Calhoun: The NPS Institutional Archive
Theses and Dissertations
Thesis and Dissertation Collection
1954
Protons, deuterons, and tritons from photonuclear reactions.
Wertheim, Robert Halley
Massachusetts Institute of Technology
http://hdl.handle.net/10945/14535
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FROM PHOTONUCIEAR REACTIONS
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Halfay Wertheim
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^etter on front cover:
PROTONS, DEUT
,
ND TRIT
i
FRC]
Robert ^alley W'ertheim
PROTONS, DEUTERONS,AND TRITONS FROM
PHOTONUCLEAR REACTIONS
by
ROBERT HALLEY UBRTHEIM
u
B, S.
f
United States Naval Academy
(1945)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE BBQUIREMENTS FOR THE
DEGREE OF MASTER OF
SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June, 1954
ABSTRACT
Title:
"Protons, Deuterons, and Tritons from
Photonuelear Reactions*
Authors
1
Robert H» Wertheiic, Lt., U. l« Navy
B. S., U. S. Naval Academy (1945)
Submitted to the Department of Physics on May 21,
1954 in partial fulfillment of the requirements
for the degree of Master of Science.
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A scintillation counter telescope hes been constructed
vith which the yields of protons, deuterons, and tritons
photoejected from Be, C, and Pb targets by 280 and 140 Mev
bremsstrehlung vere investigated. Relative yields of the
protons, deuterons, and tritons agree with measurements of
deuteron-to-proton ratios by De Wire et al(3) if one assumes
that the Cornell group did not resolve tritons from deuterons.
Differential cross sections for £0 to 40 Mev particles are
in reasonable agreement with Levin thai and Silverman v£*U considering that the deuterons and tritons seen here were counted
as protons in these earlier measurements.
The angular distributions of SO to 40 Mev protons and deuterons show forward
asymmetries. Within the experimental uncertainties, the tritons also can have forward angular asymmetry. The percentages
of the number of deuterons to the number of protons per unit
energy interval at 90© to the beam are 15.8 * £«g for 3e,
12.7 + 2.2 for C, and 19.8 + 3.1 for Pb. These ratios appear
to be""oroportional to A/2. "Cor responding triton-to-proton
ratios' are 4.8 + 1«S, 3.0 ± 1.0, and 5.1
1.5 for Be, C,
Pb, respectively.
!
All the above observations are consistent with a model
wherein the deuterons and tritons are formed by photoprotons
and photoneutrons which pick up additional nucleons. Both
deuterons and tritons are found, though in somewhat smaller
numbers relative to the protons, when the beam energy is reduced to 140 Mev, indicating that mesonic effects alone cannot
account for the production of these particles.
Thesis Supervisor:
Jack W. Hosengren
Instructor in Physics
Massachusetts Institute of Technology
.
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TABL n OF
:
I*
II.
III,
IV,
Introduction and Theory
VII.
VIII.
IX.
.....
General
B.
Choice of scintillators
C.
Counter construction
D«
Electronics
.
6
8
«
9
10
Experimental Arrangement
an.l
Measurements
17
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17
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19
A.
Geosaetry
B.
Measurements
C.
Mass resolution
•
.
.............
Reduction of Data sad
I suits
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P5
.
Energy calibration
£5
.........
.....
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C.
Aagtalay distributions
D.
Relative particle yields
E.
Absolute value of differential cross sections
F.
h/Z aependence
Conclusions
.
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31
.
.
38
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34
,
xtenslons of Present Vork
38
Acknowledgment
Appendices
H!blio?r*phy
1
6
.
.............
A*
Rough data
VI.
......
Equipment Design and Construction
A.
V.
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Construction Detail.
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Anticoincidence Count
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Calcul^te-i HttpfliMit
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truction
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SMttfeMTf to Protons,
Tritons
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Angulcr Distributions
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A/Z
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INTRODUCTION AME THEORY
I.
Of the several theories advanced to explain the neutron
and proton yields of photonuclear reactions, none predict
within several orders of magnitude the large numbers of photodeuterons that have been observed.^
*
Byerly and Stevens^
'
measured the energies and angular distributions of protons,
deuterons, and alpha particles, and the energy distribution
of neutrons from copper irradiated with 24 Mev betatron
bremsstrahlung, identifying the particles by grain density
of tracks and their range in photographic emulsions.
The
ratio of the yields of 2-6 Mev deuterons to £-13 Mev protons
was found to be G.38 ± 30 percent and they concluded that
(4)'
neither the statistical model v
evaporating from
photo-effect^
*
terons observed.
s
'
which pictures particles
compound nucleus, nor a direct nuclear
could account for the high number of deuHowever, Cameron^
'
has suggested that a
radially polarized deuteron could be favored over a proton
in the statistical decay of a compound nucleus.
Stevens suggested that a
r pick-up B
Byerly and
process might be responsible
for the deuterons and if so, that one would expect to see a
few tritons as well.
The pick-up mechanism will be described
in detail in later paragraphs.
Another early measurement of the relative deuteron to
proton yield was made by Smith and Laslett v
'
who irradiated
o* JbaoruYb*
nc
on
r
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a copper target
with 65 Mev bremsstrfthlung.
Using the meas-
ured radius of curvature of tracks produced in the magnetic
field of
IS" cloud chamber to identify deuterons and protons,
a
they reported a relative yield of about 0,5 in the energy interval of
1 to £0
Mev.
Like the grain density method used by
Byerly and Stevens, this technique is relatively insensitive
to mass; hence, experimental uncertainties in their measure-
ments were large.
(3)
De Wire et al,v
using
&
scintillation
counter telescope
to distinguish deuterons from protons, measured yield ratios at
90° in the laboratory system resulting from bombardment of Ag,
3r, Al, Mo, V, C, Cu, and Pb targets with 310 Mev bremsstrahlung.
The equipment consisted of two Kal(Tl) crystals which measured
quantities proportional to dE/dx and E.
The two outputs were
multiplied electronically giving a product pulse approximately
proportional to M
Q D O Q*O
'
Z E
Pulse height analysis showed good
resolution between proton end deuteron groups.
Deuteron-to-
proton yield ratios for 40 Mev particles were found to increase
0,12 for C to 0.24 for Pb with 10 percent statis-
with A
frora
tics.
Angular distributions of deuterons with 40 Mev mean en-
ergy from C, Cu, Ag, and Pb wers reported to be roughly the
same as those for photoprotons of equal energy.
These workers
concluded that the A and I dependence, energy dependence, and
the angular distributions of the deuteron yislds were suggestive
of a
(y/x)
or (y,p) reaction followed by a pick-up process.
tritons were reported.
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The pick-up process suggested by some of these workers
may be described as an inverse stripping reaction^
and Hadlay &n& Xork*
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YorkJ
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observed that bombardnei.-ts of nuclei
with 90 Mev neutrons result in an unexpectedly large yield of
deuterons with energies of the Mtti order as the incident neutrons, and >ith angular distributions peaked sharply forward.
ealova^
•**'
obtained similar results using a proton beam.
The
theoretical treatment of Chew and Goldberger v •' which is in
reasonably good agreement with the observed data, postulates
a
sudden rearrangement wherein
a
proton is transferred from the
target nucleus to the passing neutron.
It assumes that the prob-
ability of producing a deuteron of % particular momentum
? by
an incident neutron with momentum k depends simply on the prob-
ability of finding a proton of momentum (K * k) in the nucleus.
Recent evidence from (p,t)^
"*'
and (n f t)^
'
reactions
indicates that the pick-up process may be responsible for a
considerable fraction of the triton yields observed, especially
when there are two loosely-bound nucleons available in the target nucleus.
Thus, the deuterons and possibly tritons observed
in photonuclear reactions could be the result of a two-step
process; the photo-ejection of a neutron or proton which then
picks up one or more partners in escaping from the nucleus.
Insofar as the measured cross sections from these experiments
can be applied to photo deuterons, there is an order-of-m^gnitude
agreement with the photodeuteron to photoproton ratios seen*
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If this is the correct model, one should expect to Tina deu-
terons and perhaps tritons with angular and energy dependences
following those of the parent neutrons and protons.
Another possible nsodel involves the photodisintegration
of a nuclear subunit, such as the pseudodeuteron proposed by
lift)
Levinger^
'
to explain energy spectra ana angular distri-
butions of high energy photoprotons.
disintegration of
a
In a similar manner, a
pseudo-alpha particle within the nucleus
might result in tvo recoiling deuterons, or a proton and a
triton.
When photons with energies above the meson threshold are
involved, it appears that many of the observed photonuelear
reactions are proouced by photons captured by meson-contributed
mechanisms.
Results of studies^*
-
"
of stars proouced by
high energy x-rays in photographic emulsions indicate that they
may be produced by the production and reab&orption of mesons
inside the nucleus.
The resulting nuclear fragments might be
expected to include aeuterons and tritons, especially since
the heavier hydrogen isotopes have been Identified in substantial numbers in secondary particles froiu nuclear interactions
of cosmic rays.
Menon and Hochat^
%/
examined the 15 to 50 Mev particles
from cosmic ray stars, using the multiple scattering as
func-
tion of residual range in photographic emulsions to differentiate
between deuterons, tritons, ana protons.
The measured emission
I
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91 A hlO
e
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i
ratio from st?.rs corresponding to nuclear oxcit&tiona of less
than 300 Mev was (d + t)/(p
4
t)
* 0.21
± 0,08.
This is
in agreement with the theoretical treatment of Le Couteur^
'
who applied Weisskopf's evaporation model to highly excited
nuclei, and included both the effect of thermal expansion of
the nucleus on the nuclear harrier and the neutron excess during
statistical decay.
Good agreement has
felso
been round between
observed energy and angular distributions from cosmic ray stars
and the predictions of the theory of evaporation fr«8 an excited
nucleus.
Since photomeson production is thought to be a single
nucleon process, and meson yields are observed to vary as A
one might expect that the numbers of reabsorbed
stars would vary as A
1/3
'
''
,
inmni producing
.
There are other possible interactions involving mesons,
both real and virtual, which coula be responsible for photodeuterons or tritons.
For example, a bi&h energy photon might
interact directly with a two or three nucleon nuclear su^unit
to form a meson and a recoiling deuteron or triton.
i'he
cross
sections for such processes should be extremely low, hovever.
The experiment to be descrioed was undertaken to Improve
and extend the data available on the photonuelear yields of
protons, deuterons, and tritons.
Specific requirements included
the positive identification of these particles and the measure-
ment of their angular distributions and relative yields,
>:ith
maximum photon energies both above and below meson threshold.
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EQUIPMENT DESIGN AND CONSTRUCTION
General
The principle of simultaneous measurements of energy
and specific energy loss (dE/dx) to identify charged par-
ticles was chosen over other identification techniques for
its ease of instrumentation using scintillation counters
and for the relatively good discrimination offered between
protons, deuterons, and tritons*
In Appendix
I
it is shown
that over a limited energy range the product of dE/dx and E
is approximately constant for a given particle, and for par-
ticles of the same energy, the ratios of specific ionizations
(dE/dx).
are
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proton
As is indicated schematically in Fig. 4, the counter
telescope consisted of four counters.
Counters were des-
ignated 1, 2, 3, and 4, referring to their sequence in the
telescope assembly.
To be counted, a particle was required
to cause a coincidence in counters No. 1 and Ho. 3 without
causing an anticoincidence in counters No. 2 or Mo. 4$ thus,
Wo« 2 defined the telescope aperture and No, 4 defined maxi-
mum range, while Nos. 1 and
3
measured specific energy loss
and energy respectively.
The outputs of counters No. 1 and No. 3 were placed in
quadrature on the plates of an oscilloscope with any anti-
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coincident output from No*
2 or Ho*
4 flashing a
neon bulb.
Both scope face and bulb were photographed.
Since the prod-
uct of the outputs of counters No. 1 and No.
3
were approxi-
mately constant for a given particle (see Appendix I), the
loci of the end points of the scope traces followed a series
of hyperbolas, one curve for each type of particle.
With a
proper selection of amplifier gain, the presentation of the
proton, deuteron, and triton hyperbolas could be optimized.
Iso-mass lines for this telescope were calculated using
the curves of Aron v
'
and are shown in Fig. 5.
Energies
indicated on the curves refer to particles leaving the target;
therefore, to obtain the energy of the particle that was photo-
produced, energy lost in the target must be added.
7or the
thin targets used in this experiment and in the energy range
considered, mean energies lost in the targets ranged from 2
Mev for £0 Mev protons to 1 Mev for 50 Mev protons.
The upper limits to the curves were set by the stopping
power of the back Nel crystal.
A particle with energy greater
than these maxima would enter the No. 4 anticoincidence counter
and would not be recorded.
The theoretical i so-mass lines of Fig. 5, of course, do
not indicate the uncertainties in mass resolution expected in
an actual experiment.
resolution
One of the dominant factors affecting
of this equipment was statistical fluctuations in
the energy lost in the counters by charged particles.
It can
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be shown that in the thin Kal(Xl) crystal this Lands u-Symon
fit)'
effect v
percent.
was quite important and was of the order of +S
Statistical fluctuations in photomultiplier photo-
cathode and dynode multiplication contributed an additional
+5 percent in the front counter.
Variations in phototube
voltages, although held to +0.£ percent, may account for var-
iations of +1*4 percent in overall tube gains.
In addition,
very lrrge effects could be contributed by imperfections in
the crystals and nonuniform light collection.
Uniformity of
the useful area of counter Ko. 3 was measured to be +5 percent
using a coll ima ted beta source, however, SEiall variations in
the thin crystal of counter
i»o.
1 could
be much ©ore importent.
Thus, an overall uncertainty in measurements of dE/dx less
Since m ~ (dB/dx)
than £10*4 percent was not expected.
$
this meant a minimum uncertainty in mass resolution of ±13. B
percent.
Choice of scintillators
B.
Sodium iodide, thallium-activated, was chosen as the
scintillator for both dE/dx and E measurements because of
its linear response.
b\
a
comparison with the potential mass discrimination avail-
able using anthracene.
of
In Appendix II, this choice is supported
Hal(Tl) has
a
conversion efficiency
<~8.4 percent (conversion efficiency C
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(hv
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emitted, and
Af! ir>
ll number of photons
energy lost in the crystal
"by
the charged
particle), and Is highly transparent to its own radiation
which peaks at 4100
fc«
Its emission spectrum is yery well
matched by the cathode frequency response of available photomultipliers*
The disadvantages of Nal(Tl) over other scin-
tillators ere its relatively slov (0.25 ^see) decay time and
its deliquescence.
The latter property posed special design
problems for the counters.
The anticoincidence counters which defined solid angle
end energy range accepted by the telescope had no such restrictions on linearity of response imposed on 8o. 1 and Ho. 3;
therefore, plastic scintillators were chosen for ther.
The
plastic was polyvinyltoluene with terphenyl added, commercially
eve liable as Pilot B from Pilot Chemical Co.
Individual coun-
nstruction details are shown in Figs* 1, ?, and 3»
ter
c
C«
Counter construction
In the nanuf&cture of the thin crystal for counter No.
1, use was jaade of the deliquescence of Nal.
thick
Ifc]
A 1 R G.P., 1/8"
wafer purchased from Tracerlab was placed in a Jig
consisting of a 20 ail thick celluloid pattern cemented to a
Incite block.
The crystal was reduced to the thickness of the
celluloid by wiping it with a wet cloth stretched over a flat
board.
It was then placed in a dry box where the excess
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moisture was removed by alternately dipping into glycerine
and wiping it off.
176* 7
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The finished crystal was measured to be
4 percent mg/em
•
It was sealed into counter No, 1
to which was attached a side arm containing PgOg drying agent.
The crystal was seeiired to the front counter window by small
strips of scotch tape.
As may be seen from Figs, 1 and 4, it
was viewed at an angle of 45° by its phot ©multiplier.
This
configuration was chosen to maximise light collection at the
photocathode with a minimum of stopping power in the first
counter.
The large Nal crystal for counter No. 3 was prepared by
placing it in a lathe and reducing its diameter to 3 7/8* by
rubbing the turning crystal with a wet cloth stretched over a
board.
It was then placed in a dry box and sealed into its
counter to which, like No, 1, a container of PgO-was attached.
The finished crystal had a measured thickness of 4172.4 mg/cm
The construction of counters No. I and No. 4 presented no
particular problems and can be followed from an examination
of Fig. 3.
D.
Electronics
A block diagram of the equipment is shown in Fig. 4.
Output signals from the cathode followers were shaped to
square pulses by delay line clippers and amplified by linear
Model 501 amplifiers.
Outputs from the No. 1 and No.
3
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amplifiers were delayed for 1 usee and then placed on the
y and x plates of the oscilloscope.
Undeleyed output sig-
nals which were above levels set on the Schmidt discriminators,
in coincidence with each other and with
a
2000
ftsec
gate
triggered by the synchrotron peaking strip, triggered a blocking oscillator the output of which intensified the oscilloscope.
Any signal from counters No. 2 or No, 4 in coincidence with
the output of this blocking oscillator flashed a neon anti-
coincidence light which was photographed along with the
oscilloscope trace on 16 mm Kodak Linagraph Pan film.
The camera used was a Bell and Howell with f/1.5 lens.
In order to obtain the necessary intensity to make the photo-
graphic process possible, an oscilloscope was constructed with
a
5XP11 cathode-ray tube operating at 12 kev.
Continuous film
drive was provided by an electric motor coupled to the camera
through a reduction gear.
The motor speed was adjusted to
the Ho. 1 and No. 3 coincidence counting rate in order to pre-
vent excessive overlap of traces.
X and t axes were photo-
graphed at least once on each film roll and were used to pro-
vide a reference when measuring the pulse coordinates.
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EXPERIMENTAL ARRAEOSHEtfT AKD MEASUREv-.EKTE
I**.
A.
Geometry
Figure 6 is
a
photograph of the apparatus as arranged
The counters of the telescope were
for this experiment*
mounted on
I
5/8* plywood base and the assembly was aligned
to a common horizontal axis.
The base was then securely
bolted to a steel turntable.
The target holder consisted of a frame of thin lucite
which was held at an angle of 45° to the beam by a rod through
the turntable axis.
The center of the target frame was aligned
optically with the telescope axis, 8 inches from the front
counter.
Beam position and eolliraation were checked by ex-
posure of Polaroid Land Camera film at the target position.
*?
Each of the thin targets used, 149.19 mg/cm
C.
and P70.8 mg/cm
3e, 103.8 mg/cm
p
Pb, had substantially larger areas than
the beam, whose dlaseter was approximately 1 5/8" at the tar-
get center.
The position of the lead shielding was adjusted
to minimize background counting rate each time the turntable
angle was changed*
With the arrangement described, the angular resolution
of the telescope was defined by the anticoincidence aperture
(counter No. £), and was estimated to be ££.3° at 90° and
±2,7° at 45° and 135°.
In making angular changes the targets
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were held fixed at an angle of 45° to the
so that the
beara,
effective target thicknesses "were increased by a factor of
y/2
B.
over the values listed above.
Measurements
MMN
The major portion of the measurement," were
maximum beam energy of 280 Mev.
on each target at
a
4.5°,
with a
At least two runs v*;*e made
90°, and 135° to the beam as well as
no-target run for background at each angle.
In addition,
several runs were made on the Pb target at 90° using a beam
energy of 140 Mev.
Final data were read from the developed film by projecting
in a microfilm viewer.
Coordinates of the end points of traces
not accompanied by an anticoincidence pulse were plotted as
shown in Fig. 7.
Principally with the Pb target, some short
traces falling inside x = 3,
7^3
were seen.
These were
probably electrons or mesons and were not plotted.
in addition,
I
There were,
few traces not plotted whose random shapes indi-
cated that they were due to accidental coincidences.
It was
found that some of the traces with y coordinates less than
about 1,3 had no identifiable origins.
This was attributed
to Jitter in firing the multivibrator of the
TCo,
1 discrim-
inator, and undoubtedly resulted in the loss of some of the
more energetic protons.
analyzed, beyond x
For this reason, no proton data were
13, corresponding to about 40 Mev.
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A few traces with
off the scope were
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secsi
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in all runs except those at 1/2 beam
These could have been from multiply charged nuclear
4
3
fragments, possibly He or lie nuclei.
energy*
Mass resolution
C.
By normalising the observed data of Fig. 7 to th
t
theor-
etical curves of Fig, 5, one obtains a mass se&le from which
the pulse height distribution of Fig. 8 was plotted,
as may be
Seen from this figure* there are clearly three groups of par-
ticles corresponding to protons, deuterons, and tritons.
I he
proton mass is resolved to ±^0 percent, not much poorer than
the theoretical sikximum of ±13. £ percent which was computed
earlier.
In Appendix 111, it is shown that the statistical mass
resolution Am, for any singly charged particle relative to
- 0.64
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Mr
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and
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Thus, considerable overlap of the tails of the deuteron and
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and tritons with numbers large enough to give good statistics.
Although small variations in aapliiier gains and tube
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IV.
A.
REDUCTION OF
LV.g;
.-
2*
:
.
Energy calibration
Calibration of the energy seal© was made by identifying
the proton end point at x = 13.3 with the calculated value of
51.1 Mev sho*«i in Fig. 5 for protons which just got through
counter No. 3.
Because of the loss of higher energy protons
into the No. 1 discriminator
Mas
discussed earlier, the use-
ful energy range for comparative particle yields was limited
to 20-40 Mev.
B«
Bough data
The numbers of traces counted in each particle group as
well as those traces not accepted for reasons discussed in
the preceding section are summarized in Table 1.
Yields in the
energy groups £0-30 Mev, 30-40 Mev, and £0-40 Mev calculated
for equal beam monitor readings and corrected for background
are listed in Table I with corresponding standard deviations.
C,
Angular distributions
The variations in yields with angle have been plotted for
protons, deuterons, and tritons in Fig. 10.
Values at 45°
and 135° are plotted relative to the values measured at 90
The errors on the curve are statistical.
There is general
.
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Table 1.
Particles
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Although
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D.
Relative particle yields
The observed de\ teron-to-proton (d/p) and triton-to-
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marized in Table
Errors listed are standard deviations
3.
due to counting statistics only.
agreement with
tlxse of De
These data are in reasonable
Wire,^' particularly if one assumes
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fey
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the Cornell group.
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with the a/p
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E.
Absolute value of diff erentia
|
cross sections
The following differential cross sections in n barns/Q-
Mev-steradian for £0-40 Mev particles at 90° to the 280 Mev
beam have been computed
Preform
Deferens
tKJJMI
Total
Be
1.21
± 0.11
0.191 + 0.0£7
0.058 + 0.014
1.46 ± 0.11
C
2.47 + 0.23
0.314 + 0.055
0.074 ± 0.026
2.85
Pb
1 1.5
17. 1
3.40
1 0.99
0.89
+ 0.14
± 0.24
£1.5
± 1.8
(One Q, or equivalent quantum, corresponds to £80 Mev of photon
energy } i.e., the number of Q is the energy in the beam divided
by the maximum photon energy.)
The beam monitor calibration
for 3?0 Mev, 11.55 x 10 ' Q/mouse, has been used for the £80
Mev beam with the assumption that the error so introduced is
not significant.
Corresponding weighted mean values for £0-40 Mev protons
computed from the measurements of Levinthal and Silverman^
are 7.89
\x
'
'
barns/Mev-Q-steradian for Pb and 0.60 p barns/Mev-
Q-steradian for C.
Comparison of the measurements at 70 Mev
by these investigators with the measurements of Btflfc"
'
indi-
cate that their data may be low at least by a factor of four.
This is in agreement within the uncertainty of the beam cali-
bration (+20 percent) with the values calculated in this experiment for the sum of the cross sections for protons, deuterons,
and tritons.
-
€ 3a
t
t«
Arils
••
.0
t
WTO,
,0+
•
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rffli/aaa
e
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4
-lias ma^f
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anoi
ft
II
XrfT
tart
Variation of cross sections with |.tonic number is
similar to that measured by Levinthal and Silverman.
F.
k/Z dependence
The d/p ratios measured at 90° for Be, C, and Pb,
as
well as the value published by De Vire for Cu are
plotted in
Fig, 11, against A/Z of the target nucleus.
be a linear relationship, d/p
oc
a/Z.
There appears to
As was indicated earlier,
the d/p value reported by De Wire for Cu probably
included
some tritons.
life
&A
•*
a*
^elliae be
i
UCwr
:
a atf
\fc
erf*
V.
COKCUIblUN?
To summarize the results of this experiment!
(1)
Large deuteron and triton yields have been measured
from widely dissimilar nuclides irradiated by 260 Mev
bremsstrahlung.
(£)
Doth deuterons and tritons are found, though in
smaller numbers rel&tive to the protons, when the beam energy
is reduced to 140 Mev.
(3)
Angular distributions of protons, deuterons, and
possibly tritons are roughly similar.
(4)
There appears to be a linear relationship d/p
A/Z.
oc
It will be shown that none of the above observations are
inconsistent with a pick-up process for production of dettterons
and tritons*
The deuteron and triton pick-up cross sections^
'
*
ll.ljJ.x
measured by bombardment of nuclei with neutrons and protons
indicate that the d/p and t/p ratios here reported are of the
order of magnitude to be expected from this mechanism.
A crude
prediction of the d/p or t/p ratio to be expected from pick-up
can be made by taking the ratio of the measured pick-up cross
section to the total nuclear cross section.
Such comparisons,
of course, cannot be taken too seriously, since the two experi-
ments are quite different.
In one case a monoenergetic neutron
;
I
bdiiiaasB nsecf ©varf
sMsi
si* ^aot tit ba* incroJi/©:
ni
jtoubei
.veK
bat
aliwOl Nil iniis^X
,e,.
.
\A
.
oliali v
£ q\b qlrfeaoi**!©! %S9oiL
91B 9BQk*9ri9ZdO ©YOd©
(**
8itt
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i ©**
eaoJJtirf
© ©d o* Bnasqg* 9i*si?
©flOIl #«rf*
HVOrf©
©rtt
©Jdxjio
lo »1B
J
i©J*r©I> a
**& 9$a^Xbnl
?©? e
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lo ie
c©Jo©qx» ©a
qi
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,?nosli*^:
-iasqx©
(*)
Jtaloun lo tfnaadtaadffiod x<* *>»*#»*•*
.
A
xldiae
6Ci
9t eaoro qir-ofoi
u:
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inbte* yd efcsm ©d
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fta©
o* .toI^oss
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ov
)
9TB sorted
or proton beam Is Incident upon a nucleus in its ground state
from which one particle is removed, while in the photonuclear
reaction, the parent proton or neutron originates in the nucleus
by some unspecified mechanism and possibly picks up a partner
or partners from a highly excited assemblage of nucleons.
Both
the pick-up cross sections and the observed d/p ratios are
energy dependent, and it is unfortunate that at this time there
are no published experimental cross sections for deuteron and
triton pick-up using bombarding particle energies in the range
covered by this experiment.
Since both deuterons and tritons were observed using a
maximum beam energy no greater than meson threshold, it is
probable that me sonic effects do not play the dominant role
in the photoproduction of these particles.
A more convincing
case could be made if more data had been obtained at reduced
energy; however, the low intensity of the M.I.T. synchrotron
beam at this energy made satisfactory exposures prohibitively
long.
The similarities in the angular distributions of deuterons
to those of protons of the same energy is consistent with a
pick-up process, since in this process the deuterons are dragged
along with the parent protons (and neutrons)
.
A contribution
from photomeson reabsorption, on the other hand, should be
roughly isotropic.
$ TS
>
bdT-tesdo
Stxlcf
bat enolJosa ea*
9T8
see
•tarn
xurtt
leJati
i3*x»fi*
asecf tmrmhr
u
i
ai
trtroub^ J» b»flj
^>arf
****>
•*«*
W
*&*
...
<"0"
id
siatple linear relatione
.
10 betveen d/p
ratios and A/2 tempts one to propose an equally Itflt expla-
nation using the pick -up aodel.
It
yields
tire
here.
Alt.
n found experimentally v
v
h.
-~
proportional to
%
"
/
that photoproton
for article anergics considered
le*» duta are available on energetic photo-
neutron:., Italy yields se#$a to be similar to those of the protons,
Therefore, assume
*n where K
and
V»
Si
"
<
K H > P nd
2
are the numbers of photoprotons and neutrons,
If
respectively, K. and K~ are proportionality constants, fLg and
P d are energy-dependent functions expressing the probabilities
of proton-neutron &n& neutron-proton pick-up by an outgoing
particle, Ntf I ^ and
formed.
B^
are resulting numbers of de-aterons
The deuteron-to-proton r**tio then is
p
KjZ
H
p
*5
Iff
If, as is reasonable fron the similarity in the measurements
of York and £elove, we assume P
^
«P
^
we get
..
•£$1
't-fia
4
£
qfB«*X
»X»JtJ*i
•
•
m
p<J
a
i
'
ii
i
ii
1
1
ii
P
If we further assume that K^
The nature of fL^ and P
«
,
Kg, we get, finally
should be considered further
It has been tacitly assumed in this development that the pick-
up probabilities themselves do not vary with A*
It sight be
reasonable to expect the Pd's to be proportional to the prob-
ability of a nuclear encounter which, for example, eould be
1/3
proportional to the nuclear radius, R A ' • This would predict
d
A*/3
& **•*
On the other
that
, in die agreement with the data*
J
—
hand, if th« pick-up occurs only at the nuclear surface, as
suggested by Chew and Ooldberger,
v
'
P nd and P d would depend
on the nuclear surface densities of protons and neutrons
respectively.
Thus, more precise measurements of the d/p
ratios over a wide range of nuclides might yield information
both on the pick-up m^chanisis and on the nature of the nuclear
surface.
—
M
r^s
•» #v
adtar? 3»****M«ao» od
n
-doTij axis
aaiiaar.
$x
'••
I
)
t g*
w
|3I
^
.OJUioda
;;**•*
5.
*****
ajw
•***« wr
^
*o ai
«ld# «i &«nra«-
va ©a aaTlaasarffr
.:..
.
.
a*»*
>»<*
***
«
a*i* rf**T*t
«'
aaaaaa*
t
VI.
EXTENSIONS Ql PRESENT WORK
The results of this experiment suggest several further
investigations
(1)
It would be desirable to extend the particle energy
range investigated, using absorbers,
(?)
The A/Z dependence indicated should be verified by
irradiating additional target materials,
(3)
More data should be obtained at low beam energies
to reduce any mesonic contributions.
(4)
Ranges of observation should be shifted to examine
the doubly charged particles that are ejected and to determine
the relative yields of Ke
3
and He
4
•
This last point is particularly interesting because if
3
tritons are formed by a pick-up process, some He^ should be
seen as well*
TOte^i* ftlftiftaj erf* fcaaJx©
ctf
eldsilasb »4
.
»bne
v ©d
'>»
$Ci
i"
9H
©31'.
DOB
•«*
IO «JOJl»*X
•**!•**» •«•
VII.
ACKNOWLEDGMENT
It is a pleasure to express my appreciation to Dr. J*
W. Rosengren for the opportunity of performing
research under his direction.
my graduate
His contributions included
not only the equipment design but also
a
major share of the
hard work in the conduct of the experiment.
\,:.~:
lO 9
IV
40
VIII.
APPKHBICES
APPENDIX
I
For a heavy particle of charge 2, nonrelativistic energy
E,
and mass M, the rate of energy loss in a given material due
to ioni nation
W
is
p
dx
This may be written M/ftl = aZ f(M/E) where a is a constant.
From the range-energy tables of Aran,
Ag over a range of 10-150 Mev, R
cc
E
^
it may be 3een that in
'
1,
(Ag is considered
.
here since Its stopping power most nearly approximates that of
Nal.)
Differentiating, we get d£/dx ~ 1/E
*
73
.
Comparing this
expression with the theoretical relation ve obtain
Thus, measurements of 1 and dft/dx suffice to identify the ionizing
particle.
g 0-17
M
For a given particle, the product | x (&Z/5.x) m aZ E
which $m very nearly constant over
a
*
limited energy range; therefore a
plot of dE/dx vs 1 should approximate a hyperbola.
73
,
ajt
.J
:
*
be-
a
.
_
x>
(.x*t
Iflls
ail*
tU^
.
-
:sa«
.
for particles of the same energy,
(dE/dx)
'
pre ton
and
(^^
N
'proton
-
3°' 73
-
M>
APPENDIX II.
CHOICE OF Nal(Tl)
If the fluorescence efficiency, dL/dE, of a scintillation
crystal is a function of the specific ionization, £E/dx, of
the particle, we may write
fpoia
Teylor et i|#
WI
for
^I(Tl) scintillators,' 4& ~ tf
ax
ax
deuterons and protons vith energies above 1 Kev.
on the other tend,
high energies.
8U
(dL/dx?
v
7
r
g approaches
(dt/
v
'
(ff)°'
For anthracene,
in the 14*1* at
Therefore,
m
*!
proton
#73
= ^°
* 1.66
(dL/dx).
and
6"
mor
^ t»> «i
*
0.73,
(B
'proton
for a given energy (Nal)
Q. 6g
„ 1#3? (anthracene)
Thus Nal(Tl) is an inherently superior scintillator where
particle
identification is important.
• vB.r
I
'ill* •©«•»• --.
no
.(MNI^tt)
•Is AT
Vt-i
)
-
*«•
fi
**
nB
APPENDIX III
RELATIVE MASS RESOLUTION
Considering statistical fluctuations alone, if the
number of photoelectrons collected at the photoeathode of
counters No. 1 and Ho. 3 are
r,Ae
and n-E, respectively,
—1
the relative pulse widths are r 1
A
and r^ «
vx^Ae
'
1
—«*--
,
Vn^E
where n is the number of photoelectrons emitted per Mev lost
in the crystal.
charge,
g
Since
From Appendix
'
~
for particles of the same
I,
73
,
(f)
AE ~
E(f>**
whence . ~
dE/dx, we may write
m - »(Afi) 1#s?
Thus the relative uncertainty in mass,
*m«
^^L^^ ^
m v/(l.g7)
2
(r
2
AE )
# (r E )
2
Assuming statistical errors only, we substitute
r
AE
and r
get
E *°
r, - 7(1.87)*
-^
j*,
.
r-,
and r* for
;
0ftt
l:,.^.._.
.,..-..
_ jyiiliB
V
IV
V
*
%8
•
)«
-
ft
^^
8iWn
A
V
«
Since S > 10 A E, and n^ > n^, the second term under the radical
can be neglected.
When this is done, the variation in mass,
Am
Substituting
AE ^
Am
*
m mr
B
»
hd&jjL
yn, AE
0.73
K(f)
vre
,
get
i*£&
where K and K» are constants.
. KtE°* 36m
'
64
Therefore, the mass resolution
of any particle relative to the mass resolution of a proton of
the same energy is
Am
Am
p
0.64
<
v(f-)
m
A
n
trf*
i*bau
ore**
< I »o/
baooee
JfVmilf
"5
«
13
<
A
)
.
tevens, Phys. Rev. 81, 54 (1951)
(1)
P. R. Byarly, Jr. and W. I«
(?)
V, H. Siaith and L. J.
(3)
J. V. De Wire, It Silverman, and B. Wolfe, Phys. Rev.
dg,
Laelett, Phys, Hey.
jg§,
523 (195£)
519 (1353); Bull, Au. Phys, Soe.
££, 41 (1354)
Blatt and V. F. Weisskopf, John Wiley and Sons, (195£)
(4)
J.
(5)
J. 8, Levinger and
(6)
2* D. Courant, Phys, Rov. Jgj
(7)
C. T, Butler,
(8)
5. T.
(9)
Si F. York, Phys. Rev. £5,
v-u
11.
&« i-cie, Pays. Rev.
85, 577 (19B8)
703 (1951)
Proc, Roy, £oc.
(London) AgQQ. 55 J (1351)
Butler and I« E. Salpeter, Phys. Rev, §8, 133 (1952)
1467 (1949)
(10)
J. Hadley and H. F, York, Phys. Rev.
(11)
W. Selove, Phys,
(1£)
G, F. Chew and M. L. Goldberger, Phys. Rev.
(13)
B. L. Cohen end T. H. Handley, Phys. Rev, jfc 514 (1954)
(14)
G, L. Frye, Jr., Phys. Rev. 92, 1086 (1954)
(15)
J. S. Levinger, Phys. Rev,
(16)
A. G,
(17)
L, D. Miller, Phys. Rev. Jfc
(18)
5. Kikuchi, Phys.
(19)
J, G. Wilson,
¥
80,
345 (1950)
Rev. 02, 13E8 (1953)
j§4,
77, 470 (1850)
43 (1951)
Cameron, Phys. Rev. 86, 435 (1058)
Rev. £&,
MM
49!L
(1951)
(1950); ibid 8£, l£55 (1951)
"Progress in Cosmic Ray Physics", Interscience Publishers, Inc.,
(195£)
XI
t
%
tA*t
.
-
tl *SL
-
I
«
B
i
uua uwivv
E
_
I
v
&
.
•
!
(?0)
K. J. Le Couteur, Proc. Phys.
(21)
IU a. Aron, B. G. Hoffman,
Soc.
(London) A£3, 259 (1950)
F. C. Williams, AECU-663
(revised 1949)
)
(t|J
B. Rossi,
"8101 Energy Particle**, Prentice-Hall, 19S3U
C. J. Taylor,
V« K. *«*fcMfe&»9 M. S« Remley, F,
8,
Eby,
End P. C. Ki'Uger, Phys. Rev. 84, 1034 (1951)
(&*)
C. Levinthal end A.
Ob)
J. C. Keck, Phys.
Silverman, Phya. Bev. 8&,
Kev. 05, 410 (1958}
(M
(1951)
(I
,,8844
Frotons, deutercns,
and tritons from photois.
nuclear r
Protons, deuterons,
:'
'tens
i
.
a
n
thesW47
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