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Anomalies in Elastic Scattering at Isobaric Analogue States.

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Annalen der Physik. 7. Folge, Band 28, Heft 4,1973, S. 315-320
J. A. Barth, Leipzig
Anomalies in Elastic Scattering at Isobaric
Analogue States
By S. A. EL-KAZZAZ,
M. ABDELHARITH
and L. M. EL-NADI
With 4 Figures
Abstract
Excitation functions for proton elastic scattering on MnSs at proton energies from
1320 KeV to 1480 KeV have been measured at the angles 135' and 160".Anomalies in
the differential elastic scattering were observed a t E,, = 1350 f 4 KeV, 1385 f 4 KeV
and 1445 & 4 KeV respectively. These resonance states are the isobaric analogues of the
ground, first excited and second excited states in MnS6respectively. Analysis of the results
showed that these resonance states are best fitted to a J" = 3+, 2+ and 1+which is in excellent
agreement with the J" values of the corresponding states in Mns6. The total widths and
proton widths of these states were determined.
1. Introduction
Proton elastic scattering experiments have proved to be powerful tools
for the determination of spin and panty of nuclear energy levels, since it
permits the determination of the orbital angular momentum of the captured
proton. This is due to the fact that the shape of the excitation function near
a resonance level is completely characterized by the orbital angular momentum
of the captured proton.
I n the present paper, proton elastic scattering on Mn55 was studied in the
energy range from 1320 KeV to 1480 KeV. The excitation function of the reaction Mnm (p, y ) Fes* in the same energy range [ l ] showed resonance states
which are the isobaric analogues of the low lying states of MnMwhose spins are
known from atomic beam experiments [2], (n, y ) reaction studies [3, 41,
study of the t9 decay of C Y 6 [5] and (p, y ) studies on Mnm [6].
2. Experimental Procedure
The 2.5 MeV VAN DE GRAAFFgenerator of the A.R. E. Atomic Energy
Establishment provides the beam of protons. The energy resolution in the proton beam was better than 1 KeV. The targets used are of the self supported
type prepared by vacuum evaporation of metallic Mnm. The target thickness
was about 35 pg/cma.
The elastic scattering measurements were carried out in a special scattering
chamber [i']. The beam entrance slit was 3 m m in diameter. The scattered
protons were detected using three Silicon surface-barrier solid state detectors
placed at go", 135" and 150" to the beam direction. I n front of the detectors
316
Annalen der Physik
*
7. Folge
*
Band 28, Heft 4
*
1973
the scattered particles were collimated with a 20 mm long, 5 mm diameter
copper collimator with its face 80 mm from the target. A diaphragm of 3 mm
diameter was placed just before each detector. The angles used were chosen
according to the detector dimensions and the present experimental geometry.
Pulses from the detectors were first preamplified, then amplified using an
ORTEC type low noise linear amplifiers and the resulting voltage pulses were
analysed using two 512 multichannel analysers. The elastic spectra obtained
showed proton groups elastically scattered from the target under investigation
and weak groups due to carbon and oxygen. These proton groups are well resolved a t angles greater than 90'. For this reason, the experimental results were
analysed a t the angles 135' and 150" only.
I n measuring the excitation function of the reaction, Mns(p, p) Mn&, the
energy of the accelerated protons was varied in steps of 2.5 KeV from 1320 KeV
to 1480 KeV. In each step, the data were taken per 6 micro-coulombs of charge
at a target current of about 0.15 pA producing small statistical uncertainties
in the proton yield. The excitation function was measured two times to test
the reproducibility of results.
3. Results and Discussion
The excitation function of the reaction Mn&(p,p ) Mns is shown in Fig. 1.
In this excitation function deviations from coulomb scattering were observed
a t proton energies 1350 & 4 KeV, 1385 f 4 KeV and 1445
4 KeV. These
resonance states are the isobaric analogues of the ground, first excited and
second excited states of Mnm. The resonance states observed in the elastic
x10
3
50
48
-5
44
-
42
46
n
0
L
2
40
=
38
E
a
36
34
32
r
-
t
..
4
I
1.325
1.375
1.125
P r o t o n Energy (MeV)
1.475
Fig. 1. MnS6 proton elastic scattering data
at two angles exhibiting analogue resonances. Arrows indicate resonances that
have been analysed
317
EL-KAZZAZ,
ABDELHARITH
and EL-NADI:Anomalies in Elastic Scattering
Table 1
Stgef6in
I
E ~ (xF e T
MeV
MeV
0.000
11.471 f 0.074
11.497 f 0.074
11.582 f 0.074
0.02F
0.111
i
(P,P)
1
En exp.
MeV
( E expMeV
1.350 f 0.004
1.385 f 0.004
1.446 f 0.004
I
~
I
1.303
1.330
1.415
47
55
30
i
scattering work are in fair agreement with those observed from the reaction
Mn=(p, y ) FeS6in the same energy range [l].
The energy of the isobaric analogue states was calculated on the basis of
the universal coulomb displacement energy formula [8] :
d E c = (1.444f 0.005) (z/A1/5)- (1.13 & 0.04) MeV
= 8.553 f 0.074 MeV
The energy of the first isobaric analogue state in FeS8 corresponding to the
ground state of MnS6 is = AEc AB, where AB is the difference in binding
energies between Fe6B and MnM [9]. Knowing that the Q-value of the reaction
Mn=(p, y ) Fe6B is = 10.1915 f 0.0048 MeV, one can deduce the expected Ep
values for the resonance states mentioned before. Table 1, shows the results
of such calculations.
+
0.66
0.64
0.62
a
L
m
L
”
.0
-a
L
Q
5
0
0.56
0.54
0
0.52
0 .50
Fig.2. &f.nu profon elastic scattering d&t8
8nd the best fit for the resonance state at
&d r=-7-KeV. [Sblh line f& 1 =3,
daahed
line for l ( 2 = 1) 2.4(1 = 3)]
+
1
.
1
.
1
.
1
.
1
.
1
Proton Energy ( M r V )
.
1
318
Annalen der Physik
0'50
0.48
1t
1.355
*
7. Folge
*
Band 28, Heft 4
*
1973
f
1.375
1.415
1.395
P r o t o n Energy (MeV)
Fig. 3. MnS6proton elastic scatteringdata and
the best fit for the resonance state at Em=
1385 f 4 KeV, Z? = 3, r, = 4 f 0.4 KeVknd
line for 1 ( I
1)
+ 1.6 ( I = 3)]
Theoretical differential elastic scattering cross section [lo] for each of the
above resonances for different spin assignments was calculated using the formula :
do
do
do
do
= m ) c o u l o m b + m)resonance + m llnt e f i e r e nc e
and applying the R-matrix theory [Ill. I n this case the interference term is
given by [12] :
x Re [iT;&C(O)] Pl(cos 0).
In the present case, the potential scattering was expected to be very small since
the resonance states observed are below the coulomb barrier, also all the nuclear
phase shifts were taken to be zero since they are not expected to alter the size
of the resonance parameters [lo].
The differential elastic scattering cross-section has been programmed for the
1
ICL - 1905 E Computer for the special case of spin particles scattered from
for two angles a t a time and for pure inlet channel spin.
Mnu ground state
The cross section -for all possible J n values with different
and
(taking
F, and rflfrom Ref. [l],where =
I', rfl)
was calculated with chosen
r r, + +
r,
r
319
EL-KAZZAZ,
ABDELHARITHand EL-NADI:Anomalies in Elastic Scattering
Mn55 (p,p,
0.58
0.56
--,,
.-c
0.54
0.52
a
a
L
a
L
.m
-; 0 . 4 8
-
0.46
0
0.44
.$
b
Fig. 4. Mns5proton elastic scattering data and
the best fit for the resonance state a t E, =
1445% 4KeV,Z, = 1,1'n=3f0.2KeV;nd
r = 15 KeV
l
.
l
,
I
1.415
.
l
,
1.435
I
,
I
1.455
.
I
1.475
P r o t o n Energy (MeV)
1 values. The experimental results were compared with the calculated cross
sections and the best fitted data are then adopted.
Analysis of experimental results showed t h a t the above mentioned resonance states in the reaction Mne(p, p ) MnS6a t proton energies of 1350 f 4 KeV,
1385 f 4 KeV and 1445 f 4 KeV are best fitted t o 3+, 2f and I+ states with
lp values 1, 3 and 1respectively. Figures 2, 3 and 4 show the result of the fitting
of the experimental data t o the theoretical calculations. Table 2 summarizes
the nuclear parameters, obtained from such fitting, for each of the resonance
states mentioned.
From Table 1 the observed coulomb energy shifts differ about 20-50 KeV
from the calculated ones, indicating that the coulomb displacement equation
Table 2
Elastic scattering parameters for Fe68 levels and comparison t o MnS6levels
E,, lab
KeV
1I
MuS6
P)
(a9
Eex.(FeS6)
MeV
~
2 V
IGV
1 f 0.2
1385 f 4
11.497 & 0.074
4 f 0.4
9
"
1445 f 4
11592 f 0.074
3 & 0.2
15
I
3
2
1
0.026
+
1+
I
(Mns6)
MeV
Eex.
0.000
11.471 f 0.074
1350 f 4
1 I
Mus5 (4P) [I31
Jn
~
0.111
I
In
l ( 1 = 1) +
2.4 (1 = 3)
+
1 ( I = 1)
1.6 ( I = 3)
1
320
Annalen der Physik
* 7. Folge *
Band 28, Heft 4
*
1973
could be adopted successfully for nuclei in the f;/z shell. As clear from Table 2
and Figures 2, 3 and 4, the proposed spin and parity assignments are in good
agreement with the corresponding M n s states. The experimental data for the
three states are fitted through pure 1 values, although in Mn=(d, p) reactions
[13] mixing of I was observed for the first two states.
From the present results, one may conclude that elastic scattering of protons through nuclear isobaric analogue regions can be a powerful means of
measuring the properties of the nuclear levels, and the “R-matrix Theory”
fits the elastic scattering data successfully.
The authors would like to thank Prof. M.EL-NADI, for his interest and
encouragement during this work. The help of Dr. M.SIMBELin Computer
programming is greatly acknowledged. The authors are also greatful t o the
A. R. E. Atomic Energy Authorities for allowing them t o carry out the present
work in their laboratories, and would like t o thank the VAN DE GRAAFF
group
for the efficient operation of the machine.
References
[l] OTTO,G., R.MEHNERT
and G.TOMASELLI,
Nuclear Phys. A 109 (1968) 118.
[2] CHILDS,W.J., L.S.GOODMAN
and L.J.KIEFFER, Phys. Rev. 122 (1961) 891.
[3] D’ANQELO,N., Phys. Rev. 117 (1960) 510.
[4] ESTULIN,I.V., A.S.MELIORANSEY.
and L.F.KALINEIN, Nuclear Phys. 24 (1961) 118.
B.J., A. W.SCHARDT
and T.T.SHULL,Nuclear Phys. 16 (1960) 357.
[5] DROPESEY,
[S] SAKAI,M., R.BERTINIand C.GEHRINQER,
JAERI-1184 (1969).
[7] SALEH,Z.A., Thesis, Atomic Energy Establishment, A.R.E. (1970).
[a] ANDERSON,
J.D., C.Woaa and J.W.MCCLURE,Phys. Rev. 188 (1965) B 615.
[9] MATTAUCH,J.H.E., W.THIELE and A.H.WAPSTRA,Nuclear Phys. 67 (1965) 1.
[lo] MOORE,C.F., P.RICHARD,C.E.WATSON,D.ROBSONand J.D.Fox, Phys. Rev. 141
(1966) 1166.
[ll] LANE,A.M., and R.G.THoMAs,Rev. mod. Phys. 80 (1958) 257.
[12] Fox, J.D., Private Communications (1971).
[13] COMFORT,J.R., Phys. Rev. 177, no. 4 (1969) 1673.
G i z a , Cairo University, Department of Physics, Facult,y of Science Atab
Republic of Egypt.
Bei der Redaktion eingegangen am 24.November 1971.
Anschr. d. Verf.: Dr. S.A.EL-KAZZAZ,
Dr. M . ~ D E L
HABITH
und Dr. L.M.EL-NADI
Department of Physics, Faculty of Science, Cairo University
Giza/Arab Republic of Egypt.
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