NOTICE: THIS MATERIAL MAYBE
I.
PROTECTED BY COPYRIGHT LAW
(TITLE 17 USCODE)
A STUDY OF TiHE C'5 (He', p)Ar• REACTION
Mabini M. Castro
B. S. Chem. Eng., University of the Philippines
(1958)
Submitted in Partial Fulfillment of the
Requirements for the Degree of
Master of Science in Physics
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGI
(1964)
Signature of Author
...........
Department of Physics, August 24, 1964
Certified by
,____~c~
I:
i-
Thesis Supervisor
Accepted by-
Chairman, Departmental Committee on Graduate Students
A STUDY OF THE C135(He
,
p)Ar
REACTION
by
Mabini M. Castro
Submitted to the Departnent of Physics on August 24, 1964 in partial
fulfillment of the requirements for the degree of Master of Science in
Physics.
ABSTRACT
The energies 3and
angular distributions of the proton groups obtained
5
fo.n enriched AgC
targets by bombardment with 6.5 Mev singl.y-charged
He3 beamn furnished by the YIT-ONR electrostatic generator, were studied
from the data recorded on emulsion plates in conjunction with the broadrange, multigap, magnetic spectrograph. Thirty-two excitation energies
are reported corresponding to the excited states of Ar37 .
Angular distribution curves are presented for some of the levels.
Those corresponding to the ground and second excited states also contain
an attempt for a theoretical fit, using the DWBA program and the optical
parameters extrapolated from the Ca40(He 3 )-run. The fittings are not
totally convincing, although there is a qualitative indication that the
captured particles have a total orbital angular momentum of L = 2 in
both states, supporting the idea of no parity change in the reactions
to the ground and the second excited states.
The experimental Q-value for the ground state reaction is 9592 ± 10
kev, which has been obtained at 890 using the incident energy calculated
from the-position of a proton group from the Cl3 (He3 ,a)C1 2- reaction
Thesis Supervisor:
Title:
H. A. Enge
Professor of Physics
TABLE OF CONT&ETS
Page
I.
II,
Introduction
1
Ther
3
E~erdnental
•III,
IV,
Arrangement and Procedure
7
Tu'ets
V.
VI,
9
Data Analysis
!0
Recstts and Discussion
14
LIGURJZ
enerator
18
Firure 2
The Generator-Spectrograph Apparatus
19
Figure 5
The Spectrograph
c
a• i Its Supporting Structure
20
FITure
1- The
Figure 4
Fiub
-
IOT-ONR
M$ TABLES
The P. rin
2
Spectrograph Components
e 5 - Tor View of the Spectrographw
F~.
gre
BCov
P
6 - Energy Snectrtm of Protons
Figure 7
-
22
Levl No,
l
at 60 Degrees
23
azugar Distribution Plots
2
-iYuSpctrm of Prot ons &"oveLeýveI No. 11
8 S- Erery
at 150 Degrees
Table I
- Eccitation Eergies of AP7'
Fgure 9 -
ergy Level Diagrzm of Ar
26
27
28
-1I.
INTiEDULCTION
This study is intended to gather more information on the energy levels
of Arr
by means of the reaction Cl-" He", p)Ar
The choice of He" as
the bombarding particle came about after the success of obtaining a 12 Mev
doubly-charged He" beam in a previous experiment.
However, it was unsuc-
cessfully tried in this run so that finally a singly-charged 6.5 Mev He'
beam was used.
The choice was further motivated by the desire to simuland C1" .
tareously gather data on two other isotopes, namely, Ar
The ground state of the target nuclei has a spin and parity of 3/2
.
Then on the basis of the shell model( 1 ) , the oroton configuration in the
unfilled level is (irld/ 2 )1 . But from the model alone nothing as definite
could be said about the neutron configuration, except when the oairing
energies of the protons and the neutrons. are equl, in wgich case it would
be as given above.
Now, when the target nucleus in its ground state accepts a neutron
and a proton from the He3 particle, it is reasonable to expect that in
the formation of.the ground state of Ar' , the proton goes into the 1"3/
level.
Also, the neutron may be expected to go into the same level, un-
less the pairing energy of the neutron is different from that of the proton
so as to create a hole in the 2sl/2 level (which might then conceivably
be filled up by a neutron from the ld5/2 level).
This state of affairs are indeed complicated, with the ground state
being of even parity but of possible spins of 3/2, 1/2, or 5/2.
It
is
not hoped for in this study to resolve these interesting points but only
to possibly limit the number of choices.
Of immediate interest is the study of the low lying levels of Ar-3
in order to deduce the modes of excitation.
A possible single Particle
excitation would be for either nucleon to land into the 1f7/2 level,
giving that state an odd parity.
Considering, however, that the 1f7/2
level is beyond the closed snell at the magic number 20,
a more orobable
excitation would be an occupancy rearrangement of the three levels of ld5/2,
2sl/2 and ld3/2, at least for low excitations.
The few known energy states of Ar3 7 have been obtained, notably, by
(d,p)i- ) and (p,n)-3) reactions on Ar 6 and 137 , respectively. The
excitation energies were tabulated by Endt et al.
In the works of Suk-
harevskii and that of Yamamoto et al, determination of the possible spins
and parities of a few of the states has been initiated using the standard
Butler-Born approximation. They have 1n = 2 for the ground state formation
implying a 3/2+ or a 5/2+ state. Yamamoto et al have further reported
i n = 0 for the first excited state, and In = 2 for the next three excited
states that they had seen. However, since a negative parity state is expected in this range of excitation energies, its non-appearance was a bit
puzzling.
-3II. THEORY
The shell model nuclear level system uo to the magic number 20 is
as follows:
(s1/2)) 1p
1 ( p1/2) 2(1d5/2) 6(2sl/2) 2(1d3/2) 4
It is seen that between the magic numbers 8 and 20 are three close-lying
levels whose order of occupancy determines the configuration of the ground
The ground states, of course, are those
possessing the greatest binding energies. If, for simplicity, it is asstates of 17r8 and 18Ari9
sumed that all the levels up to 1d5/2 are filled, then depending on the
pairing energies P of the nucleons, three cases could arise upon putting
in additional nucleons:
A) When Pd3/~ PsL2 is greater than twice the separation energy between the two levels, then the binding energy is increased whenever
a oair is formed in the 1d/•
2 level.
Thus, for Cj
, the configura-
tion is reached as follows:
(2sl/2)1(1d3/2)0 to (2s1/2)O(ld3/2) 2 to (2s1/2)1 (1d3/2) 2 for
the protons; and (adding a step more to the above sequence) to
(2s1/2) 0 (1d3/2) for the neutrons.
For Ar3 7 , the above sequences
end in (2sl/2) 1 (1d3/2)4 for the neutrons, and in (2sl/2)0 (ld3/2))
for the protons.
To specify the total angular momentum to which the
particles couple, the shell model coupling rules state that for odd-A
nuclei only the odd-numbering nucleons determine the ground state
properties, that in such cases, the said nucleons usually couple
their spins so as to give a total angnular momentum equal to that of
the last oartJially-fil'ed orbit.
This statement implies that w4hen
there is an even number of nucleoaýns, then they form a set of pairs
each with angular momenieum c upled to zero.
This state of affairs
is termed as normal ground state coupling, and one pictures it as
a state wherein the last odd nucleon orbits with an angular momentum
t
about an even-even 'nucleus'
of the rest of the oarticles which counle
their a:nzular momenta to zero.
Thus,
for this case of Pd3'2- P12
2(Ed/2- E
• 11'), the ground state spins of CC1
and 1/2+, respecti,7mely.
and Ar
are 1/2+
-4B)
When
2
(Ed3/2- $sl/2
,
)
(Pd3/2- P/2)
(Ed3/2-
Es/
2 ),
then
increase in binding energy may be gained by teking a nucleon from
the completed 2sl/2 level to form a pair ,.ith another lone nucleon
in the 1d3/2 level.
For C135, the configuration is then (2si/2) (1d3/2) 2
for the protons and (2s1/2) 2 (1d3/2)2 for the neutrons.
For Ar3 7 , it
is (2s1/2) 2 (ld3/2) 2 for the protons and (2sl/2)1 (1d3/2) 4 for the neutrons.
The corresponding spins are, respectively, 1/2* and 1/2+ for C13 5
and Ar37
C) Lastly, when the difference in pairing energies is less than the
separation energy, then no gain in binding energy is accomplished
by forming pairs in the ld3/2 level. The configuration for C135 is
then (2sl/2) 2 (1d3/2) 1 and (2sl/2) 2 (1d3/2) 2 for the protons and the
neutrons, respectively, giving rise to a spin of 3/2.
For Ar3 7 , it
is (2s1/2) (ld 3/2)2 for t'he Drotons and (2sl/2) (ld3'2))
trons.
for the neu-
As this is a neutron hole in the closed shell at A = 20, the
spin is then that due to the hole, which is 3/2.
The fact that the observed spin and parity of the ground state of
C135 is 3/2
+
means that the proton configuration of the unfilled level
is (i2ld3/2)1.
Assuming that the 1d5/2 level is filled the neutron con2 , (2sl/2)0(1d3/2)
or a mixture of
figuration is either (2s1/2)2(1d3/2)
these two.
In the formation of the ground state of Ar3 7 , it
will be the
neutrons which will determine the ground state spin and parity. Depending
on which neutron configuration is correct for C1 35, the spin will either
be 1/2+ or 3/2+.
It is oossible to write down the configurations of some of the excitjed
state of Ar3 7 from a knowledge of the ground state configuration. Assuming
this to be (7r1d3/2)'(yld3/2) ,3 then the possible configurations of some
of the low excited states are:
d.........(r
3/2) 2(yld3/22) 2(ylf7/2)1
..........
..... "....1
(ld3/2)
2 (y2si/2)1(y1d3/2)
d3/2 ) 2(yld5/2)5(yZsl/2)
(a)
4
(b)
2(yld32
(c)
(C)I
........
(2s/2)(rld3/2) (yld3/2)3
..
Except (a),
... (r•..(id5/2)
5
r2sl/2) 2 (d3/2f)
(a)
()
(yld3/)
the illustrated states are of even parity.
The respective
spins are, of course, the vector sum of the individual spins.
It is known that angular distributions of the outgoing particles in
stripping reactions give definite information on the parities of the states
of the product nuclei.
In the (HeD,p)-reaction,
the difference between
the final and initial spins of the heavier nuclei is simply the vector
sum of the orbital angular momentum and the spin of the stripped n-p sysThe angular distribution performed on the outgoing proton yields
a total 1-value for this n-p system. Depending on whether this 1-value
is odd or even, the parity of the final state is correspondingly odd or
tem.
even.
The 1-value is determined by comparing the experimental curves with
the theoretical curves obtained by using the distorted wave Born approximation method for stripping reactions.
It utilizes a Saxohn-Wood nuclear
potential of the form
V(r) =
rl+e
A
The parameters appearing in the right side are known as the optical parameters. V is the average single-particle real potential, and W is the
absorption potential responsible for the capture of particles from the
incident beam. The quantity in the denominator is essentially the Fermi
. the point at
is the distance to
radial distribution function, where
half maximum, and A is a skin thickness taken as the distance betweer the
26.894 point.and the 73.11? point of both Vrells. Knowledge of the opti.cal potential•, along with the Coulomb potential between a point charge
and a charged sphere of radius Rc, yield the distorted waves t0 be used
-6in the DWBA.
The amplitudes of the resulting angular distribution curves
will vary according to the lower integration limi-t of the distance
between the target nuclei and the absorbed n-p system.
known as the cut-off radius R.
This limit is
-7III.
Y2EPRIMENTAL AA!CNGEMEINT AND PIRCEDURME
The MIT-ONR electrostatic generator (5) shown in Figs. 1 and 2 was
operated to produce a 6.5 Mev, singly-charged He" beam. The beam emerges
vertically from the bottom of the tube and is deflected to a horizontal
position by means of an energy-analyzing magnet. It then passes through
a set of slits which may be adjusted to limit the maximum beam energy spread.
The beam enters the spectrograph
chamber through an electrostatic
quadrupole lens which produces a reduced (by approximately a third in the
vertical direction) image of the energy-defining slit on the target which
is attached to a holder that is mounted, at 450 angle to the beam, near
the bottom, and at the center, of the chamber. After passing through
the target, the beam may be collected by a Faraday cup at the opposite
side. The beam strikes the rotating target slightly off-center so as to
diminish carbon build-up.
The spectrograph is illustrated in Figs. 3, 4 and 5. The particles
accepted by the twenty-cix gaps are limited in the horizontal plane by
a - slits.
The B - slits serve to define a solid angle which limits the
exposure zones on the nuclear track plates.
Selection of zones is accom-
plished by manually turning the carousel holding the gaps-shoulders onto
which the plates are firmly attached.
These shoulders are constructed
to follow the very slight curvature of the magnet focal surface.
The magnetic field is measured 'by a proton-resonance flusmeter situated at the 890 gap.
In the experiment that was done, the magnetic
field is 10.1806 kilogausses.
Except at 00, all gaps were loaded with Eastman-Kodak NTA, 50 !1 thick
plates. No Aluminum foils were placed in order to accept all the pro.ton,
deuteron and. alpha groups. During the rather many days run, the vessel
was opened twice, once to taike out the uppermost plate (C-plate) of 910
and once that of 22.50 to study the state of the exposure. At the end
of the long exposure (19,875 p-coul) three targets were broken and one
badly thinned.
It was originally intended to use all three zones --
one for tar-
get thickness determination,j one for the angular distribation, and the
last for a (He', He%)-ran at 6.5 Mev on C13 5 to fix the optical parameters.
The run, however, met with many delaying problems among which were ion
source troubles.
In some points, ýIwhen the source started to act up, the
terminals seemed not to hold 6 Mev.
Further, the solid state detector
monitoring the target failed to function properly so that there was no
way of telling when the target breaks, inasmuch as the TV circuit was
also inoperative.
Finally, the machine became very unstable for leng-
thy periods of time that it was decided to stop the run after only the
angular distribution exposure was made.
The plates were scanned by high-magnifying microscooes, with the tracks
sorted out according to whether they are due to protons, deuterons or
alphas, by observing the length and grain structure.
No counting could
be made from the 7.5 -plates as they have been yellowed by intense He3
particles scattered in the gap.
Counti.ng is made for every half-milli-
meter strip on Zone I which was exposed to 19,875 Cýc.
-9-
IVe
TAR.GETS
The silver cnioride enriched in C11
Carbon Chemicals Co., Oakridge, Tenn.
was supolied by the Carbide and
Solid targets were prepared by elec-
tron bombardment of AgC1, using an electron gun, onto carbon backings
suopported by small rings which may then be conveniently attached to the
machine target holder.
The approximate thichnesses of the targets were
determined using the thickness gauge which utilizes Po a's (5.305 Mev)
reduced in energy by passing through air. The thickness of the target
is ýhen inferred from the distance through which the detector is moved
to measure the same energy it had without the target.
air-equivalent.
This is the mil-
In this experiment, the target thicknesses are over 17
-m.a. e,
Since ordi.aarily Ag2 is PreParsd fLrom nitra
s it may be exeeted
to contain a minute amount of the isotopes of nitrogen and oxygen.
groups from these, together with those from
be found.
C1 2
and
C1
Proton
, may, therefore,
-10V.
DAT.?
....
YSIS
The number of protons per half-millimeter strip
distance along
Figs. 6 and S.
the olate for each angle.
ere olotted against
Typical spectra are shown in
The positions of the proton groups arising from the expec-
ted contaminants were marked in each spect-um,
usi n.g the value of 6.5 Mev
Visual inspection usually suffice
for the energy of the incident beam.
in fixing the positions of the states of Ark.
In some cases where doub-
lets were indicated by unusually wide widths of the peak, comarison of
the behaviour of the group in question was made on majority of the angles,
This was especially done for the groups 11-~2, 15-16, and 17-18.
In some
of the angles the overlapping of these levels partially disappears,
a structure of two close-lying levels.
Moreover, the absence of
showing
:knoln
contaminant groups in these positions for most of the angles convinced
this author that these unusually wide groups are doublets.
As the data had been accumulated over a long period of time, it is
possible that the field had drifted somewvhat.
As a result the ceaks are
not smooth, but, rather, showing a saw-toothed structure.
To aid in the
determination of the third-height position of the -peaks, the number of
protons per half-millimeter strip averaged over three cor1nsecutive strios
w•as plotted against distance for the oeak under consijeration.
what has been plotted in Fig. 6.
It
This is
was often found that this third
height oosition Jis within a half millimeter from a third height position
determ.ined along the high energy side of the non-averaged pe&a." For the
doublets cited above,
such procedure is destructive rather than helpful_
In these cases, the third-height oositions at different angles were obtained by extrapolation, using as a guide the values obtained from some
angles where the doublets are more-or-less separated.
The Q-values of the levels found were read from a Q versus d
tabulation calculated by a computer program developed earlier for the
The numbers are based on an incident energy of 6.5
Mev and a field setting of 10.1806 kilogausses. The working equation is
the relativistically corrected Q-equation shown below, in conjunction
with the " versus d gap calibration anrd the relationship betw'een the energy
MIT 7-904 computer.
-11-
and Hp.
In powers of (H )2 this relationship is
E(kev)
1011i
HLp2
( 7)
E5MH )8+
,6
F)+
where F = 9652.021 emu equiv-1.I .
M = atomic mass unit
The Q -equation is:
QEout
Ee
rec
rel
rel
in-E.. + mout E
m
in
m
out
res
2mresS1
E
=
rec
=
res
brel =
@
=
where
En + Erec +
-
res
2cos0
)1/2
E. E
mre (min
in mout in out
res
E in + E2out - Erec - cos
(mi.
M
.E
u
in dut in out
+tout
)2(
.
in
m
the classical recoil energy of the residual nucleus
the mass of the residual nucleus
the relativistic correction term
the angle in the laboratory system between the outgoing
particle and the incident beam
To get the excitation energies, the Q-values of the excited states
were subtracted from the Q-value of the ground state formation.
This
should tend to minimize all the systematic errors.
Because of the absence of a reasonably intense contaminant proton
peak at 890, the value calculated( 8
using an alpha group coming from the
C13(He', a)C 1 2 reaction was adopted in the determination of the ground
*The original equation from which this was derived is (in emu)
2
where
e
in0
_F
14
ZH 2
out
-12-
s5 3
T7
3 . This incident energy
state Q -value of the reaction C1r (He , p)Ar"
is 6.48 Mev. This calculation has to be at 890 because it w,:as the field
here that was measured by the fluxmeter.
Angular distributions were plotted for levels nos. 0, 1, 2, 4, 5, 6,
7, 8, 9, 10, and 19. These are shown in Figs. 7a to 7j. Except for
Figs. 7a and 7c, all are in the laboratory system.
The error bracket
- (N)1/ 2 where N is the total number of
The transformation to the CM system in which Figs.
shown at each point is simply
protons in the group.
7a and 7c are plotted was simplified by the use of a table( g) prepared
on the basis of the following relationships:
SinC -)
Sin@
M +M
S
M.
2"
13 1 + 1
x2
M2,4
1 (9)=
G(xv)
2
E1
I(Q)
G(x,O) = (U - X sin
o
+ (1 - Xsin
2
where the subscripts refer to the incident, target, product and outgoing
nuclei
the asterisk to the CM variables.
Since no inelastic scattering of He3 on C135 was done in this experiment,
it was thought best to use the parameters extrapolated from the 12 Mev
Ca (ie,He )Ca - run previously made in: this laboratoryT
for the DWBA curves. These pareaneters are
V = 43.000
W = 7.000
For Ar37 (p),
Ro = 1.544 f.
Rc = 1.544J f.
the optical parameters used were
in calculating(10 )
A = 0.6584 f.
V = 50.000
W= 10.000
A = 0.450
R = 1.250
R = 1.250
It was mentioned earlier in this paper that the ground state and the
second excited state of Ar
have even parities.
Thus, only even Ln's
are allowed. Using the general selection rules, assuming 3/2 or 5/2 for
the final spin state, then
for Jf = 3/2,
for Jf = 5/2,
L= 0, 2,
= 0, 2
L = 0, 2,
-=0, 2,
when S =1
when S =0
6 when S = 1
when S =-0
Theoretical curves for various cut-off radii R were calculated by computer
for L = 0, 2, 4 for the ground state and 0, 2 for the second excited state.
The better-fitting curves are also shown in Figs. 7a and 7c, where the
need for better values of the optical parameters is obvious.
-14VI.
RESULTS AND DISCUSSION
The result of the ground state Q -value calculations at 890 is
Qo
=
9592 + 10 kev.
The error quoted comes from the following considerations.
There are
systematic errors coming from systematic effects from hystersiis and
magnetic saturation; from observed consistencies of previous data, this
is about 5 key. There are also systematic errors from (a) H calibration
(b) Po source, misalignment and surface
by the Po a-source (0.0o20o),
contamination (O.O040/); and (c) validity of the third height point as
the peak position (0.04 0/).
The root sum of the squares of these three
is 0.060/0, and this error is 0.6 Q key when Q is in Mev. The total
sysctematic error, calculated as the root sum of squares, is then 8 kev.
This was then increased to 10 key to cover up whatever error has been
missed
The excitation energies obtained in this work and listed in Table I,
represent the mean of values deternined from majority of the angles. The
errors quoted are standard random errors
S-
Ex
2
n(n- l)
and the difference of the systematic errors between the ground state and
the states in question. The error from hysterisis and magnetic saturation
is estimated as 3 key; and that from calibration and third height position
as 0.6 E kev. Then the root sum of squares is the total error quoted.
the levels in parenthesis are either postulated or doubtful. Some -proton peaks that have been observed were unusually wide, and
this characteristic persisted at all angles. This is the case for the
In particular,
groups (11-12), (15-16), (17-18), (21-22-23) and (25-26).
the group (21-22-23) has a width approximately three times that of its
In Table I,
neighbors, namely, nos. 19 and 24. Where contaminants could be respon-
-15sible, it results in a distortion of the peak; firstly, in intensity, and
secondly, in the Q-value read from the third height position of the highenergy slope.
And in some angles, a structure corresponding to several
overlapping peaks could be seen. For group (11-12), the maximum height
of no. 12 is less than that of no. 11 for angles below 52.5 ° . Between
52.5 and 112.50, they are comparable, and above 112.50, that of no. 12
is again less. For (15-16), below 450, protons arising from the formation
of N1 5 (5.28 and 5.3 Mev) and 016 (9.85 Mev) affected both the intensity
and the third height position. At 52.50 up to 82.5 ° , the heir~ht of no. 16
is less than that of no. 16; around 97.56, they are comparable; and at
1200 up, that of no. 16 is greater.
For group (17-18),
no. 17 has remained
always less that no. 18, but the peak structure remained the same.
Similar
observations were found for the last two groups mentioned above. Perhaps,
group (21-22-23) is a doublet instead of a triplet -- in such a case,
either no. 22 or no. 23 is doubtful.
One other point is the appearance of a group or groups of protons
of weak intensity between level nos. 19 and 21. While at some angles (1050,
02.5
, 127.50 and 1500) the peak, is such tha t a third height could be
1
read, at some it is impossible.
possible!
And still at some, two third heights are
Because of this, it was given a doubtful nature.
For comparison, the excitation energies found by othier workers are
also tabulated in Table I. Good agreement is generally exhibited. The
comparison with the results of Yamamoto et al shows that the level at
2.214 Mev observed in the present work has been missed. Their experiment
was done using a 4.05 Mev deuteron beam from a cyclotron, on an isotopically
enriched Ar 6 gas target. The proton tracks were recorded on Ilford C-2
enralsion and the counts per cm
were plotted against range.
On account
of background, no other groups could be resolved between 1.63 Mev and
2.54 Mev. Their angular distriibtions performed on the levels they observed
showed that the final states are of even parities. However, it is in this
range of excitation that an odd parity state could be formed. Its nonappearance was tentatively explained by stating that the 1 = 2 distributions
are not really classical stripping curves, so that the a3signment of
1 = 2 for both the 2.54 and 3.55 Mev levels on the basis of the fitting
of their angular distributions with the Butler-Born curves must be questioned.
While this is all valid, there is still the possibility of an
intermediate level which might have been missed.
This odd-parity state
might very well be the 2.214 Mev level observed bhe the present study.
Unfortunately, this couldn't be checked at this stage, partly because of
the low intensity of this level, and partly because of the t'crdeness'
of the optical parameters used in the present analyses for CU (ne ) at
6.5 Mev. Perhaps it might be simpler to make a complete angular distribation (d,p)-run on Ar
using a machine with a higher resolution than a
cyclotron.
Angular distributions were plotted for levels that are not too
clsely separated.
These are the majority of the levels below no. 19.
As can be seen in Figs. 7a - 7j, they are of low intensities. Levels
above no. 19 are relatively more intense, but they are close to one another.
Moreover, this is just about the region at forward angles where grTups
from contaminants start to crowd each other.
All the angular distributions indicate a compound nucleus formation
in addition to stripping.
An estimate of this amount may be subtracted
from the experimental points, assuming it is constant throughout the angles.
It was, however, rather pointless to do this at this stage of the analysis
since the optical paranmeters are more or less crude.
The effect of such
a procedure on a semilog plot would be to pull down the lower points at
relatively greater distanices than the higher points. Thus, in Fig. 7a,
the points above 300 might be improved, but then the ones lower will go
faorther down the theoretical points. It will be noticed that these points
are already below the corresponding theoretical points. While this may
show the way to adjust the parameters, the fact remains that the contrib-
uti.on from a compound nucleus formation mechanism is still unknown.
r"
Qualitatively, however, the fitting along the first maxima of both
Figs. 7a and 7c suggests that L = 2 so that the final state has an even
parity, in agreement with the shell model assignment. The accepted n-p
system has been assumed to be a deuteron in the DWBA. This does not
rule out the 1S
state, however. The vectorial summation of the initial spin,
L = 2 and either of S = I or 0 yields possible half integral spins from
1/2 to 9/2, consistent with the shell model assignments of 1/2, 3/2 or 5/2.
Unfortunately, it does not limit the choices (only L = 6 would do this, along
with the already existing possibilities from the (d,p) experiments).
In closing, let it be stated that in spite of the low counts in the
experimental distribution curves, they are not without structure. It is
still possible to fit them, 'but only after a better set of optical parameters has been found. Concerning the excited states of Ar". , thirtytwo levels are being reported.
ACKNOWFLEDGMENTS
The author is grateful to Prof. H. A. Enge for his supervision of the
work. He is indebted to the staff of the High Voltage Laboratory, in particular to Dr. W. H. Moore and Mr. A. Sperduto, for their invaluable assistance during the experiment. The DFABA calculations were performed by Mr.
H. T. Chen. Thanks are also due to Mrs. H. Young for the IiBM-:7904, programming work, Mr. A. Luongo, for the preparation of the targets, Mr. W. Tripp,
Miss S. Darrow, Mrs. M. Fotis, Miss S. Dittmann, Miss V. Piza and Mrs. C.
Harvey for their patience in sorting out the particle tracks, and to Mr.
D. Baker for the preparation of the figures.
The author's gTratitude goes also to his wife, Cristina, for her constructive 'nagging' toward the completion of this work, and to Mr. N. Rao
who should be commended for his high proficiency with the calculating
machine.
ONA STABILIZER
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Figure 7.
'
,
7
C (He p) Ar
Excited State No. I
Q - 8.19 MeV.
E, = 1.406 MeV.
it J
(a)
4
35
7
Cl (H',p) Ar
Ground State
L=2
Q = 9.59 MeV
T
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37
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L=2
0 - 7.98 MeV
I
15
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30
45
60
90
75
105 120 135 150 165180o
LE
LAB. ANGL
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3
37
Cls (He , p) Ar
Excited State No 5
Q - 6.80 MeV
Ex 2.792 MeV.
too
20
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100
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A
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Excited State No. 7
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Ex 3.266 MeV.
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Q =6.42 MeV.
Ex 3.167MeV
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Ar
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3
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Excited State No.8
S=6.08 e.
Ex 3.515MeV
Excited State No. 9
Q * 5.999 MeV
0n
!
Ex 3.598 Mev.
o
240
220
200
180
160
140
120
io
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60
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30
45
60
75
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135
150
65
LAB.ANGLE
LAB. ANGLES
("' i
i
37
3
Cl (NH, p)Ar
I (k)
Excited State No.10
0=5.9 MeV.
Ex" 3.693 MeV.
-·-35
3"
3
'p)Ar
CI (He
Excited State No.19
0= 4.86 MeV
Ex =4.729 MeV
e
100
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1201
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90
Lab. Angle
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. I
150
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-27TABLE I. EXCITATION ENERGIES OF Ar37
( ) =postulated on the basis of unusually wide structure
(( ))= doubtful level
L ev-
"
Davison
cZucefe
.5.
1 This Work6
L.
No Exmev,.V
.
E-.SA
6
..L4
3
..
)
'Fergusson
·
12.25 -10
i
2.27
.i
2.2 L
ta'Stels6n
et'amamoto
x2.A
5
5 ;2.792j-4.
_
.93.697
6.•
,,3.515
± .32
:3-
5
2l5
14.277 ±
*(17) 4.562
L
24
5235..10
.5
.
5021
.
27 5&.747
6.0166
.50.(2) "55.I,
5
194.729
.9781 5-5'
2
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6
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C
5
C
5
5
5
IIIIIIIIIII
rC
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_
5
.,203
66
6.
I
II
II
I
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I
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II
I
I
-o62
{ii
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5
----
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3 .003
.930
3.693
&-d
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o
-
-
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679
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I)
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-
Five 9.o
nerg?
Di-gram of AL37
3/2(-), 51/2(4)
112(j)
1.607
1.406
i
3/2(+), 5/2(4)
Is
Ar
7
I9
0o
-29-
I
X
N. G. Mayer and J. H. D. Jensen, Elementary Theory of Nuclear Shell
Structure, John Wiljy and Sons, Inc., New York, 1955.
2.
P. Davison, J. Buchanan &ES.
Pollard, Ph.ys. Rev. 76, 890 (1949).
A. Zucker & W. Watson, Phys. Rev. 80, 966 (1950).
V. 0. Sukharevskld,
Soy. Phys. JETP 2, 981 (1959),
S. Yamamoto & F. Steigert, Phys. Rev, 1_1, 600 (1961).
3.
P. H. Stelson & W. M. Preston, Phys.
eva.
&6,807 (1952),
A. T. G. Ferguson & E. B. Paul, Nucl. Phys. 12, 426 (1959).
4.
P. M.e Endt & C. Van der Leun, Nucl. Phys. ~,
5.
W. W. Buechner, A. Sperduto, C. P. Browne & C. K. Bocikelman, Phys.
222 (1962).
Rev. 2, 1502 (1953).
6. H. A. Enge &W. W. Buechner, Rev. Scl. Instr.
~s,
155 (1965).
7.
H. A. Enge, Table of Charged Particle Energies versus Magnetic Field
Strength X Orbit Radius, A. S John Griegs Boktrykkeri, Bergen.
8,
K. Abdo, S. M. Thesis, Mass. Inst. of Tech., 1964
9.
J. B. Marion & A. S. Ginzborg, Table for the Transformation of Angular
Distribution Data from the Lab. to the C.M. System, Shell Development
CGo. (1949).
(private communication).
10.
H. Chen, •igh Voltage Laboratory, Mass. Inst. of Tech. (private
communication).
11.
H. A. Enge, Ph.D. Thesis, Universitetet I Bergen, Published, A. L.
John Griegs Boktrykkeri Bergen (1954).