these counters).
The two arms were then put in coincidence forming the
circuit AX. AX was then put in coincidence separately
with each of the three pairs of trigger counters
(L2,R2; L3,R3; L4,R4) forming Xl, X2,
and X3.
The
triple coincidence of these three circuits formed the
master trigger MT.
Thus the coincidence AX provided a
preliminary indication of an event and was used as a
gate to open the more stringent logic network X1, X2,
and X3, the coincidence MT being the final indication
of a double arm coincidence.
Up ,to this point, the Cerenkov counters have not
been inserted into the logic. Two of the Cerenkov
counters (LC, RC) were not used in this experiment.
From the diagram it can be seen that coincident pulses
from the two Cerenkov counters HL and HR were used to
signal that electrons have passed through the arms.
-38-
The electron flag MP was formed by logic similar to
the master trigger logic. The preliminary coincidence
AP was used to gate the final network forming MP.
Events in which an electron was indicated in one arm
fired the circuit MK, and they constituted less than
5% of the data. All events which satisfied the MT
trigger were recorded. The final choice to discard
events with MP or MK on was made later in the production
of the data library tape to be described.
Accidental coincidences were monitored by parallel
logic networks with different coincidence resolution
times. Correction for this effect could then be made
later by extrapolating the rates for the different
coincidence widths T to T = 0. This will be mentioned
again in our discussion of systematic corrections. At
all times, however, this correction was kept below 2%.
E. The Data Handling System
For each event, pulses from the hodoscope counters,
the master trigger pulse MT and the electron pulses MP
and MK were read into a matrix of gated latches. A PDP-8
computer was triggered by the MT signal, and under
-39-
program control, scanned the latch matrix. This information was decoded by the computer which then did the
following things:
(1) Produced a display of all events in the run
showing their distribution in the hodoscopes. This
display was useful in checking for counters which
failed to operate or whose efficiency had fallen
because of some equipment failure.
(2) Separated events which were characterized by
one hodoscope bank failing to record the event, possibly
due to some inefficiency, or in which two or more
counters in one bank fired, possibly a random coincidence. These events could not be sorted into kinematical
distributions, but since they had satisfied the trigger
requirements, they contributed to the total normalization.
Both categories of events totaled between 5% and 10% of
the counting rate.
(3) Wrote the events on magnetic tape in undecoded
form. Each event consisted of 16 six bit words, including
the hodoscope information, special latches, the run
number and event count in BCD format. This format is
shown in Fig. 9.
(4) Transmitted the events to an IBM 360/75 which
ran on-line. This on-line system performed a number of
tasks. A block diagram of the system is shown in Fig. 10.
-40-
Events received by the 360 were binned in resonance m,
p, and t, and divided by the spectrometer acceptances
and other relevant quantities, providing cross-sections
which were sent back to the PDP-8 for immediate display.
The results of previous runs were saved on disk data
sets and combined spectra could also be commanded from
the PDP-8. All data could be dumped onto magnetic tape
for further analysis.
(5) Printed out all run parameters, event plots
and cross-sections at the end of each run.
F. Systematic Effects and Corrections
During the experimental runs all systematic effects
were monitored, and the information obtained was used
later to make corrections to the data.
Data was taken at both spectrometer polarities to
insure that the spectrometer was indeed symmetric. The
agreement of the two rates confirmed this symmetry.
The voltages on all counters were kept constant to
within ±5 volts and all magnetic fields were held stable
to within 3 parts in 10 .
-41-
Normalization runs were made every few hours,
and the reproducibility of the rates measured in these
runs was better than ±1% at all times.
All data were taken with the resonance p close
to the maximum photon energy kmax (kmax/p1l. 2 ) so as
to minimize inelastic contributions.
The targets were chosen with purity greater than
99.9%. The thicknesses of the targets were chosen to
keep the corrections for beam absorption and pion
absorption uniform, and to give yields much greater
than the target-out rater Fig. 11 is a table containing
information on the targets used in the experiment.
Additional systematic effects were treated as
normalization corrections. The corrections were all
made to the number of quantameter sweeps (equivalent
quanta of the photon beam) recorded in each run. The
correction formula used was
(18)
QM corr= QM
GM MT
rawx---x-x(1-DT)x
UGM X1
1 x(1-NA)x -1-
1-BL
RA
-42-
We shall discuss each of the terms in this expression,
corresponding to each individual correction to the raw
quantameter sweeps (QMraw) needed to get the corrected
sweeps (QMcorr).
(a) Due to the structure in time of the synchrotron
spill, the electronics were gated on only during the
central, useful portion of the beam pulse, by gating
signals from the synchrotron. However, the quantameter,
a slow device, could not be gated. Two monitor circuits,
one gated (GM) and the other on at all times (UGM) were
used to correct for the additional quanta recorded
during periods when the gate was off. Typically, this
correction was 2-3%.
(b) When an event was recorded by the latch matrix,
a new could not be recorded until the PDP-8 computer
completed its scanning sequence. During this time, a
busy-anti signal held the electronics inactive. The
circuit MT, previously described, was controlled by
this signal, the coincidence X1 was not. The ratio of
the rates in these circuits provides an accurate
correction for this effect, typically less than 4%.
(c) The dead-time (DT) correction was done in the
following way. Noting that
(19)
DT = (rate)(resolving time) (duty factor)
-43-
the resolving time of the circuits, already described
as 160 MHz circuits, was multiplied by the rates in the
hottest counters L2 and R2. These rates were measured
every half hour during the runs and the synchrotron
intensity was regulated by these measurements,
so as
to control the dead-time correction. The rates were
then averaged over the runs and used in this calculation.
The duty factor is a function of the synchrotron beam
structure, and is used to convert the average rates in
L2 and R2 into instantaneous rates. Using a triangle
approximation for the pulse shape, and noting that the
synchrotron ring was only partially filled (this filling
factor is a function of the machine energy, intensity
and the skill of the operators) formula (19) can be
rewritten as
(20)
DT = (L2/R2 rate)(1/160x106)
x(1/(fill factorx2x50xspill width(sec)x2.75))
where the constant 50 comes from the 50 pulses per second,
2.75 is an empirical correction due to clipping, 2 comes
from the triangle approximation and a typical spill
width is 5x10-4 seconds. Dead-time corrections were ,2%.
-44-
(d) A portion of the photon beam was absorbed in
the target before it could be recorded in the quantameter.
This beam loss (BL) correction was calculated using
formulas for photon absorption from Fermi'3
(21)
n
no
= e
o(cm2 =
Z2
137
28
e
183
9
Z
3
2
27
This is based on the assumption that most of the photon
absorption is due to pair production, valid for 7 GeV
photons. Comparison with more recent calculations of
T.M. Knasel'4 showed excellent agreement. In addition,
a series of special runs were made with target thicknesses
of carbon ranging from 0 to 5 gm/cm 2 tO check the
sensitivity of the count rate to second order effects,
in beam loss and pion absorption. The rate was linear
within 1%, and is shown in Fig. 12.
(e) Absorption of pions in the target and in the
spectrometer material (nuclear absorption NA) was
treated by a combination of measurements and theoretical
calculations. Cross-sections for elastic scattering and
absorption of '+ and r- mesons on Beryllium, Carbon,
Aluminum, Copper were taken from Longo and Moyer's,
Values for other elements were obtained by interpolation
(see Fig. 13).
These cross-sections were used to calculate
-45-
the pion loss in the targets and in the spectrometer.
The assumption was made that the total cross-section
(absorption and elastic) accounted for the loss before
the last magnet MA since elastically scattered particles
would be swept out by the magnetic field. After the MA,
particles scattered elastically through small angles
would still be accepted, so only the absorption crosssection was used. The use of the Longo and Moyer
cross-sections and the assumptions mentioned was
checked by varying the amount of material in the
spectrometer. This was done by changing the gas pressure
in the Cerenkov counters, both for the counters before
the MA magnets, and the pair after the MA's. The
measured change in the rate was in good agreement
with the calculated values. The corrections for pion
absorption for the spectrometer and each of the targets
is listed in Fig. 11.
(f) Accidental or random coincidences (RA) were
monitored during the experimental runs by a series of
parallel logic networks with different coincidence
widths, already described. The rates in the circuit
AXW (15.3 nanoseconds resolution) and AX (5.9 nanoseconds resolution) were then extrapolated to zero
resolution time, this rate being considered the true
-46-
rate. During the runs, the synchrotron intensity was
controlled to keep the accidental rate less than 2%
of the total rate.
An additional precaution taken to minimize
systematic corrections was the use of helium bags at
all places possible along the spectrometer. This
minimized the target-out contribution. Target-out
runs were taken for each setting of the spectrometer
and the measured rates were subtracted from the
target-in rates for the various targets.
-47-
V. Analysis
A. Preliminary Steps
Events written on magnetic tape by the on-line IBM
360, in the format shown in Fig. 9, were decoded by an
off-line program. Events for each run were grouped into
a matrix of dimension 22,500 = 2x5x15x2x5x15 corresponding to the hodoscope combinations. The matrix, plus
all important run parameters (run number, spectrometer
setting, synchrotron energy, quantameter sweeps, etc.)
were then written onto a data library tape. This tape
contained such a block of information for each of the
278 data runs, ordered according to target, resonance
momentum, and spectrometer angle, so as to facilitate
the analysis.
This tape was then used to sort all the events for
a given 'central resonance momentum (4.5, 6.0 and 6.7
GeV/c) into a 4-dimensional matrix (A,m,p,t ) of
dimension (13,20,10,20). The 20 intervals in dipion
mass spanned a range of 400-1000 MeV/c 2 , -the 10 momentum
intervals covered 3.5 to 7 GeV/c, and the 20 transverse
momentum transfer intervals went from 0.0 to -0.04 (GeV/c)
2
-48-
The high statistics of the experiment (more than one
million events), the use of the large number of elements
and the organisation of the data into a matrix of
kinematic quantities enabled careful study of the
dependencies of the data on each of the individual
dynamical quantities. Variation of the cross-sections
on m, p, t_, and A could easily be isolated and the
effects of cuts in these quantities could be studied.
The kinematic assignment of the events to this
matrix was done using Monte-Carlo generated assignments.
Events were generated in the target, and transported
through the spectrometer. Magnet transport was done
using fourth-order magnet transport equations. Tests
for accepted events were made at all magnet apertures
and trigger counters. The transport included the effects
of multiple scattering in the target and along the
spectrometer, since this phenomenon smears the resolution
of kinematic quantities.
Since the spectrometer was symmetric, the simulation
was done only for pions traveling along one arm and the
generation of the pions in the target was flat in momentum and polar angles. Accepted events were binned in
-49-
hodoscope combinations, producing an assignment of
<p>, <e>, and <ý> for each single arm hodoscope
combination. This single arm simulation was extremely
fast on the computer, enabling very good statistical
accuracy of the assignments.
The pion pairs for each experimental event were
then assigned a p, 6, and ý for each member of the pair
and the kinematical quantities of the dipion system
could be calculated. The events were then binned in the
data matrix.
Correction by the spectrometer acceptance factor
was required to extract cross-sections d 2a/dadm from
the data matrix. These acceptances were also calculated
by a Monte-Carlo technique, using a transport which
included both arms of the spectrometer, pO mesons were
generated within the target, allowed to decay, and the
decay pions were transported through the two spectrometer
arms. The transport, like the single arm program,
included the effects of multiple scattering, but in
addition, simulated the decay of pions in flight.
This Monte-Carlo program produced an acceptance
-50-
factor for each hodoscope combination, as well as for
the entire spectrometer window. For pO production with
a differential cross-section d2a/ddm, the counts in a
given
(22)
hodoscope combination is given by
d2o
f(k,km....)
W(s2') d2d2'dmdk
dmdk
f(kkdk
N = Nt Qeff fhod dodm
dSdm
k
4Tr
where N is the number of events, Nt the number of target
particles per cm 2 , Qeff the effective quanta (formula 15),
f(k,kmax) is the weighting due to the bremsstrahlung
spectrum (formula 16), W(0') is the p0 decay angular
distribution in the c.m. system, and "hod" designates
an integral over the phase volume of one hodoscope
combination. This integral can be performed over the
whole spectrometer window as well. Inserting a factor
to transform the integral to one over dp (not dk) and
assuming the variation of d2a/d2dm(m,p,t) to be small
over a single hodoscope combination we can rewrite (22)
(23)
N = Nt Qeff
f(kk_
k
hod (k
d2dm
W(') ddn'dmdp
dd2'dmdp
pk 4Tr
The integral portion of this expression is the
unweighted acceptance of the combination "hod", and
can be written in the usual Monte-Carlo prescription
-51N
(24)
ACChod
I
(
Ntrial
x
if
succ f
k
CCf(k
=
Tr
ka)
ki
AmnpAna
-
Piki
'
47r
where N
is the number of Monte-Carlo successes, and
Ntrial is the number of Monte-Carlo trials. The sum is
performed for each event which succeeds in surviving the
transport. A sufficient number of Monte-Carlo successes
was generated at each spectrometer setting to reduce the
effect of statistics far below the experimental statistics.
The 4-dimensional matrix of data was then constructed in the following way. After each event was assigned
a bin in the space of A, m, p,
and t_,
it
was divided
by Nt and Qeff to produce a count rate, and further
divided by ACChod to yield dz2/dadm(A,m,p,t_). This
simplified procedure, however, ignored the effect of
the spectrometer's finite resolution. An event observed
in a given hodoscope combination, and assigned an m,
p, and t_ on the basis of that combination may actually
have a different m, p, tl,
within the spectrometer
resolution. This can have an appreciable effect on
d2 0/dadm particularly at the edge bins of m, p, and tl.
-52-
For example, for infinite statistics and perfect resolution, a plot of the cross-section as a function of t
in the coherent diffraction region might be expected to
look like Fig. 14 where tmin is the minimum momentum
transfer possible. The effect of spectrometer
resolution could smear this shape in a manner shown by
the dotted, so that some events would be assigned t
values below the physical limit. To minimize the effect
of this smearing on the fitting to be applied later, a
correction must be applied. The procedure used
necessitated assuming a production mechanism and
weighting the acceptances. Previous experimental
measurements 26 show that, above 2.7 GeV/c, the form
(25)
d2a = p 2 2mR(m)f (t)
d2dm
can be used. This procedure assumes all events are from
coherent production and the function fc (t) used was
from the, paper of K1lbig and Margolis' discussed
previously. The mass dependence is a Breit-Wigner form.
As each Monte-Carlo event was generated, it could be
assigned an mo, po, and to from its generated kinematic
parameters. A second set of mh, Ph, and th was assigned
on the basis of the hodoscope combination it was "observed"
-53-
in, the assignment being made on the basis of the
single arm quantities described previously, in a manner
analogous to the experimental events. The weighted
acceptances were then calculated according to
N
(26)
1
WACChod =
(
Ntrial
x
succf(k
sE
i=1
k
i
m.)
ki
Tr
Poik
i
W(__i
i
47T
pi2moiRi(mi )fc. (toi)) AAQ'AmAp
which is similar to formula (24). The procedure for
construction of the matrix of d2 a/dQdm(A,m,p,t,) was
then modified by using the following expression instead
of (23)
(27)
d'o
(A,m,p,t
1
d2dm
) =
N
f
(A,m,p,t,)
NNNtQeffWACC
Comparing this procedure with the one using unweighted
acceptances showed no effect except at the edge bins
where the distortion due to resolution was effectively
removed, indicating the production mechanism chosen
was essentially divided out and would not affect
later fitting attempts.
-54-
B. Dynamical Dependencies of the Data
The 4-dimensional data matrix comprises a comprehensive collection of the results of this experiment.
With it, all the dynamical dependencies of the data
are revealed, and the cross-sections it represents
are the measured quantities, independent of any
assumptions of models, production mechanisms and
background contributions.
A given slice of the data, for a particular
resonance m, p, and t_ as a function of A, illustrates
the major physical processes measured. For example,
choosing p = 6.2+0.2 GeV/c, the cross-sections are
plotted versus m and t1 for all the nuclei in Fig. 15.
The po resonance is clearly observed. The t-dependence
illustrates the diffraction production on nuclei.
The contribution of non-resonant background can
be seen from the variation of the mass spectral shapes
as a function of A and t1. A clearer illustration of
the dependence of this background on A can be seen in
Fig. 16 where the spectra for three elements at
resonance <p> = 6.0 GeV/c has been divided by the
-55-
p and t_± dependence isolating the mass dependence. In
the absence of background, the spectra should be
identical. Note the difference on the low mass side
of the resonance peak. In addition, the less rapid
fall-off of the spectra below the central mass indicates
the skewing of the resonance shape.
At this point, no significant physical assumptions
have been introduced in the presentation of the data
and the portion of the cross-section matrix shown in
Fig. 17 represents the measurement in a pure form.
Further analysis requires the use of theoretical models.
C. Model-Dependent Analysis
The data matrix was then fit to a function of
the form
(A,m,p,tl
(28)
=
2 mRn(m)p 2
(fc+finc) + BG(A,m,p,tJ)
dQdm
where the first term represents the resonant contribution
and the second term is the non-resonant background.
Rn(m)
is a parametrization of the mass shape, fc is the
coherent production cross-section as a function of A,
-56-
t
,
t.L, opN'
R(A), and B, the ratio of the real to the
imaginary part of the forward scattering amplitude on
a single nucleon. finc represents the analogous
contribution from incoherent processes.
The coherent contribution was calculated using the
model of K61big and Margolis 8 . We have already written
the expression for this contribution in formula (13)
with the Woods-Saxon nuclear density. Ifo1 2 is the
forward differential cross-section on a single nucleon.
The attenuation of nuclear matter is represented by
exp(-(a'/2)fzpdz).
The effect of nuclear shape is
given by p(z,b)Jo(bVT!T7, and the mass change between
the photon and the p0 gives the factor exp(iz/ T).
The model of Von Bochmann et al '6 was used to
incorporate the effect of nuclear correlations in this
expression, resulting in a modification of the po-nucleon
cross-section. The new quantity a' includes 5, the
correlation length, and g(b,z), the correlation wave
function.
The ratio of the real and imaginary parts of the
single nucleon scattering amplitude is 8. A measurement
-57-
of yp total cross-sections up to 6.0 GeV1 7 gives ý = -0.2,
consistent with a determination made in the measurement
of the interference between po+e e
pairs"s
.
and Bethe-Heitler
The value of B = -0.2 was used in this analysis.
Incoherent contributions were treated according to
the prescription of Trefil' 9 and the background was fit
with a general polynomial in A, m, p, ti.
Because of the uncertainty in parametrizing the
mass distribution of a wide resonance, several forms
were used in the analysis. If
(29)
r(m,F(m))
= r(m)
=
mpr (m)
1
r (m2 -m2 ) 2 +m2 r 2(m)
p
P
is the relativistic p-wave Breit-Wigner shape due to
Jackson 2 0 , the various forms used were
(30)
Ri(m) = r(m) (m /m)
R2(m)
= r(m) + I(m)
Ra(m)
= r(m)
(mp/m)
+ I(m)
R4 (m) = ro(m) = r(m,fo)
Rs(m)
= r(m)
-58-
where
m2
(31)
I(m)
= D
m
(m2 -m 2 ) 2 +m2
P
P
2
(m)
comes from the Siding interference mechanism 9 , and
(32)
F(m)
(m/2-m
m
is
(m /2)2
p
2
7T
a mass-dependent form of the width of the resonance
peak. The factor (m /m)
4
is the Ross-Stodolsky factor 1 0 .
This factor has also appeared in a model by Kramer and
Uretsky 2 1.
D. Fitting
The fitting was done with the CERN program MINUIT 2 2 .
In order to reduce the contribution of background and
incoherent processes, the data was restricted to the
kinematic region dominated by coherent pO production.
This was done by making the cuts Itl<Itcl , t
GeV 2 /c2 ; 4.8 GeV/c <p< 7.2 GeV/c; and m>mc,
= -0.01
mc = 600
MeV/c 2 . The sensitivity of the fitting to these cuts was
studied. The results were insensitive to changes of mc
by +100 MeV/c2 or tc by 0.01 (GeV/c)2 .
-59-
Similarly it was found that the background function
(33)
BG(A,m,p,t)
1
= ( E ai(A)m)(
i=O
m
Z b (A)pl)(
j=o j
n
k
Z Ck(A)t)
k=O
could be restricted to 1=2, m=n=O since the fits did not
improve for higher orders.
E. Nuclear Radii Determination
By fitting the data as a function of t
with equation
(28) a determination of the nuclear radii R(A) for strong
interactions was made. Previously, nuclear density information had been taken from electron23or proton24 scattering on complex nuclei involving the assumption that
the densities for electromagnetic and strong interactions
are equivalent or ignoring the Coulomb interaction of
the proton. A determination from po mesons is free of
either complication.
In addition to the restrictions placed on the data
above, separate fits were made to the t1 -dependence of
each of the six mass intervals between 690 and 870
MeV/c2 . This was done to minimize the sensitivity of
the radii determination to the parametrization of the
-60-
mass dependence. Fig. 18 lists the results of these
fits in the first six rows. The background function
was assumed to be zero. For the heavier elements
(A>27), the six radii agree with each other indicating
the non-resonant background is very small or is
produced diffractively. The lighter elements Be, C and
Al do not show such consistency, the radii varying
from one mass bin to another. This indicates that
despite the restrictions made to the data, there is a
considerable contribution from background.
To further study the effect of background, fits were
made with various explicit assumptions. For example:
(a) Background independent of p and t,, (b) Background
BG(A,m,p,tL) dependent on p and tL bin, (c) Background
a smooth function BG(A,m) represented by a power series
in m and all mass bins fit simultaneously with Ri(m) as
in equation (30),
(d) Background a smooth function
BG(A,m) with the distribution R2 (m) used. Rows 8, 9,
10, and 11 of Fig. 18 list the results of these fits.
For A>27,
these fits and those made with the choice of
no background are consistent.
Row 12 of Fig. 18 lists the best values for the
-61-
radii, these being weighted averages of the individual
mass bins. Fig. 19 shows these values and the fit to
the scaling law
(34)
3
R(A) = roAA'
The individual fits to this law are also listed in Fig.
18, as are the rms radii corresponding to the best values
of R(A), calculated according to25
(35)
R2 rms = 0.6R2 + 1.4s
2
The errors in this calculation range from 2% on
heavy nuclei to 10% on lighter elements. This can be
attributed to the increased sensitivity to the background and the skin thickness for A<27. In addition,
the model of K61lbig and Margolis is better for higher
A. The fitted rms radii are insensitive to the skin
thicknes's parameter s, this having been checked by
fitting with s = 0.5 fm and s = 0.6 fm and noting no
significant effect, independent of A.
-62-
F. Resonance Parameters, Differential CrossSections, Total Cross-Sections And Coupling
Constant
For fixed A, p, tl, the data was fit to equation (28)
to determine the mass and width of the resonance. Independent of the mass parametrization used, the width was
(36)
0o
= 140 + 5 MeV/c 2
The results for the resonance mass are shown in Fig. 20
for each mass distribution, and the best value determined
from fits with Ri(m), R2 (m), and R3 (m) is
(37)
m
= 765 + 10 MeV/c2
Inserting the values for R(A), m p,0 and BG, the
data was fit for the coherent differential cross-section
do/dt(A) t=O. Values for such cross-sections for 6=O0
Itl=0.002,p=6.54,kmax= 7 .4, are tabulated in Fig. 20,
with the errors. The index n on these En's corresponds
to the various mass forms described. The errors include
the uncertainties in R(A), mp, To, and the background.
Fig. 20 also lists values for the ratio of chi-squared
-63-
to degrees of freedom X2 (A)/DF(A) for these fits.
Ri (m),
R2(m),
R3 (m) give better fits than the other
hypotheses. The fits for R 1 (m) are shown as the curves
in Fig. 15 as well as in Fig. 21 where the background
contribution is also shown. The background per nucleon
is independent of A, indicating it is predominantly
incoherent. The A-dependence of the El cross-sections
is shown in Fig. 22.
Using the measured radii R(A) and the value 6=-0.02,
fits were made for apN , If 0 12, and using (14), y 2 /47r
pN
p
The results are also tabulated in Fig. 20 and the
values are consistent from one mass hypotheses to
another. Choosing the values corresponding to ZC
(38)
apN = 26.7 + 2.0 mb
Ifo
0
2
= 118 + 6 pb/(GeV/c) 2
Y 2 /41 = 0.57 + 0.10
Checks made on the fitting procedure included the
successive elimination of the light elements Be, C and
Al. The insensitivity of the results to this procedure
indicated the heavy elements dominated the analysis,
consistent with the use of the model of Kl1big and
Margolis. In addition, application of more restrictive
cuts in m, p, and t_ did not significantly effect the
results. Changing 8 by ±50% led to only a 10% change
in y2/4w and less than 1% change in the radii R(A).
Finally, apN changes by only 1 mb for a 5% variation
of R(A).
-65-
VI. Comparison With Other Experiments
The study of photoproduced po mesons on complex
nuclei has been a controversial field. At times there
have been dramatic disagreements between various
experimental groups.
The experiment described in this
thesis was motivated by a desire to resolve the
discrepancies.
The complications of treating nuclear
physics effects, parametrizing the resonance line
shape and subtracting non-resonant contributions have
been major sources of controversy. Therefore, in this
experiment, the analysis was as general as possible,
including several alternate hypotheses.
The situation is now somewhat improved, due to the
experiment reported here, other recent experimental
efforts, and a substantial amount of communication
between the various groups involved.
Fig. 23 is a table listing the various experiments
we wish to compare. The experimental conditions, results,
and any special factors in the analysis are shown.
The early experiment of Asbury et a126 was analyzed
-66-
using simpler nuclear models, specifically, the prescription of Drell and Trefil s with a hard sphere
density. No provision was made to include the effect
of nuclear correlations, or the real part of the scattering amplitude. A subsequent analysis of this data
by Margolis 2
7
using a Woods-Saxon density and including
ý gave a number for
apN slightly lower than the original
result.
The most recent analysis of the data of McClellan
et a128 gives results which agree well with those
reported in this thesis. Previous disagreements can
be attributed to assumptions made in the analysis, such
as the failure to include B. Background was treated
using the Siding interference' and no other contribution.
As in all the current experiments, the model of Kblbig
and Margolis was used for the coherent amplitude with a
Woods-Saxon density. Two sets of nuclear density
parameters were employed, one from their own "best-fits"
with an optical model, and one set from electron-scattering data (Hofstadter data). The results are shown
in the figure.
Data from SLAC (Bulos et a1 2 9) gives a opN in
-67-
agreement with other efforts. However, the coupling
constant y2 /4w is somewhat high. This can be attributed
to differences in this group's data. The higher coupling
constant comes from their cross-sections which are about
30% lower. In addition, analysis of their complex nuclei
data alone gives da/dt(yp) t=0- 7 5 pb/(GeV/c) 2 . Further
analysis is being carried out.
Finally, an experiment by a group from Rochester,
Behrend et a130 was carried out on the Cornell
synchrotron. This group used a Ross-Stodolsky1 o modified
Breit-Wigner and the Kilbig-Margolis model. Nuclear
densities chosen were Woods-Saxon forms, but for the
lighter targets Be and C they employed harmonic wells.
They used B= -0.02 but did not include nuclear
correlations. They were able to fit their data for
da/dt(yp) t.0 but preferred to extrapolate the number
quoted in this thesis to their energy region. The results
obtained;, as can be seen from Fig. 23, are consistent
with this paper.
The situation to date is that the experimentalist
is capable of measuring the photoproduced po spectrum
on nuclei to a precision where superior theoretical
models are required for their exact understanding.
-68-
BIBLIOGRAPHY
1.
N.M. Kroll, T.D. Lee and B. Zumino, Physical Review
157 (5), 1376 (1967).
2.
3.
J.S. Trefil, Physical Review 180 (5),
1366 (1969).
J.S. Trefil, Physical Review 180 (5),
1379 (1969).
R.J. Glauber, in Lectures in Theoretical Physics,
(Wiley-Interscience, Inc., New York, 1959), Vol. I,
page 315.
4.
D. Julius, thesis, Cornell University, 1969.
5.
S.D. Drell and J.S. Trefil, Physical Review Letters
16, 552 (1966).
6.
L.J. Lanzerotti et al, Physical Review 166 (5),
1365 (1968).
7.
G. Bellettini et al, Nuclear Physics 79, 609 (1966).
8.
K.S. Kilbig and B. Margolis, Nuclear Physics B6,
85 (1968).
9.
P. Siding, Physics Letters 19, 702 (1966).
10.
M. Ross and L. Stodolsky, Physical Review 149,
1172 (1966).
11.
R.R. Wilson, Nuclear Instruments 1, 101 (1957).
F. Peters and E. Raquet, DESY Internal Report 52-69/1,
1969.
-69-
12.
H.W. Koch and J.W. Motz, Reviews of Modern Physics
31,
13.
920 (1959).
E. Fermi, Nuclear Physics, (University of Chicago
Press, Chicago, 1950).
14.
T.M. Knasel, DESY Report 69/8, 1969.
15.
J.M. Longo and B.J. Moyer, Physical Review 125,
701 (1962).
16.
G. von Bochmann, B. Margolis and C.L. Tang, Physics
Letters 30B, 254 (1969).
17.
J. Weber, thesis, DESY, 1969.
18.
Ii.Alvensleben et al, Physical Review Letters 25,
1377 (1970).
19.
J.S. Trefil, Nuclear Physics
20.
J.D. Jackson, Nuovo Cimento 34, 1644 (1964).
21.
G. Kramer and J.L. Uretsky, Physical Review 181,
1311, 330 (1969).
1918 (1969).
22.
F. James and M. Roos, CERN 6600 Computer Program
Library Write-Up D 506.
23.
H.R.
Collard, L.R.B.
Elton and R. Hofstadter, in
Landolt-Boernstein Tables, (Springer Verlag, Berlin,
1967), New Science Group I, Vol. 2.
24.
R.J. Glauber and G. Matthiae, ISS 67/16.
25.
P.E. Hodgson, The Optical Model of Elastic Scattering,
(Oxford University Press, Oxford, 1963).
-70-
26.
J.G. Asbury et al, Physical Review Letters 19,
865 (1967).
27.
B. Margolis, Physics Letters 26B, 524 (1968).
28.
G. McClellan et al, Report submitted to the XV
International Conference on High Energy Physics,
Kiev, 1970.
29.
F. Bulos et al, Physical Review Letters 22, 490 (1969).
R. Larsen, Private communication.
30.
H.J. Behrend et al, Physical Review Letters 24,
336 (1970).
-71-
FIGURE CAPTIONS
Fig. 1
Feynman diagram for photoproduction and decay
of p0 mesons on complex nuclei.
Fig. 2
Feynman diagram for photoproduction and decay
of p0 mesons on complex nuclei showing intermediate virtual pO propagator from vector
dominance model.
Fig. 3
a) Schematic diagram of scattering problem
treated by Glauber theory.
b) Hard-shell nuclear density.
c) Modified Gaussian nuclear density.
d) Woods-Saxon nuclear density.
Fig. 4
S3ding mechanism
Fig. 5
Bremsstrahlung spectral functions.
Fig.
The symmetric double-arm magnetic spectrometer.
6
Feynman diagram.
Fig. 7
Sample spectrometer acceptance window.
Fig. 8
Schematic diagram of trigger logic.
Fig. 9
Data tape format.
Fig. 10
On-line data handling system.
Fig. 11
Information about the experimental targets
including absorption of the photon beam in
the targets and absorption of decay pions
in the targets and along the spectrometer.
-72-
Fig. 12
Pion pair yield as a function of carbon
target thickness.
Fig. 13
Plots of pion absorption and elastic scattering
cross-sections taken from Longo and Moyer. A
linear interpolation was done to extract crosssections used in correcting data.
Fig. 14
Sketch showing smearing of t-dependence of
do/dt due to spectrometer resolution.
Fig. 15
For <p> = 6.2+0.2 GeV/c the differential
cross-sections are displayed as a function
of A., m, p,
Fig. 16
tl.
Curves are fits (see text),
Mass spectra for three elements after removal
of p and t dependence showing presence of
non-resonant contribution. <p>= 6.0 GeV/c.
Fig. 17
Production differential cross-sections for
all elements in a selected m, p, t_region.
Fig. 18
Summary of nuclear radii.
Fig. 19
Best values for R(A) and fit to R(A) = roA /3
Fig. 20
Summary of results of fits for nuclear radii,
differential cross-sections, apN' resonance
parameters and y-p coupling constant.
Fig. 21
Result of Zi fits for p = 6.2 GeV/c, all
elements. Incoherent background is shown.
-73-
Fig. 22
A-dependence of d
dt
Fig.
Comparison of various pO experiments.
23
=0(A).
-
74-
Fig.1
/11.
/
--- C---Tv
Fig. 2
/
a
Ti'[
/
A
------it
P
PF
-75-
I-
0L
aa
C)
1.L.
L0
ti
o
d
ۥ
..
Cf
j
•CL
Q.
.
-76-
/TL
A
A
A
iT0
0
Fig.4
-77-
r
E
E
Tra
X
E
E
Ne
'4-
C0,
I
aC
CU,
co
LO
LL
-78 -
c-f
+n
+r
+t
(0
01
Go3
or
-79-
NI
I
I
-80-
aJ
w
6)
Li
-
T
0
LAI
-81-
1
I
1
I
ttt~tI
ADC OUTPUTS
T
T
14
3
1'
2 QR15
QR14 QR13 QR12 QR11 QR10
I QR9 QR8 QR7
QR6 QR5 QR4
C,
) QR3 QR2 QR1 QL15 QL14 QL13
QL8
) QL12 QL11 QL10
WORDS
IQLsIQLsIQLliL..IL3L2IQL1 I
QL6 LS QL4 QL3 OL2 QL1
ITRSI TR4 ITR 3I TR 21 TRi IQL9 I
IA
I
T-1--"
I TL5 I TL4 I TL3 I TL2 I TL1 I MP I
-+--I T-{vI M
I
TAPE
JI MKSIL1QL7 1 MK
]
I
SI
1~ IA Ii I 2
RUN NUMBER
4-I8-11
21
(BCD FORMAT)
I
14 8
EVENT NUMBER
(BCD FORMAT)
1
'
8
I
I
1
2
2 14
8
·
I'
I t1I21LIR81112I1
VII
1
I
L
3
4
5
TRACKS
PDP - 8 DEC TAPE
Fig. 9
0
/
DIRECTION
-82-
LLI
<
cn
C,
.J
z
uI
0
-83-
TARGETS
ELEMENT
THICKNESS
pT
BEAM LOSS TE-ABSORP.
Z
A
(cm)
Be
4
9.01
1.5
2.85
1.6
6.87
C
6
12.01
1.5
2.52
2.3
4.11
Al
13
26.98
.5
1.36
2.2
2.13
Ti
22
47.90
.2
.897
2.1
1.31
Cu
29
63.541
.1
.910
2.8
1.22
Ag
47
107.9
.1
1.06
4.6
1.42
Cd
48
112.4
.07
.585
2.5
In
49
114.8
.12
.792
3.5
1.07
Ta
73
180.9
.06
5.8
1.36
Ta
73
180.9
.04
.694
3.8
.91
W
74
183.9
.02
.422
2.4
.56
Au
79
197.0
.02
.452
2.7
.59
Pb
82
207.2
.05
.522
3.1
.68
U
92
238.1
.025
.602
3.9
.78
(g/cm)
1.04
i: - ABSORITION IN SPECTROMETER IS 13.3%
Fig. 11
(%/)
(%)
.79
-84-
RELATIVE
YIELD
300
E
7
200-
100-
-i
-
/
II
i-
THICKNESS OF
CARBON TARGET
·3
r
I-
1cm.
I
2cm.
Fig.12
I
3cm.
-85-
0 (mb)
1000-
+o (TCiL)
4 o (TEs)
4 0( t;BS)
100
Be
S-I-
_ ____1
4 .
C
4
·
A
1
·
Fig.13
·
·
rr··
·
I
|
·
I
-86-
L
zIZ
2l
01
-87-
LL.
LL
-88-
2
2
o0
f--o-
-+-
>•Y
•E
+
/
WOO
0o
c--
i
U_
\
'..
\--4
II
i
m
l
I
-4-n
'
"
I
"
I
.
.
.
.
'
\
\
i
6
a,
\U*
-4-
-
~'-a.
-
\
-891 •"r
BERYLLIUM
-T = I
in
I
0.001
pb/sr.MeV/c Z vs. m(MeV/cZ),p(GeV/c) and t, (GeV/c)2
I
0.003
m 1
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975 I
1005
P_-=
I 11.3
1 11.0
I 12.0
I 12.9
| 16.1
I 17.0
I 21.8
1 30.6
I 36.1
I 32.1
I 20.2
I 12.1
I 9.0
I 5.2
I 1.7
I 1.7
±
+
±
±
+
+
±
+
+
±
+
.
±
+
+
±
2.2
1.8
1.7
1.6
1.3
1.4
1.5
1.5
1.5
1.8
1.8
1.4
1.3
1.2
0.8
0.8
0.5 +
0.6
1 1.1 +
495 1
525 1
555 1
585 I
615 1
645 1
675.1
705 1
735 I
765 I
795 I
825 1
855 1
885 I
915 I
945 I
975 1
1005 I
8,sGEVC
I
0.007
0.009
.
6.1
5.4
14.6
15.2
5.6
7.8
11.7
19.0
29.9
19.9
16.7
4.0
4.9
3.6
12.4
1.2
+
+
±
+
+
+
±
+
+
+
+
±
±
±
±
5.2
2.5
4.6
4.7
2.8
3.5
2.7
3.1
3.0
3.3
5.7
2.1
2.6
2.6
5.6
1.3
7.9
4.9
9.8
13.5
8.2
13.6
13.9
20.1
29.8
20.1
10.1
9.9
3.5
-3.7
+
+
+
±
±
.
+
+
÷
±
+
+
±
±
4.9
3.0
3.9
5.0
3.9
3.8
4.6
5.0
3.5
3.4
8.2
3.2
2.3
5.3
10.8
7.8
10.0
13.6
8.3
20.8
22.7
26.9
29.9
18.5
11.2
7.4
4.0
3.1
9.3
±
±
±
±
÷
±
±
±
_
±
±
9.0
5.3
8.1
18.8
13.6
14.6
26.0
33.7
26.2
17.7
T
8.5
7.8
4.1
-0.6
+
+
±
±
+
±
±
+
_
4.3
4.8
3.0
6.2
3.3
2.4
5.9
4.8
2.8
2.9
3.0
3.4
2.0
1.1
+
6.4
3.3
3.7
3.7
2.4
3.5
3.2
3.3
3.1
2.8
2.6
2.9
1.8
1.6
5.5
14.5 ± 13.2
13.4 ± 5.0
12.2 ±
6.6
16.8 ±
7.0
12.9 t
3.4
13.6 ±
4.3
0.2 ±
4.0
18.8 +
+
+
+
_
+
±
+
+
+
±
+
+
+
+
+
+
±
+
+
_
3.0
2.6
2.5
2.2
2.3
2.1
2.4
2.3
2.1
2.6
2.6
2.1
2.2
1.3
1.3
1.3
14.5 ±
9.7 ±
15.0 ±
16.2 ±
18.8 +
15.8 ±
21.7 28.5 ±
37.2 ±
41.1 "
21.5 +
9.2 ±
5.31
2.8 1.2 "
1.9 +
0.9 +
0.8 4
8.6
4.0
3.3
3.0
2.8
2.1
2.3
2.6
2.6
2.7
2.0
2.7
1.6
1.4
0.9
1.2
1.0
0.8
32.2
8.0
17.0
11.8
14.3
12.8
22.6
26.7
25.7
29.1
20.8
10.2
6.7
2.2
2.7
2.7
0.3
+ 51.6
+ 3.8
÷ 4.3
± 3.7
_ 2.9
± 2.5
÷ 2.5
+ 3.6
+ 2.9
+ 3.0
+ 2.4
÷ 2.3
t 2.1
± 1.4
± 1.4
÷ 2.1
" 2.4
.P
= 66
GEYV/Ct
5.1
5.7
6.9
11.5
7.7
14.4
14.7
17.9
26.2
29.7
27.9
15.9
8.1
6.7
2.1
2.3
2.3
13.1
9.5
12.2
11.1
7.1
13.0
22.9
23.4
30.1
20.9
10.3
7.1
6.9
2.8
4.8
1.2
4.2
3.5
3.2
3.5
2.3
2.1
3.3+ 2.6
" 2.9
+ 2.9
+ 2.7
2.5
+ 2.0
_ 2.0
÷ 2.9
t 1.3
1.1
P = 6.2 GEV/C
1
-1
I
0.005
12.2
10.2
13.0
12.7
15.9
22.3
23.2
30.6
38.6
39.9
25.8
15.1
9.0
4.3
2.9
0.7
0.4
1.0
±
±
_
±
+
+
±
±
±
+
+
±
+
+
±
+
±
±
4.9
2.3
2.0
1.9
1.6
1.4
1.4
1.7
1.9
1.8
1.4
1.4
1.2
0.9
0.7
0.9
1.0
0.7
SI
495 1
525 I 32.5 ± 15.6
555 1 12.5 + 3.3
9.1 ±
4
±
±
±
_
585 I 14.5 ±
2.5
15.2 ±
4.0
615
÷
2.6
14.9 ±
3.8
9.0 +
3.3
13.0 ±
5.2
645 I 24.5
675 I '24.8
705 I 32.4
735 1 40.3
765 1 43.9
+
2.1
22.2 - 3.1
15.4 ±
3.4
18.1 +
3.4
15.8 +
5.8
+
1.7
21.7 ±
23.6
±
±
±
1.9
2.2
2.4
37.8 _ 3.2
39.0 ± 3.3
39.9 ± 3.0
I 28.8
1 14.8
1 7.3
I 4.7
| 2.0
I 2.2
1 1.3
I 3.1
±
±
±
1.7
1.1
1.1
1.0
0.8
0.6
0.6
2.2
24.3
14.4
7.9
2.7
1.0
1.5
795
825
855
885
915
945
975
1005
1 18.0
+
+
±
±
+
±
±
2.0 ±
5.3
-
3.2
14.5 +
3.0
12.0 ±
2.7
30.0 +
43.2 +
35.9 ±
2.8
4.2
4.2
29.6 +
26.2 ±
26.5 +
4.1
3.2
3.5
22.4 ±
26.0 ±
29.1 ±
3.5
5.2
4.2
2.4 22.2 _
1.9 11.3 1.4
7.5 ±
1.1t 1.6 +
0.6
0.6
0.8 -0.1 +
4.1 +
2.0
2.5
1.8
2.2
1.3
.7
0.9
3.4
20.5
11.5
2.7
3.6
3.3
1.3
3.5
2.1
1.9
2.0
1.5
1.2
14.5
9.7
3.1
0.6
0.4
5.5
2.5
Fig.17a
_
+
+
+
±
" 2.5
± 2.9
" 1.6
.
1.6
± 1.4
± 4.1
1.7 ±
1.8
-90-
CARBON
-1
-T = I
0.001
in pb/sr.MeV/c
d
1
___- __A,
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
I 10.9 +
1 14.9 ±
I 13.1 +
1 17.1 ±
I 16.8 +
I 22.2 +
] 26.6 +
1 31.1 ±
1 40.8 +
I 39.8 ±
I 26.8 +
I 16.2 +
I 10.6 +
1 6.6 +
1 3.3 +
i 1.4 +
I 0.3 +
I 1.4 +
1.8
1.9
2.1
2.0
1.5
1.8
1.7
1.5
1.6
2.0
2.0
1.8
1.6
1.3
0.8
0.6
0.3
0.8
0.003
_1
:
5.2
13.7
10.8
11.1
13.1
20.2
25.3
26.8
31.3
35.4
23.8
17.7
4.0
2.1
4.0
1.2
0.0
+
+
+
+
+
+
+
±
+
4
±
+
+
t
+
+
±
.I.
ml
Z
vs. m(MeV/c2 ),p(GeV/c) and t. (GeV/c)
2
0.005
]
_-.
I
0.009
8 GEYLf..- _
5.0
11.4
7.4
13.4
18.8
14.2
20.2
27.0
34.9
34.7
13.8
18.9
7.1
0.3
1.9
2.0
2.2
1.0
3.4
3.2
2.5
2.6
2.3
2.5
2.7
2.4
2.2
2.9
3.8
3.0
2.1
1.3
1.2
0.6
0.8
0.007
1
+
+
+
+
+
+
+
+
+
+
+
+
±
+
+
+
+
2.6
3.2
2.9
4.0
3.8
2.3
3.2
2.7
3.1
3.6
3.8
4.5
2.3
1.4
1.2
1.1
1.3
1.3
6.2
10.2
11.1
10.6
11.3
8.4
12.0
24.2
31.5
23.0
17.9
10.9
10.5
1.9
3.2
2.9
-0.4
+
+
+
±
±
+
+
+
±
+
4
+
+
±
+
±
.
3.6
3.5
3.8
5.1
4.9
5.2
2.9
3.3
3.0
3.5
8.2
4.1
4.2
1.9
1.9
1.3
2.2
6.0
4.9
9.4
12.0
13.5
12.5
16.3
16.4
29.8
20.9
8.6
10.7
0.2
-4.2
3.1
0.8
2.0
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
I 15.1 ±
I 22.5 +
I 27.2 +
1'25.3 +
I 32.5 +
1 47.5 +
I 54.1 ±
) 46.1 .
I 34.0 ±
I 17.6 +
I 8.6 +
I 6.0+
1 3.2 +
I 4.2 +
1 2.5 +
I 1.3 +
,6.=
9.7
3.2
2.8
3.0
2.3
2.0
2.3
2.5
2.4
1.8
1.2
1.2
1.1
0.9
1.0
0.8
0.6
24.3
23.0
25.2
13.7
24.3
32.7
40.9
44.4
48.0
31.1
18.4
11.8
7.5
5.9
2.6
2.3
1.2
3.8
2.6
4.5
5.5
5.0
3.8
5.0
4..6
3.4
3.4
9.1
4.0
1.8
5.9
2.8
0.9
1.6
±
+
+
+
+
+
±
+
+
+
+
+
±
+±
±
-
3.8
4.8
3.0
4.5
4.1
2.6
6.8
4.9
2.9
2.9
4.3
2.5
3.4
2.1
3.7
1.0
+
+
+
+
±
+
+
+
±
+
±
+
±
+
+
±
6.7
6.2
5.3
5.3
4.2
3.6
5.4
4.3
2.8
2.8
1.7
3.3
2.2
4.6
3.1
1.1
P__•= 6.2 GEYtC
5.4 + 52.7
495 I 14.4 + 4.2 -3.8 + 8.7 98.9 , 79.6
9.5
525 I 12.2 + 2.5 13.5 - 3.9 11.5 + 3.8 19.1 ± 7.4
2.6
8.6 + 3.2 13.4 + 3.6
555 1 14.4 + 2.0 14.2 + 3.1
7.2
16.2 + 3.6 17.3 ± 4.5 18.0 + 5.2
585 I 18.4 + 2.1
9.3
615 ) 16.6 + 1.9 18.8 ± 3.5 19.9 " 3.6 19.2 + 4.9
3.2 15.8
645 I 22.9 ± 1.6 22.1 + 2.7 14.2 + 2.8 11.
675 I 31.4 " 1.7 25.8 + 2.6 23.5 + 2.7 18.1 + 3.3 15.6
705 1 37.5 + 1.9 35.3 ± 2.9 33.5 - 3.8 27.6 + 3.5 34.5
3.1 34.3 - 3.6 37.4
2.9 33.6 .
735 I 46.4 + 2.1 46.6.
765 I 46.6 + 1.9 47.3 + 2.9 37.8 ± 3.4 36.6 + 3.3 29.5
795 I 32.4 + 1.6 21.5 + 2.0 25.9 + 2.7 15.3 + 2.7 18.2
1.7 16.6 ± 3.5 15.4
4.5 .
17.6 ± 1.5 19.2 ± 3.7
825
5.2
9.0 ± 1.9 12.4 ± 3.2 13.5 ± 4.3
8.8 + 1.4
855.1
4.2
6.9 + 3.0
1.3 ± 1.1
6.1 + 2.0
885 ) 5.6 + 1.2
1.7
5.1 ± 2.8
6.3 + 3.9
3.9 ± 1.4
915 I 2.7 ± 0.7
5.5
4.8 ± 2.4
1.5 t 1.1
0.5 + 0.8
945 I 2.9 + 0.8
1.7
1.5 + 0.9
0.0 + 1.1
1.9 + 1.0
975 1 2.0 + 0.8
1.0 + 0.8
0.0 ± 0.8
1005 1 0.9 + 0.4
---------------------------------------------------
_.
495 l
525 1 16.5 +
+
+
+
+
+
±
±
+
.
+
+
±
±
+
+
+
+
g_, 6-6 GFV/C -- + 16.1
- 6.5
± 5.0
+ 4.1
+ 3.5
± 3.2
+ 3.4
± 3.6
+ 3.2
± 2.7
+ 2.1
+ 1.8
+ 1.9
+ 1.9
+ 1.2
+ 1.1
± 0.9
32.9
16.5
6.1
20.1
18.6
25.1
33.9
42.0
40.4
24.5
17.8
6.6
1.2
5.2
3.2
0.71
± 17.2
+ 5.1
+ 2.7
± 5.1
+ 3.7
± 3.5
- 3.0
+ 4.1
4.4
± 2.7
- 2.1
+ 2.5
+ 2.1
. 2.0
+ 2.3
1.4
Fig.17b
13.0 ± 17.9
23.8 ± 7.1
7.6 - 3.3
4.6 + 5.8
18.1 + 3.8
24.8 + 4.2
3.7
24.4 4
39.3 + 3.9
3.8
32.3
25.5 ± 3.8
8.7 ± 1.8
7.2 ± 2.9
4.0 + 3.6
4.5 + 2.0
1.6 ± 1.6
2.7 ± 2.8
20.9
17.8
8.8
11.5
19.3
22.8
31.4
32.9
19.7
8.8
4.0
4.9
3.6
6.0
-1.5
1.3
-91-
ALUMINIU4
-r = 1
_
L
d24-0
A MR~ii
0.001.
pb/sr.MeV/c
2
0.003
1
i.
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
1 17.6 ±
I 15.6 ±
1 23.4 ±
1 23.8 +
I 26.3 +
I 30.8 +
1 32.5 ±
I 51.4 _
1 68.1 ±
I 61.7 +
I 40.7
I 24.3 ±
1 17.6 ±
I 7.3 4
I 4.0 4
I 1.6 _
I 1.6 ±
I 3.4 +
-- If
I
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
in
_.ep =-S&
3.8
2.9
3.2
2.8
2.3
2.5
2.5
2.5
2.6
3.1
3.2
2.7
2.5
2.0
1.6
0.9
1.3
2.5
12.8
17.3
20.8
16.6
12.9
27.0
34.8
39.8
49.4
53.2
27.3
26.3
18.6
6.3
3.7
.2.4
5.7
11.5
+ 5.6
± 5.0
4 4.1
+ 4.2
+ 2.9
± 3.8
+ 4.5
± 3.7
± 3.4
± 4.5
± 4.9
+ 5.1
± 5.1
± 2.9
± 2.1
± 1.7
± 4.1
_ 12.2
7.6
3.8
3.5
3.5
2.8
2.5
2.7
3.3
3.6
3.1
2.4
2.4
2.4
1.9
1.3
1.9
2.4
15.9
11.2
21.5
20.3
27.4
23.6
41.1
45.2
61.5
67.4
31.7
25.9
8.9
8.7
1.4
2.8
3.5
± 11.4
4 6.5
- 5.4
± 4.4
± 4.3
± 3.6
± 4.2
± 4.3
+ 4.3
+ 4.3
± 3.1
+ 6.0
+ 2.9
± 3.5
1.5
± 2.2
+ 2.3
1
0.005
10.0
11.2
14.5
18.3
11.0
16.7
19.6
28.2
45.0
45.7
46.9
15.8
8.0
1.6
2.4
3.7
2.6
1.6
EYLC
+
+
+
+4
±
+
+
±
±
.
±
±
4
±
4
5.4
5.0
4.5
5.9
3.7
3.3
4.1
3.7
4.5
5.3
6.8
4.8
3.0
3.0
2.7
2.8
2.8
3.1
1005 1 3.6 _ 1.5
-:
10.6
14.3
6.9
6.5
7.8
6.6
27.1
30.9
41.5
35.8
32.0
6.8
16.4
5.3
4.6 ±
9.7
5.3
4.4
4.9
5.2
5.3
5.4
4.9
4.3
5.4
.10.4
4 3.8
± 6.4
± 5.1
2.7
4.2
0.009
4.3
14.4
11.4
2.0
9.3
20.6
15.8
23.5
36.5
31.4
50.1
20.4
4.4
0.5
± 4.8
+ 6.0
± 5.9
+ 2.9
± 5.3
+ 6.0
+ 6.9
+ 7.0
. 4.7
+ 5.2
+ 26.0
± 6.2
± 3.3
.15.2
2.8 ±
3.6 ±
3.2
4.1
.
±
±
±
±
±
±
+
±
±
+
+
±
5.8
6,9
3.8
2.9
4.1
3.9
7.9
6.0
4.3
4.1
6.4
5.1
2.6
2.1
7.5
2.6
tF,6 G=Y.--_6eC-
37.4 ± 12.4
9.7 ±
6.3
11.2 +
5.5
-0.7 ±
7.0
±
+
±
+
7.6
3.9
4.6
5.7
5.1
14.3
18.1
35.3
±
±
±
4.8
7.0
4.7
5.9
6.2
47.4 ±
5.8
46.6 ±
9.1
7.2
3.9
2.8
50.0 ±
27.1 18.6 ±
6.2
5.2
3.3
36.5 +
25.2 ±
14.5 ±
5.8
4.3
4.7
14.6 +
3.9
8.1 -
4.1
6.9 +
3.5
2.9 +
1.9
4.4 ±
3,1
1.9 -
3.7
8.1 +÷
2.9
6.0 4
2.9
5.2 +
3.5
2.1
4.9 ±
3.1
4.5 +
3.7 +
2.8
2.8
6.4 +
5.4
+ 4.8
27.0 ± 11.2
17.3 +
5.9
14.0
23.0 ±
645 I 38.0 ±
675 I 47.6 ±
705 I 65.6 ±
4.3
3.4
3.1
3.6
24.1
25.2
39.3
52.1
±
±
±
±
6.5
4.4
4.4
5.1
22.4
30.2
36.6
52.0
±
+
±
±
6.9
6.3
5.1
4.8
14.4
11.2
16.8
33.9
735 I 77.5 +
765 1 78.5 +
4.0
61.4 ±
5.6
53.4 +
795 I 55.7 +
825 I 33.2 +
4.1
3.0
2.0
65.0 40.8 +
22.9 ±
5.0
4.0
2.9
55.7 +
30.7 ;
17.4 +
16.9 +
2.0
17.5 ±
2.7
10.1 ±
1.8
5.2 ±
2.2
7.8 +
1.9
2.8
2.9 ±
0.6 +
1.1
0.7
7.4 ±
÷
1005 I 1.1 +
11.3
0.8
7.2
0.0
9.2
19.5
25.2
27.6
37.6
24.5
20.7
5.0
3.7
-0.2
6.5
2.2
11.8 : 15.1
9.0 ± 10.6
_ 7.3
. 91.0 198.5 ±203.3
- 6.5 23.4 ± 11.7
5.1 ± 3.9
± 5.6
14.0 ± 6.1
± 5.9
4 4.3 14.7 . 5.1
8.2 + 3.9
± 4.5
± 3.6 30.4 ± 5.6
. 6.3 31.1 4 5.0
+ 4.9 46.8 ± 5.8
± 5.0 52.2 4 4.8
4 3.7 19.8 ± 4.0
+ 3.3 10.8 + 3.4
6.8 - 3.8
± 2.6
6.7 ± 3.2
. 2.6
3.6 ÷ 3.9
2.5
- 2.5 11.7 ± 8.4
1.8 + 1.9
t
2.8
2.6
.. P
-..
40.6
56.3
12.3
16.9
15.3
16.3
24.7
27.3
50.5
46.5
51.8
32.2
12.5
5.3
3.7
5
.5
2.•
-1.4
4.7
975 I
±
±
±
+
+
+
±
±
±
-
3.5
3.8 ±
28.6 +
855 I
885 1
915 1
945 I
1
0.007
P =P 62 GEFYV/C
I 14.3 ±
I 14.5 +
I 22.7 +
I 23.7 +
I 26.4 +
I 37.3 +
I 47.5 +
I 65.4 +
1 83.8 ±
I 73.0 ±
I 47.7 +
I 30.0 +
1 18.5 +
I 9.7 ±
1 4.3 +
I 2.3 I 4.4 ±
M__I
495 I
525 1
555 I
585 I
615 I
m(MeV/c2 ),p(GeV/c) and tl (GeV/c)2
vs.
S
3.1
1.6
0.5
1.2
Fig.17c
-92-
TITANIUM
-T =
-,~
M
1
in pb/sr.MeV/c2 vs. m(MeV/c2),p(GeV/c) and t1 (GeV/c)
AA
1
0.001
I
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
I
0.003
P = ----5.8 GFV/C
-,,
5.4 + 5.9
--~--
23.5
23.4
32.9
30.1
32.2
43.7
52.6
55.6
81.0
86.2
55.4
35.2
22.8
8.8
4.4
3.9
0.0
1.3
+
+
+
i
±
+
+
+
±
+
+
+
+
±
±
±
±
+
5.1
4.0
4,3
3.8
2.8
3.3
3.6
3.4
3,8
4.9
4.7
3.9
3.4
2.7
2.0
1,8
1.2
2.6
12.1
17.4
18.4
20.4
14.9
30.9
32.2
58.4
62.4
61.0
36.0
23.4
13.0
3.9
5.5
1.8
+
±
+
+
+
+
+
±
+±
±
+
±
+
+
±
±
4.2 +
i
0.005
7.3
6.3
4.4
5.4
5.4
4.7
5.1
5.6
5.0
6.4
6.8
6.1
5.2
3.0
3.3
1.8
11.3
6.1
8.6
20.2
26.2
31.2
39.9
53.1
59.5
27.4
25.6
16.6
0.0
5.2
+
_
+
±
±
+
+
+
+
i
±
+
±
1.7 +
5.8
3.5
5.4
5.4
4.4
5.8
5.6
6.6
7.7
6.9
7.4
4.8
2.6
4.2
3.5
0.007
I
,,
0.009
,-,,
0.5 ± 10.4
0.1 + 2.8
16.6 ± 6.9
9.4 + 6.8
21.7 " 7.5
4.5 4- 6.5
11.3 ± 4.8
28.6 i 6.2
47.4 +4 6.2
23.1 + 6.4
56.8 ± 16*2
14.1 ± 6.5
13.9 + 6.9
10.0 + 11.1
9.28
8.2
3.9 4
3.9
7.8 + 6.8
11.4
3.0
8.0
12.2
-0.8
15.7
24.1
18.0
29.8
14.8
9.0
11.4
1.1
-8.3
P. = 6..-.24EY/C
525
5.5
19.0 +
555 I 23.8 ±
4.2
21.9 ± 6.8
585 | 39.0 +
615 1 33.0 ±
5.1
3.6
37.0 ±
34.2 ±
645 I 46.2 ±
3.1
38.9 ±
5.2
26.4 " 5.3
11.4 + 4.8
675
3.3
37.5 +
4.6
4.2
22.8 +
5.3
53.5 +
30.1 +
20.5
5.4
46.7
6.7
37.7 +
6.3
21.2
4.9
4.6
3.7
3.5
3.2
2.5
2.0
75.6 ±
75.4'±
45.1 ±
17.9 ±
24.0 ±
3.9 ±
5.3 +
6.0
6.1
4.8
6.5
5.1
3.6
2.7
58.0
48.9
36.2
16.3
9.9
12.8
4.5
7.0
6.4
5.4
4.6
4.1
4.9
2.8
46.1
55.2
34.6
17.2
18.8
8.3
4.4
7.1
6.6
6.5
5.3
7.2
4.2
3.0
43.2
44.3
21.5
13.1
12.2
2.2
1.2
1.9
2.4 +
3.8
1.4 +
2.0
0.1 - 5.9
2.9 + 3.0
705
735
765
795
825
855
885
915
I 70.1 + 4.0
1
1
1
I
I
I
97.3
99.5
63.7
37.5
23.1
11.2
I 8.4
+
+
+
+
+
+
+
945 1 0.9 ±
975 I 3.0 +
1005 I
2.7 ±
2.9
1.6
2.0 ±
I 48.8 + 28.9
I 31.9 +
8.1
1 32.5 + 6.0
1 38.1 +
r%47.4 +
1 63.9 +
1 94.2 ±
1118.3
1112.7
I 77.5
I 45.3
I 28.3
I 14.8
I
I
I
I
9.4
6.6
5.4
_
.. 1M
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
±
+
+
+
+
+
8.7
5.8 +
3.4 +
4.7
6.0
4.5
4.0
4.8
5.5
5.8
4.5
3.0
3.3
2.8
2.5
1.7
1.6
2.6
27.3
33.6
30.8
40.5
46.0
72.5
79.0
95.9
58.0
31.5
24.7
11.9
7.3
3.6
6.5
2.5
3.4
8.3
21.4 ± 15.3
I 58.1.
9.2
3.0
5.2
6.5
2.0
5.8
9.4
8.9
6.0
5.5
13.6
5.6
3.2
11.8
1.7 ±
,
I
495 I 18.9 + 10.5
I 22.1 +
2
133.1 ±139.3
14.6 +
8.9
3.9 ±
7.8
20.7T
7.5
4.2 t
4.4
3.9 + 10,2
13.4 +
27.4 ±
6.7
6.0
2.4 +
9.4 +
4.1
4.1
4.5 ±
9.8 +
3.9
7.0
7.5 4
6.0
+
+
+
+
+
+
±
.
±
±
+
+
14.3 ±
"
+
+
+
±
+
+
±
+
7.2
4.3
8.1
8.8
6.0
5.2
6.0
8.0
3.1
2.3
20.5 ± 26.0
2.8
2.7 + 2.7
18.6 ± 17.5
2.3 +
4.7
P = 6.6 GFV/C
± 14. 1
± 9.0
± 8.6
+ 6.3
+ 5.5
± 6.7
± 7.3
± 7.1
+ 6.0
+ 4.4
+ 4.1
+ 3.6
+ 3.2
± 2.1
+ 5.1
± 2.8
23.9
11.9
22.4
16.1
39.7
51.1
52.8
61.4
38.0
19.8
8.2
11.5
4.1
4.2
3.3
13.1
11.4
5.6
7.8
6.3
5.9
5.5
7.0
9.1
5.3
4.1
4.4
4.6
2.7
3.7
4.6
8.1
Fig.17d
24.2
24.5
12.0
21.4
19.9
44.6
46.3
48.2
27.8
24.0
13.8
17.8
4.9
4.4
5.2
+ 12.5
± 8.5
± 8.6
+ 5.6
± 5.9
+ 7.2
+ 6.3
+ 7.9
± 7.1
+ 4.7
± 6.4
+ 7.4
± 3.0
± 6.2
+ 5.9
5.3
-3.6
13.3
28.0
22.3
36.7
40.4
35.4
18.4
11.8
6.8
1.9
0.7
7.5
6.4
±
+
+
+
+
±
±
+
+
+
±
±
+
+
6.0
7.8
7.5
11.1
5.5
6.7
9.2
6.6
5.3
5.6
4.0
4.1
3.3
6.5
7.0
-93-
COPPER
?-d
pb/sr.heV/c
1 0.003
in
m
-T = i
0.001
S_
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
20.4
19.3
23.0
27.1
34.8
42.4
57.2
72.0
95.4
95.7
68.7
36.2
29,6
5.7
4.6
5.6
2.8
7.3
4.2
3.7
4.9
5.6
3.9
4.0
3.6
3.5
3.9
4.7
5.0
4.1
4.1
2.5
2.4
3.2
1.7
4.3
14.8
11.4
17.0
29.8
22.3
34.4
43.0
54.6
69.0
54.7
38.7
32.4
18.3
16.9
5.8
6.8
0.3
.MI
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
1 25.4
1 31.5
1 28.4
i
43.7
I 28.3
I 52.8
1 66.0
1 90.1
1110.5
1110.5
1
I
1
I
I
I
74.9
45.2
25.9
13.9
8.7
8.4
1 2.8
I 3.4
I
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
1117.0 ±
1116.7 +
I 87.7 ±
1 43.4 ±
1 25.3 +
I 17.7 .
1 7.4 +
I 6.8 ±
I 4.5 +
I 4.4
vs. m(MleV/cZ),p(GeV/c) and tz (GeV/c)
1
8,9
6.1
7.3
6.4
4.4
4.8
5.4
5.2
4.9
5.8
7.7
6.8
6.2
5.2
3.2
3.4
4.7
2
0.005
I
0.007
I
0.009
GE--------------------------------------------------
20.7
13.0
19.9
16.7
8.0
5.7
7.6
7.1
5.7
4.5
6.2
5.2
6.5
6.8
8.7
7.5
4.5
3.8
2.9
3.9
22.3
28,0
34.8
38.5
59,5
48.7
39.6
23.2
11.9
3.2
1,4
5.2
--
5.2
6.6
7.4
5.3
6.3
9.5
5.3
5.1
5,6
5.8
14.9
4.9
9.3
17.1
-1.0
2.0
14,0
20.6
20.7
45.3
22.1
20.8
30.0
2.2
7.7
3.2
2.4
-2.1
----
-
13.5
2.4
12.4
7.5
12.4
13.6
33.8
33.9
20.0
15.8
22.8
11.1
17.3
5.1
6.2
7.7 -7.7
5.1
2.6
11.4
2.5 ±
9.8
2.4
8.1
5.9
6.5
5.1
10.1
9.9
4.6
5.0
21.6
8.5
5.3
10.9
5.0
P_= 6.2 GEVlYr
9.1
6.7
5.0
5.2
3.9
3.4
3.4
4.3
4.9
4.5
3.9
3.7
3.6
2.8
2.2
2.7
2.0
1.8
-11.2
36.4
19,2
34.6
24.2
34.4
41.9
61.2
84.7
80.0
47.7
11.4
16.5
16,7
2.4
7,3
2.1
-0.7
24.2
10.1
6.5
7.7
6.1
4.8
4.6
5.6
5.8
5.8
4.7
5.0
4.0
4.8
2.3
4.4
2.3
3.8
15.7T
17.6 +
20.2 ±
7.8
7.9
8.5
37.2 +
7.2
18.4 + 4.6
31.7 + 4.4
45.9 + 6.2
53.5 ± 6.1
55.8 + 6.3
36.6 + 5.1
6.6 +4 3.7
20.9 + 6.7
4.5 + 4.7
2.8 + 2.9
6.1 + 4.9
2.7 ±
-6
1 21.3 ± 17.8
I 15.2 +
I 46.9 ±
I 42.4 1,57.3 +
I 68.1 +
I 96.4 +±
2
6.2
6.6
6.2
5.1
4.1
4.6
5.1
5.6
4.4
2.8
3.1
2.8
2.1
2.1
1.9
4.5
-55.7
16.5
21.9
111.3
11.6
7.2
6.8
6.1
5.3
5.3
5.4
6.2
7,4
12.5
14.8
24.7
33.9
38.9
41.5
31.8
9.9
0.0
6,0
11.0
5.5
5.8
3.6
5,3
4,2
7.2
2.8
8.8 ± 5.3
1.0 + 10.9
10.6 ± 6.0
-006 + 3.7
17.8 + 8.3
10o3 S3.1
7,7
.
20.6
10.2 + 5.1
26.4 + 4.6
19.7 + 4.6
11.0 + 5.4
12.7 + 6.1
-0.5 + 1.5
1.4 + 6.2
8.4 + 10.6
2.9 + 3.5
4.4 + 4.5
GC-----------------------
41.7
38.6
31.1
22.5
30.7
46.0
78.1
83.9
86.2
62.6
34.1
21.8
9.2
6.1
6.8
4.4
3.9
± 33.1
+ 14.1
+ 9.6
- 9,.8
+ 6.1
± 5.5
± 6.5
± 7.0
± 6.4
+ 5.7
± 4.3
+ 3.6
4 3.4
± 3.2
+ 3.0
± 2.7
" 3.0
13.5
10.2
28.7
17.7
21.2
43.1
47.5
61.1
50.1
46.7
30.3
5.8
6.0
3.7
-0.7
11.2
17.3
6.5
8.3
8.9
6.1
6.3
5.0
6.9
7.5
5.5
4.4
4.6
5.6
2.9
1.4
6.7
Fig.17e
55.5
3L.4
17.2
16.6
22.2
29.9
43.0
42.2
44.7
27.5
16.3
2.8
9.6
1.2
6.1
7.4
10.2
+ 60.3
4 13.3
13.7T
+
17.1 4.
7.9
4. 15.3
+ 6.4
+ 7,0
± 6.6
± 5.8
+ 6.9
± 6.2
± 3.8
± 3.9
+ 7.0
± 2.2
± 4.8
± 6.0
+ 12.0
-1.2
16.4
21.7
30.6
32.6
46.5
24.9
4.4
8.8
2.6
7.5
5.6
-8.7T
9.0
8.8
9.7
±
± 10,7
+ 8.4
± 6.1
± 7.6
± 6.9
+ 5.3
+ 4.0
±
3.9
+ 6.0
+ 4.9
+ 4.1
17.3
-94-
SILVER
1A
-T = I
0.001
-M-I
in pb/sr.MeV/c2 vs. m(MeV/c ),p(GeV/c) and t.
1
0.003
-
I
i
0.005
5.1
4,4
4.2
4.3
3.1
3.3
20.0
11.2
22.2
25.4
28.6
33.8
±
±
±
±
+
±
675 I 61.7 +
7.8
5.2
5.0
5.7
4.4
4.1
3.3
43.4 +
4.8
23.8 + 4.0
3.5
3.9
4.8
4.6
48.5
65.9
52.4
42.3
+
±
±
±
4.6
4.6
5.5
6.4
33.3
39.7
34.4
23.6
±
±
+
_
+
±
3.1
3.0
2.4
2.8
1.9
2,3
14.0 ±
4.1 ±
0.8 4
1.5 ±
2.5 ±
4.5
2.6
1.5
1.6
3.2
+
±
±
+
+
±
4
+
±
±
±
+
±
±
±
±
±
11.1
7.5
4.7
4.7
4.3
3.3
3.4
4.0
5.2
4.5
4.5
3.9
3.4
2.7
2.0
2.8
3.5
2.2
I 24.2
I 30.7
I 30.8
1 43.3
I 43.6
1 48.8
705 I 82.5
735 1102.8 ±
765 1100.1 ±
795 I 65.3 ±
825
855
885
915
945
975
1005
M
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
M
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
I 41.4 4 3.8 24.9 + 5.5
j 23.2
I 13.7
I 7.5
) 10.6
I 2.7
1 2.3
I
25.7
19.5
27.2
33.7
33.2
43.0
58.8
84.4
81.5
44.7
33.1
20.2
7.2
3.6
4.0
± 10.4
± 6.1
± 5.6
+ 5.5
± 4.4
4.2
+ 4.8
+ 5.5
± 5.7
+ 4.3
± 7.6
+ 4.4
± 3.7
± 2.3
± 2.7
6.6
-0.7
5.9
2.3
3.0
20.2
10.5
13.0
23.7
22.0
28.0
40.2
54.6
50.5
32.3
10.6
8.9
7.9
6.9
3.9
-1.5
1110.0
1140.5
1135.3
1 95.5
1 58.1
30.2
1 16.2
10.0
I 6.6
6.1
7.5
- 38.4
4 8.9
+. 6.2
± 6.6
+ 5.1
+ 4.3
+ 4.5
+ 5.2
+ 5.5
+ 4.4
+ 3.2
± 3.2
+ 2.7
+± 2.4
1.7
±
2.1
+ 3.8
5.9
3.9
5.8
5.6
5.5
3.0
-1.2
7.5
4.2
6.1
5.4
1.8
4
+
+
4
0.009
4
±
+
+
±
6.9
4.1
3.9
5.2
4.3
4+ .2
16.4 ±
4.0
13.5 ±
5.2
4.1
4.4
4.6
9.7
17.1
17.2
10.6
-3.3
7.1
4.0
3.8
6.6
± .4.5 17.4.
+ 5.3 30.0 ±
+ 5.5 12.2 +
+ 5.8 26.1 4
13.0
P = A.A
I 86.3
1 43.9
1 37.6
I 53.2
1 '64.3
I 83.7
±
+
4
+
4
+
I
2
5.0
2.2
3.7
4.6
1.3
10.6
±
4
4
±
±
+
+
+
+
±
71.9
28.6
37.6
19.9
49.7
57.4
73.8
84.3
88.0
69.8
35.1
20.0
13.5
8.0
3.3
3.1
5.8
45.7
13.3
6.4
9.5
18.7
7.2
25.3
7.0
26.5
5.6
29.6
45.4
5.9
6.3
51.4
5.9
51.3
5.8- 28.1
4.5 16.2
3.4
12.4
3.5
8.1
3.1
3.6
0.7
1.6
3.5
2.1
8.9
5.0
6.2
2.2
3.6
3.8
3.4
3.7
4+ .4
16.5 + 6.1
8.8 ±
3.7
2.9
1.9
4.7
2.4
3.2
4.4 + 3.8
3.9 + 5.5
6.8
13.6
1.2 +
-5.4 +
3.0
7.6
3.2 ±
3.5
GEV/C
+
+
+
+
9.2
5.0
6.2
5.4
4.7
k
± 3.7
+ 5.2
- 5.8
+ 6.0
± 4.5
± 3.5
t 3.4
+ 3.4
+ 3.2
4 3.3
3.0
10.6
4.6
9.8
13.1
5.7
20.4
21.5
29.4
24.6
13.8
13.9
4.4
4.8
3.5
5.9
2.0
± 10.3
+ 3.7
± 5.6
± 4.9
+ 3.3
+ 4.3
± 4.0
+ 4.7
+ 4.0
4 4.1
+ 4.1
+ 3.2
± 2.7
± 2.7
+ 6.1
4 2.1
5.4
0.9
9.4
11.5
9.7
8.1
13.9
15.4
17.8
14.1
2.5
1.3
-0.5
-0.1
_
±
±
+
±
±
±
+
±
±
±
+
3.3 +
I
1
9.3
3.9
21.1
8.5
22.6
18.0
P = 6.2
I 24.2
1 46.9
I 31.6
I 31.9
I 50.9
I 56.1
1 77.0
1101.3
1128.4
1113.3
I 88.9
I 56.4
I 31.6
I 16.1
I 9.8
I 4.3
I 6.7
I 5.6
0.007
P =-5.8 GEYLC
/
+
4
±
±
+
495
525
555
585
615
645
(GeV/c)
C•vIr
6.5
6.3
8.3
7.0
5.0
4.5
5.6
7.1
4.2
3.3
4.4
3.4
2.1
2.5
4.7
7.2
Fig.17f
4.4
7.2
4.0
7.6
3.8
2.2
5.6
4.6
3.5
3.6
2.8
4.2
1.1
1.7
3.5
__,,,
54.8
3.1
11.2
15.1
25.5
19.8
26.5
35.8
30.8
16.1
14.7
3.9
4.6
2;0
3.0
5.0
+ 65.6
+± 6.1
+ 5.7
+ 8.3
4. 6.1
+ 5.3
+ 4.9
± 4.4
± 5.3
± 4.8
+ 3.2
+ 3.4
+ 3.7
+ 1.6
± 2.8
+ 6.3
-0.4
3.8
6.4
11.1
15.0
11.3
15.0
14.2
6.8
3.0
1.2
4.3
1.7
±
±
4
+
±
±
±
±
±
±
±
±
+
6.1
4.3
5.4
3.8
3.9
4.1
3.6
3.9
3.6
2.9
2.6
3.1
1.9
-95-
in pb/sr.MeV/c
CADMIUM
-A
-T = 1
0.001
M I
495
24.7 ±
525
32.2 4
555
34.0 ±
585
37.5 ±
615
45.9 ±
645
49.2 +
675
65.9 ±
705
81.7 ±
735 106.8 ±
98.9 +
765
795
71.9 +
825
40.6 ±
855
24.8 ±
885
14.8 ±
915
10.3 +
3.3.
945
975
-0.6 ±
3.6 "
1005
1
)
1
I
I
22.4
33.7
35.5
44.5
1 63.5
I 67.9
1104.1
1131.3
1125.4
I 86.6
1 49.3
I 24.0
1 14.1
I 10.4
I 4.1
I 2.0
+
+
±
±
+
+
+
±
±
+
+
±
±
±
±
1005 I 2.5 ±
_
--.I
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
6.9
5.9
6.2
4.9
3.8
3.5
4.6
6.3
5.6
4.9
4.2
3.8
3,1
2.3
4.4
3.7
1.9
+
±
±
±
+
+
+
±
+
±
±
±
±
±
±
+
+
+
+
+
±
±
+
4
±
+
+
8.6
7.9
6.4
6.3
4.5
4.7
5.0
5.7
5.7
7.0
7.0
7.0
5.0
4.0
5.6 4. 3.7
2.4 ± 2.5
4.0 . 5.1
17.1
20.2
25.8
32.6
28.9
40.8
66.3
79.3
82.8
46.7
22.8
13.3
0.4
3.3
2.2
3.0
+ 11.7
+ 8.0
+ 6.5
+ 6.1
- 5.1
+ 4.7
+ 5.9
+ 6.3
± 7.1
+ 5.5
+ 9.3
± 5.3
± 3.1
± 2.6
± 3.3
± 3.3
5.5 ±
8.7
6.0
4.9
5.3
5.9
6.6
5.4
3.7
3.9
3.7
3.3
1.9
2.2
2.0
45.2
18.2
38.8
48.4
74.1
99.4
79.9
59.2
31.5
24.2
19.0
16.4
5.0
8.3
4.5
4.0
± 14.4
± 11.7
± 9.4
± 7.1
+ 6.1
± 6.5
± 7.7
- 6.9
± 6.3
± 4.9
+ 4.3
+ 4.6
± 4.5
± 2.4
+ 5.0
± 4.7
0.005
I
0.007
I
0.009
-
Soo GFV/C
9.9
8.6
7.3
12.2
13.7
5.5
6.7
6.1
5.0
12.5
3.6
19.4
4.8
26.4
5.4
24.3
6.6
42.2
35.1
7.2
28.2
7.2
4.4
11.8
14.6
4.3
4.9
6.7
5.3
4.7
7.5
14.8
4.7
5.0
± 12.2
+ 4.9
+ 7.0
+ 7.6
4* 7.7
3.4 4" 6.2
13.7T
4.6
17.3 4. 6.1
4.9
22.7T4
12.3 ± 6.1
16.1 _+ 8.5
18.8 4+ 6.9
3.5 +4 3.9
4.4 4. 6.2
-0.5
6.4
11.9
10.0
21.5
6.3
5.3
4.2
7.4
2.7
9.1
7.7
7.8
3.9
4.1
4.5
4.2
3.8
5.2
8.1
5.1
4.3
16.0
4.7
4.2
24.0
6.9
12.6
17.0
5.9
16.8
11.2
5.5
10.8
6.4
3.4
3.00
- 6.2 GevY/C
26.6 ± 19.2
--
1 47.0 + 32.1
.10,4
I 34.8
1 46.2 ± 8.3
I
9.0
14.0
32.7
21.7
21.4
32.6
31.4
42.5
61.5
56.7
37.0
29.2
12.6
11.2
2
----
1
0.003
---_
67.3
.61.2
1 85.5
1117.0
1147.0
1153.6
1101.2
1 55.3
I 30.7
1 21.4
1 12.0
1 6.2
I 5.4
vs. m(MeV/c2),p(GeV/c) and tL (GeV/c)
P
6.5
5.5
5.2
4.6
3.5
3.5
4.0
4.3
4.9
5.9
5.8
4,7
3.8
3.9
3.7
2.0
1.3
3.7
_•_I_P _ .
495 I 32.5 4 15.7
525
555
585
615
645
675
705
735.
765
795
825
855
885
915
945
975
2
P
19.5
12.0
12.4
23.5
21.7
35.2
41.6
46.9
47.9
32.6
20.0
13.4
5.2
4.6
_ 12.0
± 7.1
7.9
± 6.1
+ 5.3
± 4.5
+ 6.1
+ .6.9
+ 7.2
± 5.8
+ 5.5
+ 4.4
+ 4.0
± 2.9
-0.0 +
=
7.6
30.9
15.6
15.4
14.3
6.8
19.1
14.6
27.6
29.4
12.8
16.3
6.9
4.2
7.1
+
+
±
±
±
±
+
+
±
±
+
+
+
3.2 +
18.5
7.2
7.9
5.7
4.7
4.9
4.5
5.9
5.6
5.4
4.5
4.5
2.6
4.6
24.4
10.8
7,5
8.0
8.0
6.0
5.3
6.6
8.2
5.7
4.7
5.7
3.8
3.0
3.2
8.7
9.2
5.2
9.8
3.0
3.1
6.5
6.5
4.3
3.9
4 6.1
+ 7.2
+ 2.8
± 2.5
4 9.4
---
18.4
14.4
2.5
6.5
18.7
27.8
43.8
27.2
5.1
7.9
8.3
5.1
1.4
11.4
± 13.5
± 7.9
+ 9.1
± 4.2
+ 6.4
± 5.9
± 5.5
± 6.6
± 5.7
± 3.7
+ 5.6
± 3.6
4 2.3
- 11.5
13.5 ± 16.0
Fig.17g
+
±
±
±
+
±
±
±
f
+
3.2
6-6 EY-
18.8 ±
16.2 _
18.8 +
17.7-1
18,7 ±
34.4 t
46.3 ±
59.3 +
45.8 +
36.7 +
22.0 ±
14.6 6.6 ±
5.4 +
1.0 +
16.8
-5.2
12.0
17.7
3.6
13.5
15.2
22.4
15.0
8.7
7.0
2.5
4.5
0.4
7.8
12.3
3.2
8.3
4.4
5.9
15.7
16.6
23.9
11.7
9.1
4.9
4.3
1.7
+ 10.2
± 10.7
+ 6.5
± 6.0
± 3.5
" 4.8
± 5.4
+ 5.1
± 4.8
± 4.9
± 4.4
± 4.2
± 2.3
3.5 +
3.9
-96-
INIUM
-
-T = 1
0.001
__r
in pb/sr.MeV/c 2 vs. m(MeV/c
1
0.003
-1
495
525
555
585
615
645
675
705
735
765
795
825
855
885
I 31.7 - 6.2
I
28.0
I 34.2
I 40.7
! 43.6
I 51.7
J 57.7
I 81.4
1103.3
1104.2
1 71.4
I 37.6
I 19.2
I 11.0
3.9
11.5
26.8
16.5
26.6
27.9
42.7
48.9
59.5
61.3
36.2
33.1
12.3
11.5
1
1
0.005
.___,=-5.8 GE-ILr
6.0
6.2
5.7
5.3
4.6
4.5
5.7
5.4
5.1
6.7
6.4
6.3
4.6
4.1
0.3
7.6
9.5
8.4
5.4
11.9
23.1
23.2
43.2
46.7
28.7
12.6
10.7
2.3
t
+
+
+
+
+
+
+
+
+
+
+
t
5.0
5.2
4.3
5.4
3.4
3.1
4.4
4.7
6.2
7.2
7.1
4.5
3.7
3.4
10.6 ±
6.4
4.7
4.7
4.4
3.3
3.6
3.8
4.0
4.5
5.5
5.4
4.0
3,1
3.1
915 I
8.9 +
3.0
4.9 ±
3.1
945
975
4.4 ±
5.5
2.0
2.9
1.9 ±
3.2
1.9
4.0
1005 1
),p(GeV/c) and t 1 (GeV/c)
+
±
+
+
+
±
±
+
±
±
+
+
±
+
+
+
+
±
+
±
+
+
+
+
+
I
2
0.007
-2.0
15.7
3.8
7.0
12.8
9.3
17.0
16.0
23.4
13.6
16.4
14.3
3.5
8.4
I
+
+
+
±
±
+
4
+
t
±
+
+
+
8.4
6.0
4.3
6.0
5.5
6.0
4.9
4.9
4.5
5.5
8.2
5.6
4.4
8.4
5.6 +
8.0
2
0.009
2.3
9.3
6.9
-0.8
7.2
4.1
10.8
14.8
14.8
2.5
5.8
7.6
-6.9
+ 2.4
± 5.7
+ 4.5
± 1.6
+ 3.5
+ 4.1
± 6.9
+ 4.4
± 4.6
+ 10.3
+ 3.5
± 5.1
± 9.8
5.4 +
5.6
---------------------------------------------
___
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
I
I
1
I
I
I
I
22.4
29.9
30.0
44.8
44.8
60.6
1 74.2
I 94.5
1132.6
1133.3
I 83.0
I 54.8
I 27.7
I 11.5
1 14.5
1 2.5
I 1.7
I 2.0
+ 12.3
+ 6.8
± 5.1
± 5.7
± 4.3
+ 3.7
+ 3.8
+ 4.5
+ 5.6
+ 5.4
± 4.5
+ 4.2
± 3.5
± 2.5
± 2.5
+ 3.3
± 2.8
+ 1.5
23.9
4.3
27.3
41.0
36.3
29.4
46.8
65.2
76.6
90.2
44.4
19.6
19.3
2.2
8.3
1.4
2.4
2.2
P = 6.2 GEYt/
± 17.3 107.0 ±176.4
4
7.2 12.1 4 9.0
± 7.6 19.8 ± 7.7
- 7.4 10.3 - 6.4
± 5.8 20.7 + 5.3
± 4.8 20.8 T 4.9
± 5.0 30.8 - 4.3
± 5.8 44.5 ± 6.4
± 6.1 52.5 ± 6.9
± 6.8 42.2 + 6.5
+ 5.0 37.1 + 5.5
+ 7.3 15.5 + 4.5
± 4.9 13.8 ± 4.5
± 3.3
1.2 ± 1.6
+ 3.1
8.0 + 4.8
± 2.6
+ 2.6 -2.0 t 4.0
+ 2.2
M_ I
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
±
±
±
±
+
±
±
+
+
±
+
±
+
4.7
3.1
6.7
4.0
4.6
5.3
5.9
4.9
4.8
4.2
3.2
1.3
6.1
6.5
3,2 +
6.3
5.9
0.1
9.9
4.3
3.9
10.6
7.2
14.9
7.1
7.2
9.0
4.4
5.4
1.5
+
+
±
+
±
+
±
+
±
±
+
±
+
±
2.8 ±
1.9 +
4.9
8.6
4.3
4.7
2.6
2.8
4.5
5.7
3.1
3.3
4.4
5.6
2.9
3.0
3.4
3.8
P = 6.6 GE•L/C
I
98.7 ± 44.1
1 44.5 ± 10.0
1 48.7
1 57.1
I 69.2
J 83.8
1113.9
1145.7
1151.1
I 96.9
1 59.2
1 30.9
1 16.9
I11.7
I 6.3
I
5.9
1.9
21.3
5.5
17.8
27.2
32.2
29.0
14.5
13.7
4.4
0.4
7.5
5.2
5.9
8.7
±
±
±
±
±
±
±
±
+
+
±
±
±
±
±
7.5
7.4
5.7
4.8
5.3
6.1
6.6
5.2
3.6
3.6
3.1
2.8
1.7
2.2
6.3
27.4
33.2
49.2
52.7
44.9
42.6
84.3
94.6
89.8
75.7
37.7
18.2
8.7
6.2
5.2
7.2
6.4
+
±
+
+
±
+
±
±
±
+
±
±
±
±
±
±
30.2
15.9
11.3
10.7
6.9
5.5
7.2
7.7
6.9
6.8
4.9
3.5
3.2
3.2
2.4
4.3
3.9
84.6
30.6
29.0
21.8
18.1
31.8
38.3
57.7
41.7
27.5
20.1
6.7
3.9
9.9
1.2
4.3
5.8
t 49.0
± 13.2
+ 8.0
+ 8.2
± 6.6
+ 5.4
+ 4.8
+ 6.9
+ 7.8
+ 4.6
+ 4.1
+ 4.1
+ 2.9
+ 3.6
+ 3.2
- 4.3
+ 6.4
Fig.17h
9.5
0.1
11.8
20.9
14.4
25.4
32.4
22.8
12.1
10.1
3.2
5.5
3.6
4.1
3.2
+
±
±
±
+
+
+
+
+
+
±
+
+
+
8.5
3.6
8.6
5.7
5.6
5.5
5.0
5.9
5.6
3.3
3.7
3.7
2.3
3.0
6.4
14.2
8.6
6.0
11.6
13.8
13.6
15.6
21.8
9.9
9.7
2.6
0.6
0.9
+ 11.2
± 8.8
± 5.1
± 7.5
± 4.1
+ 4.3
± 5.6
± 5.0
+ 3.8
+ 4.3
+ 3.7
+ 2.0
± 1.8
-97-
d
in
pb/sr.MeV/c
0.001
I
0.003
ANALUM
1
-r =
M
2
vs. m(MeV/c
I
P
20.7
27.5
30.9
39.6
43.8
54.3
59.3
83.0
105.2
97.0
69.0
41.1
20.7
12.6
6.6
*+ 5.5
+ 4.7
+ 4.6
± 4.5
3.4
+ 3.9
+ 3.8
+ 4.0
4. 4.2
± 5.0
+ 5.0
+ 3.7
± 2.9
+ 3.0
± 2.3
2.8
6.6 +
-0.5 4 1.1
9.6 + 5.8
1C05
11.4
11.1
26.4
19.1
20.2
23.7
20.1
40.0
53.3
55.4
27.8
25.1
9.1
5.1
5.7
4.2
),p(GeV/c)
I
0.005
p = c;a arpvi6.6
t
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
2
7.4
6.4
5.4
5.8
4.2
4.1
4.3
4.7
4.5
5.8
5.6
5.5
3.8
2.6
3.2
2.9
=
B
and t. (GeV/c)
I
0.007
2
0.009
GFY/G
i
9.0
4.9
5.0
6.3
4.4
2.6
4.0
3.6
4.7
5.2
5.1
4.1
2.8
2.3
6.5
14.0
7.5
13.6
10.3
21.9
12.1
31.6
26.0
19.8
12.7
8.6
0.3
-4.0 4-
7.7 +
4.1 ±
4.1 -
2.4 4"
5.3
1.5
2.2
9.1
11.6
16.1
10.3
23.4
7.3
4.9
5.7
3.2
3.8
+ 4.9
4- 1.9
- 4.4
± 3.4
+ 3.8
+ 2.9
+ 4.3
+ 8.8
43.2
+4 3.8
3.4
2.6 ±
2.1 ±
1.1 +
0.5 +
4.9 +
10.1 +
4.0 +
-3.3 ±
4.6 ±
2.6 4
-3.4 +
7.6
1.9
2.7
2.2
2.8
1.5
2.4
4.8
2.7
2.2
6.6
2.2
2.3
9.5
3.4 ±
-2.7 +
2.1 ±
-0.5 +
4.2 3.1 "
4.8 +
3.9 +
6.8 ±
4.7±
5.1 ±
0.3 +
1.7 0.6 +
3.2
4.9
2.0
1.6
2.0
1.4
3.5
3.1
2.3
1.9
2.7
3.7
1.4
3.1
-2.6
-0.1
1.2
3.6
5.1
1.0
9.9
1.7
-0.2
0.4
1.1
0.8
1.6
3.0..
2.0
2.7
2.0
2.3
2.5
2.6
1.8
1.5
1.1
2.0
1.3
2.3
P = 6.2 GEL/C
_
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
16.4
32.6
38.8
37.6
643.5
I 60.5
I 75.2
1106.4
1129.1
1122.5
1 85.6
I 51.3
I 32.5
I 16.1
1 8.5
I 7.0
I 8.5
I 1.1
.M
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
I.
1
I 81.8
1 31.4
1, 53.0
I 56.4
1 72.9
1 90.1
1118.6
1159.7
1149.8
1106.1
1 64.8
I 29.5
I 21.4
I 12.1
I 7.8
1 6.0
1 4.1
I
I
I
j
I
+ 11.6
+ 7.0
± 5.7
+ 5.7
- 4.4
+ 3.7
4
3.8
4.7
4
± 5.4
+ 4.9
5.9
4
3.7
4
+ 3.4
+ 2.5
L1.7
± 3.4
+ 4.7
± 1.2
44.5
0.9
17.7
28.6
30.5
25.1
45.5
52.8
62.3
57.0
41.1
17.1
14.9
7.3
5.5
2.7.
10.4
4.8
+ 23.1
+ 7.2
+ 6.8
+ 6.2
± 5.4
± 4.7
+ 4.8
+ 5.2
+ 5.3
± 5.3
4
4.4
± 7.6
64.1
+ 3.6
+ 2.4
2.2
± 5.7
+ 3.4
10.8
15.0
9.0
16.0
14.5
26.5
29.1
36.1
34.4
22.8
5.0
12.7
4.6
3.8
+
+
+
+
8.4
6.4
6.0
4.8
4+ .3
+ 3.9
4+ 5.2
+ 5.5
+ 5.4
4 4.0
- 3.0
3.6
+ 2.7
+ 1.9
0.1 +
6.2 +
6.2 ±
8.0 8.4 +
14.5 +
-0.3 7.8 14.4 4
10.6 ±
12.5 +
7.7 +
6.8 +
5.4 1.5 +
6.9 +
2.2 +
6.8
4.3
4.9
5.0
2.6
3.3
3.7
3.8
3.1
3.4
2.4
3.0
1.4
3.8
2.7
5.6
4.5
P = 6.6 GEVY/C
+ 39.6
4
9.0
+ 7.8
+ 7.6
± 5.9
+ 5.0
+ 5.5
. 6.4
± 6.5
5.1
+ 3.5
+ 3.3
+ 3.0
4 2.5
1.7
±
- 1.9
± 3.5
33.0
36.2
33.9
41.2
48.4
57.6
75.3
80.7
60.4
28.3
21.2
9.1
6.2
6.1
2.8
3.9
+ 16.0
- 9.5
± 9.4
+ 6.6
+ 6.0
± 6.2
± 6.9
+ 6.5
± 5.8
+ 3.9
± 3.4
± 2.8
± 2.5
2.1
± 3.0
+ 4.0
1.6
16.7
21.1
18.2
20.5
24.7
54.9
39.4
T
21.7
13.3
4.4
4.3
3.6
0.4
2.7
+
+
+
+
.
+
+
+
+
4
6.2
6.1
8.0
6.6
4.3
4.1
6.7
7.4
T
3.9
3.2
3.2
2.6
1.9
2.0
2.9
--
Fig.17 i
13.8
16.5
5.0
7.5
3.5
14.5
16.0
11.8
9.8
6.3
2.9
6.9
0.4
+ 10.4
± 6.6
- 6.7
± 3.7
+ 3.9
+ 4.0
± 3.6
± 4.2
± 4.2
+ 2.3
+ 2.7
± 2.8
+ 0.9
52.1
94.2
+
±
±
±
+
+
±
±
±
±
+
4
+
-98-
TUNGSTEN
-T = I
_M
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
-
0.001
525
555
585
615
645
1 30.5 ±
i 30.3 _
I 25.6 +
I 35.8
1 48.4 +
I
57.7 ±
1 66.9 ±
1 88.7 ±
1105.7 +
1101.3 +
I
74.9 ±
I 38.6 +
I 27.3 +
I 10.1 -
1 5.9 ±
I 1.6+
1 4.0 +
I
] 10.1 +
1 44.8 ±
1 27.7 _
I 42.1 ±
I 42.4 ±
1 62.2 +
675 1 79.3 +
705
735
765
795
825
1102.3
1130.6
1128.7
I 89.6
I 57.9
945
I
+
±
±
+
+
855 I 23.3 +
885 I 12.5 +
915 I 12.0 ±
975 I
1005 I
,,Y
M
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
in
I
pb/sr.MeV/c 2 vs. m(MeV/c2),p(GeV/c) and t, (GeV/c)
I
0.003
l
.
495
d 0
-3.9 ±
0.1 +
1.8 ±
I
0.007
I
0.009
P = 5.80 GEVY/C
8.4
6.5
5.7
5.2
3.9
4.7
4.8
5.0
5.2
6.1
6.5
6.4
5.7
6.3
3.5
1.6
3.7
11.3
5.0
21.9
22.7
21.1
35.5
37.4
43.8
56.7
47.2
31.8
26.3
21.0
8.7
1.6
3.3
10.7
8.7
5.6
7.7
5.2
5.7
6.4
6.4
5.7
7.2
7.6
9.5
7.3
4.6
3.1
3.3
-0.6
12.0
6.7
1.2
3.8
11,5
7.4
7.8
4.5
7.5
3.8
3.4
5.1
6.2
5.8
27.0
29.8
29.5
29.0
18.4
7.1
6.6
6.9
5.9
2.6
6.6
4.9
22.8
16.1
-1.3
6.0
4.7
8.0 +
IP
15.5
10.4
6.8
7.8
5.6
4.4
4.5
5.4
6.4
6.0
5.2
4.7
5.7
5.1
3.3
7.8
4.3
1.8
= 6.2 GFVC
+ 11.8
+ 8.7
+ 7.6
± 6.8
+ 5.4
± 5.6
* 6.2
± 6.9
± 7.1
+ 5.6
+ 10.6
+ 7.4
± 13.7
+ 2.3
+ 3.2
0.9 + 10.9
10.9 + 7.7
16.2 + 9.4
17.4 - 5.4
10.3 + 5.0
23.8 + 4.3
13.7+
5.2
29.4 + 6.9
30.8 + 6.6
18.1 + 5.0
17.6 + 5.5
9.8 + 4.1
2.0 _. 2.8
9.9 +9 6.4
5.2
10.9
32.7
36.0
18.7
42.7
49.5
71.8
68.6
42.2
24.0
9.0
3.6
2.2
-1.6
0.1 +
9.7 +
P· = A.A
23.3
13.0
10.2
10.1
7.1
5.7
6.2
7.0
7.7
6.1
3.8
4.4
5.1
6.3
2.7
5.0
8.9 + 5.5
37.9
9.6
32.0
53.6
35.1
35.0
62.1
80.7
84.6
64.5
32.7
18.2
10.1
10.0
1.4
8.2
+ 40.8
" 19.4
± 11.1
+ 13.8
± 7.5
± 6.6
± 7.2
± 8.3
+ 8.2
± 7.0
+ 5.1
+ 3.6
± 5.1
+ 5.2
+ 1.6
± 6.3
10.0
12.2
15.8
24.9
16.7
30.3
44.5
39.1
29.0
5.9
1.8
4.3
2.7
0.1
-1.0 ± 12.1
5.5 + 4.6
8.1 + 5.9
0.4 ± 6.2
9.4 + 5.3
1.1 + 5.9
6.7 + 4.2
8.1 + 5.0
24.5 + 4.7
3.3 + 5.5
22.9 ± 9.7
9.3 + 5.3
4.1 ± 3.7
6.8
6.1+
4.8 ± 9.6
11.0 + 10.8
5.1 ± 3.2
2.6 ± 2.7
2.1
2.3 ±
2.2 ± 3.0
3.1 + 2.5
5.0 ± 4.2
3.1 +
5.5
8.7 + 3.4
8.3 ± 3.8
0.9 ± 13.4
7.5 + 4.2
2.7 2.8
9.2 +
4.8 +
7.7
5.2
9.5
-_
32.4 + 23.9
I
I 19.8 +
1 37.6 ±
1 47.7 +
I 63.3 ±
i[69.1 +
I 80.6 +
1109.3 ±
1143.0 ±
1154.8 1106.7 ±
I 52.6 ±
I 31.6 ±
1 22.0 ±
1 6.5+
I 9.0 ±
I 10.5 ±
1
0.005
2
8.9
7.0
_
279.2
26.6
11.7
8.3
14.6
2.0
13.1
8.6
17.3
16.1
+242.7
± 16.8
± 6.1
± 6.4
± 5.4
+ 4.0
+ 4.6
± 4.1
- 5.4
- 4.5
12.6 ±
5.2
+
+
±
+
2.5
4.8
3.2
2.7
7.0
7.7
5.8
2.4
3.4 -
7.1
10.5 + 10.3
6.3 ± 4.4
11.0 ±
6.0 +
8.1 ±
3.1
1.6 ±
3.2 ±
2.6
14.3 +
9.4
5.4
4.0
3.8
3.5
2.9
6.0
1.2 +
Fig .17j
5.9
4.5
4.5
5.5
5.8
2.9
4.1
6.8
8.6
3.2
2.6
1.9
2.0
4.6
±+ 4.0
+ 3.3
+ 2.3
± 3.9
± 5.7
4.6 +
9.2
6.0 +
6.0
----
12.1 ±
±
±
+
±
±
3.5
C•VuIr
10.7
7.6
8.1
9.8
5.1
5.3
-3.3
7.2
-0.3
2.9
5.3
6.1
-0.5
8.4
2.0
8.7
-0.4
~--·-
9.9
4.1
3.6
6.6
2.7
2.7
3.4
3.4
3.9 + 3.2
2.9 + 2.9
2.3
1.4 ±
0.8 ± 1.7
1.2 ±+ 2.3
1.6 ± 1.9
11.0
-3.6
2.1
9.9
4.7
2.3
-0.9
14.2
+
±
±
±
+
+
+
±+
-99-
GOLD
-
t
-r = I
in
pb/sr.eV/c 2
I
0.001
I 21.8
I 22.7
1 37.3
I 40.0
I 38.0
1 54.9
1 64.8
1 89.3
1102.6
1105.1
I 67.9
I 39.6
I 25.9
I 11.6
| 15.7
I 9.4
I 0.1
I
8
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
1
M
m•
I
7.5
5.8
6.0
5.2
3.4
4.3
4.3
4.9
5.3
6.6
6.5
6.4
5.3
6.1
. 5.0
± 4.0
± 2.4
±
±
±
4
±
+
±
±
±
±
±
+
+
±
I 35.4
I 35.5
1 34.0
I 37.1
i 46.6
1 64.6
1 88a.
1103.3
1134.9
1132.4
1 92.3
I 50.9
I 26.1
I 12.6
1 15.6
1 -2.1
I 0.1
i 5.3
19.1
9.6
6.8
7.2
5,5
4.2
4.2
4,9
6.6
6.1
5.5
4.7
5.5
4.9
3.7
7.7
4.1
3.1
_P
9.9
9.7
6.1
7.6
4.4
4.6
5.4
6.0
5.7
7.3
7.4
9.3
7.6
5.4
3.0
4.5
6.8
32.0
30.3
27.3
26.6
29.3
20.8
40.9
46.3
78.1
74.4
1
31.3
19.2
6.9
10.6
4.2
3.2
4.0
3.7
+
+
±
±
±
±
.
±
±
±
±
±
.
±
+
±
±
P
+ 23.7
± 16.2
+ 10.0
± 6.9
± 6.2
± 5.1
± 5.0
± 5.6
± 6.7
± 7.3
5.3
+ 10.0
± 7.4
± 13.4
+
3.1
± 5.2
+ 4.4
+ 3.7
I
1 56.5 ±
I 54.8
1 61.1
1 90.4
1110.2
±
±
±
±
735 1160.8 +
765 1155.7 +
795 I 96.9 ±
825 I 57.9 ±
855 i 37.7 +
885 I 27.9 ±
915 I 9.2 +
945 I 9.2 +
975 1 4.0 ±
1005 I
3.1 +
10.3
9.5
6.7
5.3
5.5
6.5
7.0
5.7
4.1
4.7
5.5
6.2
2.8
2.9
3.8
10.9
28.9
37.6
36.8
49.2
70.7
77.7
72.3
42.5
34.1
16.3
8.2
6.3
6.0
+
+
+
+
±
+
+
±
"
+
±
+
+
+
5.9 +
0.005 -
18.6
10.5
12.1
7.4
6.6
6.6
7.2
7.1
5.8
5.2
3.6
4.5
4.2
3.1
and tL (GeV/c)
0.007
i
I
2
0.009
=
5.8 GEVYF
4.2 ± 7.7
7.5 + 6.8
7.3 + 4.6
0.3 ± 5.4
13.1 + 5.1
11.3 + 3.1
24.5 + 4.4
15.3 + 5.2
25.1 ± 5.9
26.5 ± 6.9
29.8
7.6
T
23.9 ± 6.8
12.6 - 5.1
-1.1 ± 2.2
-5.7
3.4
4.8
8.7
10.3
-0.7
6.5
2.6
15.9
5.2
13.8
8.0
3.7
+
±
±
±
±
+
±
±
±
+
±
8.0
3.8
4.7
6.7
4.9
4.3
4
3.5
4.2
4
4.1
5.2
7.1
3.9
3.3
4.9
3.5
6.3
1.9
1.8
2.7
3.2
8.9
7.5
8.0
0.3
2.3
+
±
±
±
±
.
±
±
±
+
±
±
4.9 +
= 6.2
fEV/C
-2*.4
13.1
20.4
18.6
11.0
22.2
23.1
32.6
30.2
18.0
6.8
11.5
6.5
8.8
7,8
8.9
5.5
4.3
4.0
5,1
6.3
6.6
4.8
4.3
4.3
6.8
-2.8 +
5.5
P
=
•
_
t
495 I
525 I 19.7 + 23.2
555 1 36.3 + 12.5
585
615
645
675
705
7.7
20.2
24.6
22.7
10.9
26.2
31.9
30.3
47.8
47.3
32.5
32.3
26.5
16.0
2.8
6.3
5.4
m(MeV/c2),p(GeV/c)
1
0.003
_
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
1005
vs.
A.A
4.8
27.0
11.2
15.1
24.3
31.1
35.7
30.1
20.6
14.2
8.9
0.9
7.42.5
=FVIC
.
8.9
9,1
7.7
8,1
5.5
4.8
5.5
7.2
4.7
4.4
4.9
2.0
4*7
5.9
6.0
Fig. 17 k
8.3
6.7
4.9
12.6
-1.9
12.1
5.0
15.4
17.7
8.1
6.6
3.8
5.9
2.2
19.6
2.0
-2.6
4.3
0.5
1.8
1.9
10.4
3.1
3.3
3.0
2.4
0.2
1.9
5.3
+
±
±
4
_+
±
±
±
+
+
+
+
2.8
7.2
2.4
2.4
1.4
1.3
4.2
3.1
2.6
2.2
2.0
5.0
2.4
8.8
8.3
6.6
.
6.2
-1.1 ±
5.4+
9.2
4.7 ±
4.5
1.6 ±
5.4
6.7 +±
3.9
3.7 -0.2 ±t
7.1 ±
4.9
3.9 ±
5.2
2.5 ±
2.9
2.6 -1.1 ±
1.7 +±
96.4
6.4
3.9
3.4
4.3
1.8
2.6
2.0
2.4
2.9
2.4
4.8
2.4
+4 9.2
4.8
+ 5.0
2: 4.9
+ 2.8
3.8
4
4+ 3.3
+ 4.5
4. 4.5
4.7
+
4. 2.8
± 3.0
4+ 3.1
4+ 2.5
4+ 15.2
4-
6.9
2.3
3.9
1.7
2.9
1.9
3.0
6.6
3.2
3.7
6.8
2.0
.
4.4
7.4
7.8
11.3
9.5
7.6
11.3
17,8
11.1
9.8
6.3
-0.6
69.2
3.0 ±
2.5
-100-
LEAD
-L-
-r = I
I
• •
in
i
0.001
_ ..
495 1 33.4 - 4.9
525 1 30.5 ± 4.2
555 1 35.7 + 4.8
585
37.1 ± 4.6
3
615 ) 42.3 ±
645 I 46.4 +
675
705
735
765
795
825
855
885
915
945
975
1005
M
64.0
I 79.9
1106.5
1106.1
I 69.9
1 40.6
I 25.0
1 12.2
) 6.1
1 2.6
I 11.7
I 3.7
3.3
3.6
3.7
4.1
4.5
5.4
5.3
4.9
4.2
4.4
3.7
4 4.5
+ 4.5
+ 3.9
±
+
2
÷
+
+
+
+
2
pb/sr.MeV/c2 vs. m(MeV/c2 ),p(GeV/c) and t. (GeV/c)2
I
0.003
I
0.005
0.007
P = 5.8 GFY/C
6.2 + 5.1.
10.3 . 4.5
0.7 1
2.8 ±
4.5
3.1
16.5 . 5.2
19.2 + 4.3
11.3 + 6.1
1.2.2 + 4.4
1.4
2.0 1
4.4
3.3
23.4
35.6
40.3
57.0
43.4
25.6
16.2
16.9
6.5
9.0
17.0
13.5
29.3
16.3
7.7
10.0
5.6
2.2
4.2
3.4
-0.1 1
4.0 ±
14.4 ÷
13.4 +
10.5 +
13.5 ÷
4.9 +
3.92
7.1 +
6.8 +
4.0
2.8
4.1
3.2
4.5
9.2
2.6
3.2
7.2
9.6
7.0 ±
,7.6 ±
24.1 1
7.1
5.7
8.8 1 4.7
5.1
±
+
4.0
4.9
.5.3
+ 4.9
+ 6.0
± 6.3
- 5.5
+ 5.8
± 3.1
4.7 +
0.1 +
3.4
7.1
I
±
÷
+
+
2÷
4
÷
±
+_
2.5
3.6
4.1
5.1
5.3
4.9
3.9
2.8
2.5
4.7
3.5
3.6 1 2.9
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945,
975
1005
1.7
0.5 +
2.5
0.5
0.9 +
0.4 +
0.9
1.8
2.9 + 2.0
1.1
4.3
2.9
4.1
6.2
15.0
2.1
+ 1.3
+ 2.7
+ 3.8
1 2.3
+ 2.9
+ 11.4
+ 1.6
4.4 1
6.3
2.8 +
-1.8 +
0.8 .
0.6 +
1.2 ..
4.3 +
2.4 1
1.2 _
2.4 +
2.7 4.62
-0.0 +
3.1 +
2.0
4.1
1.6
1.6
1.1
1.2
2.3
2.3
2.0
1.8
2.5
2.6
2.7
P = 6.2 GEV/CY
1 .
_
1
I 38.7 + 20.4
28.0 + 7.2
I 45.4 2 6.3
1 56.4 + 6.8
1,59.5 + 5.7
1 88.3 + 4.8
1121.2 + 5.2
1148.6 2
5.8
1152.7 ± 6.2
1102.9 + 5.0
I 62.9 + 3.6
28.8 + 3.7
1 18.4 + 3.7
I 11.2
4,.4
5.7 _ 1.9
1 3.2 + 2.4
1 9.5 ± 5.8
0.009
-6.1 + 12.3
495 I 29.5 + 10.1 -7.9 + 22.4 141.1 ±168.4 -23.9 +
525 1 40.2 1 6.7
5.0 + 6.2 12.4 . 6.9
3.1 2
555 1 33.1 .
4.9 20.5 + 6.4 12.7 + 5.1
4.0 +
585 1 46.2 2
5.3 25.7T
6.5 13.2 + 6.4
2.6 1
615 1 48.5 + 4.9 15.0 + 5.3 15.8 + 4.3 10.8 645 I 65.8 + 3.8 26.4 1+ 4.7
9.5 + 3.7
0.2
675 I 83.6 + 3.7 38.42
4.5 16.6 + 3.4 10.0 ÷
705. 99.0
4.4 47.4 . 5.0 28.6 +- 4.5 10.7 +
4
735 1137.6 _ 6.2 61.0 - 5.3 27.5 - 5.0 13.2 1
765 1137.4 . 5.3 65.3 + 5.8 20.2 + 5.0 10.0 +
795 I 88.3 + 4.7 39.7 + 4.7 20.5 + 4.3
7.1 +
825 I 54.9 + 4.2 20.02
7.8
1.6 + 3.6
5.8 +
855 I 30.8
4.8 11.9
4.7 14.1
4.
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6.1
885 I 15.9 + 4.0
6.2 + 7.7
3.9 + 3.2
3.5 +
915 1 10.0 + 2.7
6.0 ± 3.5
0.8 +
945
3.6 + 4.9
2.3 1 2.4
975 I 4.4 + 3.2
3.0 + 3.3
2.4 +
1005
2.7 .
1.9
0.1 + 6.6
-------------------------------------------------------------1
1
14.6
17.8
44.2
13.3
37.7
49.1
67.1
73.5
72.1
54.5
25.7
14.8
11.7
5.9
2.2
9.3
4.4
+ 15.7
2 11.5
1 8.7
+ 8.5
+ 6.6
+ 5.9
+ 6.3
+ 6.6
+ 6.3
÷ 5.6
2 4.1
" 3.0
± 4.4
÷ 3.4
_ 1.8
+ 5.8
+ 4.5
95.9
3.5
2.3
3.2
4.2
2.5
3.0
3.2
3.7
3.1
3.7
2.0
3.4
2.1
1.6
2.4
= 6,6 GFYV/C
8.2
23.9
20.4
11.7
5.7
18.0
28.7
36.0
20.7
18.9
14.0
2.1
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4.0
" 10.6
1 8.1
+ 5.9
- 5.7
t 4.5
± 4.4
± 4.1
± 5.0
± 5.9
& 4.0
± 3.6
+ 3.5
+ 2.8
+ 3.1
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5.4
Fig. 171
14.8 ± 23.1
14.0 + 7.0
1.5 ± 3.6
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2.9 + 2.9
9.8 - 5.0
6.6 + 3.2
11.8.
3.0
10.8 + 4.2
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4.0
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2.8 + 1.9
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4
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1.6 + 2.6
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2.7 + 1.9
2.4 2
1.7
5.0 _ 1.7
2.4 2 2.2
0.7 _ 1.7
1.0 2 1.9
3.1 2 2.7
2.2 + 2.7
2.5 2 2.0
-6.0 + 12.0
-101-
URANIUM
URANIUM
-f = I
S
495
525
555
585
615
645
675
705
735
765
795
825
855
885
915
945
975
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585
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975
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495
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585
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885
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dA
in pb/sr.MeV/c 2 vs. m(MeV/c2 ),p(GeV/c) and t. (GeV/c)2
A d =1'0.001
I
0.003
I
0.005
I
0.007
1
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I 14.46
1 21.3
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I 44.3
I 54.1
1 59.9
I 78.2
I 97.7
I 93.2
I 68.8
I 41.8
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1 7.8
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14.7
16.7
18.8
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21.2
41.1
48.3
43.5
24.9
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3.8
4.9
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6.0
3.4
3.5
2.1
3.1
3.9
P = 5-8 GE-YLC--3.6 + 5.6 -3.3
12.3 4 6.5
3.8
0.6
7.7 + 3.5
10.0 + 5.7
2.1
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7.1
13.7 + 2.6 -0.7
15.9 + 3.0
3.6
14.0 + 3.6
3.9
24.2 . 3.8 11.8
22.6 + 4.5
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8.9 t
3.9 11.8
13.3 . 4.1
9.4
6.3 . 2.8
7.1
1.1 + 2.2
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1.8 +
2.9
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4
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3.3
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1.7
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3.0
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±
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1.5
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0.9
1.0
0.9
1.6
1.4
1.5
1. 1
1.8
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1.9
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2.5
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I
I.
M
I 16.4
1 42.2
1 34.9
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7.8 +
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