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Elastic Scattering of -Particles on Be9.

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Annalen der Physik. 7. Fblge, Band 31, Heft 1,1974, S. 76-82
J. A. Barth, Leipzig
Elastic Scattering of a-Particles on Be9
By Z. A. SALEH,
B.MACHALI,I. I. BONDOUK,
and D. A. DARWISH
With 6 Figures
Abstract
The differential cross-section for the elastic scattering of He4 particles on Be9 has been
studied in the bombarding energy range 1.4-2.5 MeV.
The excitation functions for the elastically smttered a-particlesfrom BeQwere measured
a t six angles 90". 125", 132", 140", 160" and 160" in the centre of mass system.
A clear and pronounced resonance is observed in the measured cross-section a t incident
a-particle energy 1.93 MeV. Analysis of the data in terms of the single level approximation
5'
theory leads to the assignment J" = - for the observed resonance. Reduced and partial
2
widths for elastic scattering were determined.
1. Introduction
Although a large number of experimental and theoretical investigations of
the Be9 target nucleus and the C13 compound nucleus have been reported, information about the elastic scattering of a-particles by Be9 is very limited. All the
information about the compound nucleus CI3 from reactions of a-particles with
Be9 were obtained through (a - n ) reactions [1-71.
2. Experimental Procedure
The 3r-2.5.11 type electrostatic generator of the A.R.E.A.E.E. was used
to accelerate a helium beam which after acceleration passed through a 90'
deflecting magnet and a system of collimating diaphragms and entered the
scattering chamber [8].
The He4 scattered from the target were detected by four semiconductor
counters mounted radially with respect to the target at 20' spacings.
Four sensitive preamplifiers amplified the signals which were fed to the
amplifiers and then through a mixer t o RIDL-400 pulse height analyser. The
beam was collected in a FARADAY
cup and measured with a A-30-9A current
integrator.
Self supported Be9 was used as a target on which a very thin layer of Ag was
evaporated, the target thickness was about 15 keV for 1MeV a-particles. The
high energy resolution of the detectors in use leads t o the conclusion that the
a-particles elastically scattered from Bee are well separated from those scattered
on C12 resulting from the cracking of the carbohydrates of the vacuum system
and 016 present as target contamination even a t low energy and small angles
(Fig. 1).
Scattering of a-Particles on Bee
77
To avoid the necessity of accurately stabilising geometry and beam current
integration, the yield of a-particles scattered on Bee was normalised with respect
t o Ag, which certainly obeys the RUTHERBORD
law in this energy range
(Fig. 2). Owing t o this procedure, the errors arising from finite size of the beam,
target position, and detector solid angles were negligible. The combined uncertainities are estimated t o yield a probable error f5% in the relative value of the
cross-section.
A":
i' h'
'66'
I
I
1.60
+Em
2.0
IlablMcV
25
Fig. 2
Fig. 1. Typical pulse height spectra obtained at Ea = 1.6 MeV
Fig. 2. Yield of a-particles scattered from AgioB devided by the RUTHERFORD
scattering
3. Experimental Results
The elastic scattering of a-particles on Bee has been studied a t six angles
between 90' and 160' (centre of mass) in the range of bombarding energy
1.4-2.5 MeV.
To test experimental accuracy and reproducibility of the results the measurements were repeated twice; a reasonable overlap of the two sets of results wm
b
obtained.
Cross-section measurements were carried out in steps of 20keV and are
represented as fraction of the corresponding differential cross-sections for
RUTHERFORD
scattering. A clear and pronounced resonance is observed (Fig. 6)
in the measured data which corresponds t o a level in the compound nucleus
a t excitation energy 11.97 MeV.
Elastic scattering is a useful tool for the study of virtual energy levels of the
resultant compound nucleus. The scattering is described in terms of parameters
associated, with the energy levels of the compound nucleus. These parameters
are the energy of the virtual level El, the angular momentum Jnand the reduced
width ya.
By the use of the WIGNERand EISNBUD
[9] one level formula the parameters
can be assigned from the cross-section data.
Z. A. SALEH,F. &OUI,
78
I. I. BONDOUX
and D. A. DARWISH
To compare experimental results with theoretical analysis a reasonable
choice of measurement conditions is needed. That is why our measurements
were carried out under finite angles satisfying the condition
Pl
(COSO)
= 0.
It is not difficult t o verify that under the angles of scattering satisfying the
.above mentioned condition the resonance form in the cross-section will not
depend on the interference between COULOMBand resonance scattering.
Since we are dealing here with reaction of spinless particles and a target
with arbitrary spin I both inlet and outlet channel spins will be limited t o only
(:
one value which is equal t o -target
spin
1
. The reaction was carried out with
low energy a-particles and a t such low energy the orbital angular momentum
seldome exceeds two.
Table 1 Possible values of the total angular
momentum -
I
I
4
O
I
2
Table 1 shows the possible values of the total angular momentum, bearing
i n mind that we have only one channel spin.
The radius of interaction r is usually the same for all partial waves arid €or all
2 values; it is choosen in this work t o be 4.53 fm.
The differential cross-section for elastic scattering of a charged particle of
spin i with an arbitrary spin, I, can be written in the form
-db_ - [(2i + 1)(21+ 1)l-l 2 1 fP(@,@) 12dB
df2
where the reaction amplitudes
am,
f p are defined by [lo]
79
Scattering of a-Particles on BeQ
= arctan
3 which is the hard sphere phase shift, YF-ma' (0,
@) are the norQl
malised spherical harmonics, azis the RUTHERPORD
phase shift.
21 arctan-7.
a1=
a,, = 0.
S'
Er is the resonance energy, I', and I'lJare the total and partial level widths
respectively, Fl and 4 are the regular and irregular functions respectively.
y p are the spin functions, s, s' are the incoming and outgoing.channe1
spins. K is the wave vector of a-particles. M is the reduced mass of the system.
8=1
r,
ZZ'ea
q =-liV
parameter of COULOMB scattering; the resonance phase shift
is defined by
= arctan
P J ~
/3
[2(Err- E )1.
Mathematical derivation of the cross-section formula was carried out bearing
in mind that:
1. the level is isolated,
2. we have only one inlet and one outlet channel spin,
3. the lowest 1 value gives a contribution,
4. hard sphere scattering is equal t o zero.
Calculating @,,for the case of Bee(&,a)using BLOCK
[Ill tables it was found
t h a t @,, is nearly zero and accordingly the potential scattering Q1for 1 > 0 will
be forbidden.
6 0
L O
2.0
6 0
L.0
2.0
60
LO
20
12 0
80
L O
Fig. 4
Fig. 3
Fig. 3. Resonance phase shift for the resonance observed
Fig. 4. Theoretical isolated resonance shepee for the elastio scattering of a-particleson Be".
The resonance energy is taken to be 1.85 MeV and the total width200 keV
Z. A. SALEII,F. MAOUI, I. I. BOHDOUK
and D. A. DARWISR
80
Moreover for the first step of calculation we considered t h a t the &-particle
channel is the only one opened. After achieving the final forms for different L.S.
representations, the resonance phase shift was calculated considering a total
width of the compound level of 200 keV and a resonance energy of 1.86 MeV.
Fig. 3 shows a schematic representation of the relation between the resonance
phase shift and the incident energy.
To determine the effective orbital angular momentum the theoretical curves
for resonance shape a t centre of mass angles 90°, 126", 140°, and 160' were
calculated considering all the possible values for different L.S. representations,
as shown in Fig. 4.
Comparison of the theoretical curves with the experimental results measured
a t the same angles leads t o the conclusion that the effective orbital angular
momentum is that with 1 = 1.
I
BE,,
425'
......
Eo.m :126'
e,,
1.4
1.6
18
2.0
-En
2.2
2.L
2.6
l
1.4
1.6
.1.8
- E n 2.0
I 2l.a2b 1O2.4
MeV.
:90'
O
l l a b 1 McV
Fig. 6
Fig. 6
Fig. 6. Differential cross-sectionfor the elastic scattering of a-particleson Bes in the vicicity
of tho 1.93 MeV a t @c.m = 126, 150 and 160". The solid line corresponds to theoretical fit
6+ Fa 3+ Fa
for J" = B'
- 0.4 while the dotted line for J n = -, - = 1.0
2 r
Fig. 6. Differential cross-sectionsfor the elastic scattering of or-particles plotted as function
of incident a-energy for the oentre of mass angles indicated. The dots represent experimental
6+ and Fa = 0.4
points, the solid lines represents the theoretical fitting for J" = 2
r
Scattering of or-Particles on B#
81
Now the task of analysis is reduced to determine the partial width Fa,the
total angular momentum J and the reduced width ya.
Since we are dealing with the reaction of P-wave a-particles with Beg, three
1+ 3+ 5+
values of total angular momentum are probable, viz. - 2
T-
2
To estimate the exact value of J we compare (Pig. 4)the excitation functions
calculated for each values of J with I
', = T.
5
The result with J = -was found to give the largest dip to top ratio while
2
1
3
the result for J = - and - gives a smaller dip t o top ratio with respect to the
2
2
measured differential cross-section which is not improved by changing the
a
value of rbince, as mentioned before, the neutron channel is also open for the
r
level under consideration.
As the ratio of the partial width Fat o the total width is unknown, it ifi
used as a variable parameter; it appears in the final cross-section form as follows:
r
5
For J = - the parameter
2
5
r is varied until the best fit is achieved for dip to
peak ration between the data and thory, and the best value was found to be 0.4.
3+ with - = 1,
Fig. 5 shows the excitation functions calculated for J" = 2
5+
and J" = - with - = 0.4, respectively.
2
3f
For J" = - i t is clear that i t is impossible t o have a better agreement
2
between theoretical curves and experimental results by changing the value of
5
This comparison confirms the value of - for the total angular, momentum
2
r,
r
ra
r
5
r-
Fa
of the compound level. Knowing the value of -,
r
it is now necessary t o fit the
0
theoretical value of -t o the experimental one. The resonance energy and total
flR
width are varied until the best agreement with experimental data was achieved
Fig. 6 shows the result of the differential cross-section fit in the vicinty of the
1.93 MeV resonance. The cross-section curves were obtained considering the
parameters listed in Table 2.
The parameters obtained for this level are more or less in agreement with
those of (a - n ) on Be9 [12] measured in our laboratory. I n the (a - n ) experir n
ment the same spin assignment,for the 1.93 MeV level is obtained where -
r
was taken t o be 0.6.
Z. A.
82
SALEH,F. MAOHALI,I. I. BONDOUKand D. A. DARWISE
Table 2 Nuclear data of the 1.93 MeV level
of Ben
E~
1.93
1
1
J~
1
1 I I
1
riot I ra
1
~2
180keV 172kaVI 0.36
Conclusion
The resonance observed a t a-energy 1.93 MeV was analysed in terms of one
level approximation of dispersion theory. The information gained from this
analysis is summarized in Table 2. These.data are consistent with those obtained
in ref. [12].
The authors wish t o thank Prof. M. EL-NADIfor his encouragement and
interest in this work.
References
[l] TANNER,Proc. Phys. Soo. A 68 (1965) 1195.
[2] JONES,
et al., Phil.Mag. 1 (1966) 949.
[3] BONNER,
et el., Phys. Rev. 102 (1966) 1348.
[4] RISSER,et al., Ph 8 . Rev. 106 (1957) 1288.
(61 GIBBONS,et EL,~ K y s Rev.
.
114 (1969) 671.
[6] GIBBON,J. H., et al., Phys. Rev. 187 B (1966) 1508.
[7] OROCE,et al., Nature 206 (May 1, 1966) 494.
[8] ~ U Z E I D M.
, A., et al., Nucl. Instr. and Methods 80 (1964) 161.
[9] WIGNFJ~,
E. P., EISNBUD,L., Phys. Rev. 79 (1947) 29.
[lo] REIUH, C. W., Thesis, Ph. D., The Rice Institute (1966) (Unpublished).
[ll] BLOCK,
J., et el., Rev. Mod. Phys. 28 (1951) 347.
[12] ZAEY, F., Private Communication.
C a i r o (A.R. Egypt), Atomic Energy Establishment.
Bei der Radaktion eingegangen am 28. September 1972.
Eingsng des revidierten Manuskriptes 3. Juli 1973.
Ansch; d. Verf. : Dr. Z. A. SALEH,
Dr. F. MACHALIund Dr. D. A. DARWLSH
Atomic Energy Establishment
Cairo (A. R. Egypt)
Dr. I. I. BONDOW
Institute for Atomio Physics
Cyolotron Laboratory
P. 0. B. 36
Bukareat (Romania)
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