Nuclear "Physics 72 (1965) 4962; (~) NorthHolland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
I N V E S T I G A T I O N O F T H E (d, p) R E A C T I O N O N a l p I N THE D E U T E R O N ENERGY R A N G E 1.32.5 M e V A. T. BARANIK, M. A. ABUZEID, M. I. ELZAIKI and I. I. ZALOUBOVSKY t Atomic Energy Establishment, Cairo, Eyypt, UAR
Received 15 January 1965 Abstract: Excitation functions of several proton groups (P0, Pz, Pz, Pa, P4, P6, PT, s, Ps, z0) resulting from the reaction szP(d, p)s~p were measured at angles of 30° and 150°. The total and differential crosssections are given. The excitation functions for all groups indicate a number of resonances which exhibit fluctuations in the range of 25 to 100 keV. Many of the observed resonances are uncorrelated at 30° and 150°. There is also no correlation between groups leading to different states of a residual nucleus. Proton angular distributions were measured for six energies of incident deuterons. Some of the angular distributions typical for the direct interaction are compared with those from the stripping formula with regard to nuclear deformation. The value of the deformation calculated from the angular distributions gives a nuclear magnetic moment close to the experimental value. E I
I
NUCLEAR REACTION 3~P(d, p), E o = 1.32.5 MeV; measured t~(E), a(0), tr(E, 0). Deduced l, deformation parameters fl, magnetic moments of szp and 8~p.
1. Introduction Experimental observations have shown the angular distributions o f protons f r o m (d, p) reactions in the lowenergy range to be, in general, poorly described by the simple Butler theory 1, 2) and that the C o u l o m b and nuclear distortion o f the incident deuteron and outgoing p r o t o n waves 3, 4) must be taken into account in comparison with experimental data. However, even the latter theory c a n n o t always give a g o o d fit. In addition, significant fluctuations, at which the angular distributions are rather often f o u n d in g o o d agreement with the stripping theory s, 6), are observed in differential crosssections as a function o f deuteron energy. This fact is also unexplained within the framework o f the simple direct reaction theory. In order to obtain some information about the reaction mechanism at low energies and to clarify the correlation between fluctuations in excitation functions and angular distributions, the 31P(d, p)32p reaction was studied in the present work. To compare the experimental angular distributions o f protons with the stripping theory, the nonsphericity o f nuclei must also be considered because the a l p nucleus has a small deformation, as was previously shown 7). In refs. sz3), the alP(d, p)a2p reaction was treated at deuteron energies o f 4, 6, 7, 8, 9 and 14.3 MeV and the angular distributions Permanent Address: Academy of Science of USSR, Moscow. 49
50
A.T.
BARANIK e t al.
were well described by the simple Butler formula. At low deuteron energies (E d = 1.8 and 2 MeV) the proton spectrum of this reaction was only measured 14) at 90 ° to obtain the level structure of 32p.
2. Experimental Apparatus and Procedures The 2.5 MeV electrostatic accelerator of the U A R Atomic Energy Establishment was used as a deuteron source. At the outlet of the accelerator, the deuteron beam was deflected by a 90 ° magnetic analyser and injected into the scattering chamber through a system of collimating diaphragms. Two ntype silicon semiconductor detectors were placed inside the chamber. Pulses from the detector output were amplified by the charge amplifiers and fed into a 512channel pulse analyser. The energy resolution of the spectrometer was about 1% for 21°po alpha particles. One of the detectors was used as a monitor and was fixed at an angle of 135°; the second detector could rotate from 15 ° to 150 °. An aluminium foil was used to prevent elastically scattered deuterons from reaching the rotating detector. Details of the chamber arrangement were described earlier 15). The target material was Zn2Pa evaporated onto a thin silver backing. For 2 MeV deuterons the target was about 20 keV thick. The experimental results were normalized to the readings of the current integrator as well as to the monitor. To obtain better accuracy, all experimental measurements were repeated two or three times.
3. Experimental Results 3.1. SPECTRA One of the typical proton spectra of the 31p(d, p)32p reaction at a 30 ° angle and 2 MeV deuteron energy is plotted in fig. 1. As shown, the proton groups Po, 1, P7,8 and Pg, 1o were not separated and therefore were investigated together. The joint investigation of these groups is also of interest for both the reaction crosssection value and lhe study of the behaviour of fluctuations in differential crosssections as a function of deuteron energy. A typical monitor spectrum of deuterons elastically scattered by 31p, Zn and Ag is shown in fig. 2. A very clear separation of the elastic peaks facilitated appreciably the (d, p) reaction crosssection evaluation with respect to the elastic scattering one. The dependence of the products NdE 2 (where Nd is the number of counts in the elastic peaks for 31p and Zn) on the deuteron energy E d, shows no deviations from Rutherford scattering crosssection. 3.2. EXCITATION FUNCTIONS The excitation functions of the proton groups (figs. 3 and 4) were obtained from a treatment of spectra similar to that given in fig. 1. The measurements for all the groups were carried out at angles of 30 ° and 150 ° in steps of 25 keV. The excitation functions
51
(d, p) ]R~ACTION
°' I ~
E d 200 MeV
12
30(
OL = 3(; ;
p
200
[
z u
~hi'
.tt
i
J t IL~f /~',~
1
; 1 L
~;
io
NUMPER
I~o
~;o
200
OF CHANNELS
Fig. 1. Spectra of the proton groups at 30°.
z~ ~
Ed=2325 NIeV
[email protected]
e~13¢
~Io2
Ag
150 I i
100
m so
p31
z
1oo
i~o
lio
1'so ~&o
NUMBER OF CHANNELS
Fig. 2. The elastic scattering spectrum.
2Zo
280
52
A.T.
BARANIK e t al.
for Pt3 and Pls groups were not treated because of low intensity, which leads to large errors.
do" m bl sr dp
1.50
do"
uP^,I
1.25
0.30
i.0o
o.25
mb/sr
P
2
0.20
0.75
0.I 5
0.50 0.I0
0.25
0.05
1.J5
1.i7
1/9 Ed
211
2',3
2.'5 

:5
~
119 27 Ed
IN
1.9 Ed
2.1 IN
MeV
IN
d. ~ mb/sr d~
P6
2.~
2.5
MeV
do" m b l s r
080i I I
0.50I0,40
0.30
0.30 0.20 
0.10
0,10
i
1.5
i
p
1.7
i
1.9 Ed
2 .J3
2.1 ]N
MeV
215
1.15
I
1.7
I
i
2.3 MeV
215
(d, p) REACTION
53
3.3. ANGULAR DISTRIBUTIONS Angular distributions measured at various deuteron energies are shown in fig.~fi.
do" d.n
mb/sr
0.60
0.60
0,60
0.50
0~0
0,~0
0.30
030
0.20
0.20
0.10
0.10
,.'6
i
,.~
,I~ Ed
do"
O90
J
2~
IN
21~
I ,:s
,:7
I
I
,9
2, Ed
MeV
rob/st
d.n
I
2.,
mblsr
do" d~
P3
I
23
I
2.5
[N MeV
Pg,10
0.70 0.60
Fig. 3. The excitation function o f the p r o t o n groups at 30 ° .
0.50 0.~0 0.30 0.20 I
0.10 i
1.5
12
i
i
1.9 2.1 Ed IN
i
i
2.3 MeV
2.6
54
A.T.
BARANIK
et aL
d_~ m b l s r dA
2 ~04
1
P O1
P 2
0 348
1 ;'28
I
i
I
1 152
0232 L
0576
0116
L
1.3
d~ d~
17
2.1
.
13
2.~
17
21
2.5
rnb /st 1.160
0464
0.928
P~
P
0346
r
7.b
•
ii!
0.464
0232
0116
0,232
! !
I ~.~
1.~
~,
~.; E d MeV
2.15
(d, p) REACTION
55
d'~ mb/sr 0.464
0 944
P /_
P 3
0.?08
0.346
0.472
0.232
0.116
0236
1 1.3
I
13
2,1
1,7
2.5
I 1.7
I
I
2.1
2.5
E d MeV
1.160
do' r o b / s t
0.928
P 9,10
Fig. 4. The excitation function o f the proton groups at 150 °. 0.696
0.~ 64
1.232
1 1.3
1!7
21.1
E d MeV
E,&3 5
Ed = 2.00 McV
MeV
Ed= 2.20 Me'.'
o.15t
1,
,.,,t
* 1
0.15‘
0.5 I
0.20' 1
0.10
‘I.’ rrl,“~‘z I
?
I
0.11
i
0.25
‘$1
t f
Ii14, I 0.07.
~*ff~!,rlf
f
1
f
0.30
?’ 110
1.00.
’
t’K”i’ f
0.90
I
I
I 080
111’
f 0.6OL
o.70~ 0.80
I
LL I
0.60
III1
f
11
040
hfl
20
50
80
0.50
1
110
1co
040
, i 21
Fig. 5. The angular distribution an
) MeV
Ed = 2.50 MeV
Ed: 2.40 MeV 1.10[ ~'~01 lllltlll(ttl ~,20 t li
I I i
I l ! 0.80
[t
t
°2°I , ,' ,
l I
/
tit
0.10[
i
i
•
t t t
iI l
i t
tll '
i
~
0"35[ tl
/
,
0.15[
t I
i
i
[ lt[lll
0'25i~"
'tl'
16
I tl I
tO0 [ ,i
O~ mb
,
"l~0I'
0.30 I
t
t I I t I
II
'
0.60 [
i ,
'
,
i i
11
,'
i
t
Ed MeV
I
i [ 1
'gL
i
Ed MeV
Ittlll
[ ill
!
o.2or
12
1
l, it If
0.90[
llllilll
°f
'
i
i 1D0I
P 0.1
t
0.50
i
i
i
i
i
Ed MeV
0"60 I till
t
0,30
I I I
f
't
iilllltilti
! '
i
I
0"10r
I ! I
I
I
[3/401
t ;
I
] o.
,::I
I]ll ilttlt
1v
,
,
,
B,
J
i
I
Ed
MeV
5
III I Illlllll
O'~OIl. ~tlltttlflitt 0.30
I i !
i
3
I [ !
I
i ]
0.10 I
t
0.20 [
I Ed (MeV)
.!
1.20[
1.5o
t

t
llzlllllltlll I
1.10
t I
!
'
I
'
I°° I
z
t
17
It t I! !

l
13
l
t
I 0.80i ill
I °7° i
7.0
P
!
9L
Ed (MeV)
060[ i II
O.SO
Et!  t i F
t 0./,
I
11o 1~o
!
0.6
0"40 i
so
!
i i ! I I
'l#Iz'lllIl
z~
~o
~o
,~o
:osssection for t h e g r o u p s Po, 1Pg, lo.
,~
I
! Illilil
2o
so
P 9.10
i ! i i t
8o
liO
l~eL
1.e 2 2.:2 2..<,: E,., (M,,v)
58
A.T.
BARANIK e t aL
The energies used for the measurement of angular distributions as a rule corresponded to different maxima or minima in the excitation functions. The same figures illustrate the total reaction crosssections for each of the groups.
4. Discussion of Experimental Results As shown in figs. 3 and 4, a large number of resonances in the excitation curves have been observed for all proton groups measured both at 30 ° and 150 °. The target thickness and the excitation energy (Eex = 16.517.8 MeV) of the 33S compound nucleus precluded the possibility of resonances connected with the isolated levels in the compound nucleus. Naturally one can say that the resonances, actually connected with the compound nucleus, correspond to a group of levels in the compound nucleus 16). In this case, the resonances are usually revealed in the total reaction crosssection, and one may observe a correlation between the groups leading to the vraious states of the residual nucleus as well as between measurements carried out at different angles 17). For the reaction studied, this is more or less true for about 50 70 of the observed resonances. One may consider the resonances observed for some proton groups at the energy E d = 1.85, 2.025, 2.2, 2.3 and 2.45 MeV as related to the compound nucleus a3S, since they also appeared 18) at the same energies in the (d, c0 reaction with 31p. In figs. 3 and 4 one can easily see that the excitation curves obtained, e.g. at 150 ° also have many maxima and minima which are not correlated with the patterns observed at 30 ° and thus show no evidence for a correlation in the differential and total crosssections of the group corresponding to various finite states of a2p. As was pointed out 19), the origin of such "resonances" is not yet clear and they can be attributed to interference between compound and direct processes, to intermediate resonance structure 2o,21), to Ericson statistical fluctuations 22), etc. For the reaction 31p(d, ~)29Si at similar energies the same fluctuations in the excitation curves were shown 23) to be related, in practice, with the Ericson fluctuations. The application of a statistical method 19, 23) for the given (d, p) reaction is however rather difficult because of the comparatively thick target ( ~ 20 keV), the increment of energy (25 keV) and an appreciable contribution by direct processes as well. The latter can be easily seen from the angular distributions (figs. 5 and 6). All angular distributions show patterns which can hardly be considered as compound nucleus patterns. Moreover at all deuteron energies such groups as P2 and P3 are slightly "contaminated" with the contribution from the compound nucleus and are rather typical for the mechanism of direct interactions. F r o m this point of view, it is of interest to clarify to what extent the angular distributions of the groups can be described by the stripping theory. Due to the fact that the 31p nucleus is deformed, the experimental results were compared with the stripping formula for deformed nuclei. Since the angular distributions both for P2 and P3 groups show the presence of two l, values, comparison with the stripping theory for deformed nucml is more reasonable. In this case the
(d, p) REACTION
59
ordinary selection rules undergo a modification and the mixture of two angular momenta is an immediate consequence of nuclear deformation. According to refs 24, 25), the angular distribution of protons from (d, p) reactions with nonsperical nuclei can be written as follows: dtr(0) _ G2(K ) ~ (Ii Ki Jt2nlIfKf) 2 ~. Cj2M2,, dO j
(1)
where K 2 + ~a2
G(K) = 1 K =
K2 +fl~'
/¼K2 + Kp2  K d Kp cos 0;
(2) (3)
% and fld are the parameters in the HulthOn wave function. The coefficients Cj~ are evaluated by Nilsson 26) as
Cj, = E am.~(If2n • ½E Ijf2,).
(4)
The quantities M m are expressed in terms of the radial part of the spherically symmetric wave function R m as follows:
Mm =
Rm(x)j,(Kx)x 2dx.
(5)
0
In the proton groups P2 and Pa in the alP(d, p)a2p reaction, li = ½, Ki = ½, If = 1, Kf = 1, f2~ = ½, a n d j varies within the limits
llilfl <= j <= Ii+If.
(6)
Substituting the values of the ClebschGordan and Cjz coefficients into eq. (1), the following expression for the differential crosssection of the (d, p) reaction on alp can be obtained:
dtr _ G2(K)[a2o R2o +O.2(O.866a2t _O.707a2o)ZR2j.
(7)
dO The first term in the squared brackets expresses the contribution from l = 0 and the second term corresponds to that from l = 2. The values of the am+~ coefficients were derived from Nilsson's work. To find the lower limit of integration in expression (5) for Mm, the angular distributions were first compared with the simple Butler formula (see fig. 6). From this comparison the most acceptable Butler interaction radius R i n t w a s found, then the lower limit for X o = Rint/r was estimated, where r = ~/h/MW is the width of the oscillator potential. It was earlier shown by Parkinson lo) that both the 1~ value arising from the proton angular distribution in the alP(d, p) reaction and the value of the alp magnetic moment can be explained if we assume a complicated mixed configuration of nucleons in a t p and 32p. According to Nilsson's level scheme the odd proton of 32p is found in the S, state and the odd neutron in the
60
A.T. BARANIK e t al. IT
P2 Ed: 2.3 HeV
8
I
6
4 ",, y
2
. . . . . . .
I0
30
50
70 90 P3 E d : 2.3 NeV
0~
110
130
11'0
130
a
lSO
L
Oc.m
5
3 2
t
,7 I
I
10
30
I
$0
70
90
I

l'S0
ec.m.
Fig. 6. The comparison o f the experimental angular distribution o f the p r o t o n groups Pl and p , w i t h curves calculated f r o m the simple stripping theory at 2.3 MeV deuteron energies.
Ed = 2.5
McV
G"
10
30
SO
70
90
110
130
150 Oc.m.
Fig. 7. The comparison of the experimental angular distribution of the proton group Ps with the curves calculated from the stripping formula for nonspherical nuclei at deuteron energy 2.5 MeV.
61
(d, p) REACTION
state D~. The ninth and eleventh Nilsson orbits were used for calculations. As in Parkinson's case, it was assumed that the ground state can differ from the excited one by changing the proton configuration. The comparison of theoretical calculations with experimental angular distributions for P2 and P3 groups is given in figs 7 and 8. Satisfactory agreement between theory and experiment is observed. The Nilsson coefficients am±~r with which this fitting was obtained correspond to a nuclear deG" Ed :
2.3
MeV
1.2
10
0,6
06
04
:~!
0.2
20
40
60
80
100
~20
140
160
Oc.m.
Fig. 8. The comparison of the experimental angular distribution of the proton group Pa with the curve calculated from the stripping formula for nonspherical nuclei.
formation of approximately  0.05. If the obtained deformation value fl is true, one can expect the magnetic moment of the 32p nucleus calculated at the same deformation to be close to the experimental value. TABLE 1 Experimental and calculated magnetic moments
Nucleus 3~p 81p
Experimental 0.252 1.131
Shell model 1.645 2.793
Unifiedmodel fl ~ 0.05 0.225 1.090
The calculated results are given in table 1, assuming that the deformation of the 32p nucleus is the same in the ground state and at 1 MeV excitation energy. In this case the magnetic moment of the last odd proton and neutron which contribute to the total magnetic moment of 32p is calculated according to the formula
1 {(g~ g,)[¼ Z (a20 a~l) + (  1)I~+t(I +½) Z a20] I+1 t + (g, gR)[¼ + ( 1) l ~½(I + ½)a] + gR I(I + 1)},
/2 =  
(8)
62
A.
T.
BARANIK
.?t
d.
where the coefficients a,,,* are the same as in the expression (7) for the differential crosssection. Table 1 shows the experimental values of magnetic moments to be very close to those calculated by the unified model. Calculations for 31P were carried out assuming that the captured neutron does not deform the core and hence the deformation parameter p is the same for both 31P and 32P. 5. Conclusions In the reaction 31P(d, P)~~P the competition between the direct process contribution and the compound nucleus effect is appreciable even at 1.52.5 MeV deuteron energies. The study of proton angular distributions from (d, p) reactions on deformed nuclei may prove to be very promising for obtaining some information about nuclear surface deformations and magnetic and quadrupole nuclear momenta. In conclusion the authors express their gratitude to Professor M. ElNadi and Dr. G. Vissotsky for their help in the interpretation of the experimental results and discussions and to Dr. V. Gontchar and Dr. V. Lutsik for their interest in this work. We are also indebted to the staff of the accelerator for efficient operation of the accelerator and Mr. V. Selivanov for the preparation of the manuscript for publication. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26)
J. P. Schifferand L. L. Zee, Phys. Rev. 115 (1959) 1705 B. H. Wildenthal, R. W. Krone and F. W. Prossor, Phys. Rev. 135 (1964) B680 W. Tobocman, Phys. Rev. 115 (1959) 98 W. Tobocman and W. R. Gibbs, Phys. Rev. 126 (1962) 1076 A. Z. ElBehay et al., Nuclear Physics 56 (1964) 224 H. M. Omar et al., Nuclear Physics 56 (1964) 97 C. Broude et al., Proc. Phys. Sot. 71 (1958) 1097, 1115, 1122 I. B. Teplov, JETP (Soviet Physics) 4 (1957) 31 D. Pjzaino, C. M. Paris and W. W. Buechner, Phys. Rev. 119 (1960) 732 W. C. Parkinson, Phys. Rev. 110 (1958) 485 A. W. Dalton, S. Hinds and G. Perry, Proc. Phys. Sot. A70 (1957) 586 T. Maltebeck, Nuclear Physics 37 (1962) 353 C. F. Block, Phys. Rev. 90 (1953) 381(A) D. M. Van Patter, P. M. Endt, A. Sperduto and W. W. Buechner, Phys. Rev. 86 (1952) 502 M. A. Abuzeid et al., Nucl. Instr. 30 (1964) 151 N. A. Mansour et al., Nuclear Physics 59 (1964) 241 G. Calvi, A. Rubbino and D. Zubke, Nuclear Physics 38 (1962) 436 M. A. Abuzeid et al., Nuclear Physics 60 (1965) 264 G. Pappalardo, Phys. Lett. 13 (1964) 320 K. Izumo, Prog. Theor. Phys. 26 (1961) 807 B. Block and H. Feshbach, Ann. of Phys. 23 (1963) 47 T. Ericson, Advan. Phys. 9 (1960) 425 M. Darwish et al., to be published J. Sawiekic, Nuclear Physics 7 (1958) 289 M. Z. Menta, and C. S. Warke, Nuclear Physics 13 (1959) 451 S. G. Nilsson, Mat. Fys. Medd. Dan. Vid. Selsk. 29, No. 16 (1955) pp. 168