Differential cross section results are calculated for the elastic scattering of electrons and positrons from the ground state of Rb and Cd atoms. An optical model potential approach is used for the calculation. Results are compared with the available electron impact experimental results

Pangantiwar, A. W.

Srivastava, Rajesh

English

NASA Technical Reports Server

N90-18960
- +
ELASTIC SCATTERING OF e AND e FROM Rb AND Cd
A W Pangantiwar and Rajesh Srivastava
* Physics Department,Roorkee University,Roorkee - 247 667 (India)
** Govt. College of Engineering, Aurangabad, Mahrashtra, (India)
ABSTRACT
Differential cross section results are calculated for the
elastic scattering of electrons and positrons from the ground
state of Rb and Cd atoms. An optical model potential approach
is used for the calculation. Results are compared with the
available electron impact experimental results.
I. INTRODUCTION
In the present workshop we wish to report our theoretical
study of the elastic scattering of electrons and positrons by the
ground state of Rb and Cd atoms. Since the differential cross sections
(DCS) as compared to total cross sections provide more rigorous test-
ing for theories and experiments we mainly evaluate the DCS results
at various incident projectile energies, especially at energies for
which electron impact experimental results are available. However,
the direct measurements of the DCS for positrons elastically scattered
from alkali and heavy atoms aro also becoming available. In our study
we describe elastic scattering of electrons and positrons from Rb
and Cd. atoms in the framework of an "optical model potential approach"
(OMPA) 1
II. THEORY
The choice of optical model potential used in our OMPA can
be expressed as
V (r) = V (r) + V (r) ÷ V (r) ...(l)
opt st ex pol
The first three terms on the right hand side of equation (1) represent
respectively the static, exchangeand polarization potentials. Exchange
potential is absent for positron scattering. We obtain static potent-
ial using multi-zeta type Hartree-Fock wavefunction fo_ Rb and Cd.
For exchange potential followingwidely used form is used
V (r) = (k2/2-V (r)-[(k2/2-V (r))2+8_(r)]l12)l 2 ... (2)
ex st st
Here k is incident electron wavevector, _(r} is atomic target charge
density. For Cd, T = I and for Rb, T = -1 and + 1 respectively for
singlet and triplet modes of scattering. Following functional form
of the polarization potential is chosen
4
V (r) = = (_/2r )(1 - exp [-(r/r g)8]) ...(3)
pol c
is dipole polarizability of target atom. r is cutoff parameter
(see ref. 4) and g is energy dependent adjustable parameter chosen
such that it provides best fit to electron impact exprimental DCS
data. For positron scattering g is taken unity. From the known optical
potential the Schrodinger equation is solved for phase shifts which
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https://ntrs.nasa.gov/search.jsp?R=19900009644 2020-03-19T22:58:35+00:00Z
10 3
I I I t I
\
\
\
\
\
t 1 J I I I I
20 40 60 80 100 120 140 160
Scattering angle (deg)
180
Fig. l : DCS results for e (e+)-Rb elastic
scattering at 10 eV,
present e resul ts, --- present
+
Drer;ent e re:;ult:;, • e::periment
consequently d_fine scattering amplitude and give DCS results in conve-
ntional manner
I I I. RESULTS
The detail+ of the numerical calculation along with the DC_
results for e (e )-Cd elastic scattering is being published elsewhere
and we briefly present here our e (e )-l_b elastic scattering DCS resu-
] ts. For Rb we take _ = 319 and obtain r = 3.576. The DCS resul t:_
c
are calculated at 10 and 20 eV energies as displayed through figure_
1 and 2. From these figures on comparing with experimental results
_;e find that our optical model potential describes the e- - Rb elastic
.,_cattering reasonably well while for our positron scattering result:;
.future experiments can throw some light.
30
ORIGINAL PAGE IS
OF POOR QUALITY
I04_ I I I f
I_'_ 103
,__ 102
u'l
0
u 1
10
C
_3 _°o
I I | I
• _X_
_" _" ,_ \
_oI-- l I I I J [ f I
0 20 40 60 80 100 120 140 160 180
Scatterin9 ongle (de.g)
Fig. 2 : Same a._; Figure 1 at Z0 cV.
;_I;FIZRENC ES
I Khurana, R Srivastava and A N Tripathi Phys. Rev. A 37 3720 (1988)
1; Clemet, ti and C Roetti At.l)ata.Nucl .Data Table:; 14 177 (1974)
,J 1t Furnes:_ and I E McCarthy, J.|'hys. B 6 2280 { 1973 )
R Sriva:_tt, va and W Williamson Jr Phy:_.Rev. A 35 103 (1987)
A _g Pangantiwar and R Srivastava Phys. Rev. A (lO89) In press.
[, Vuskovic, I, Malcki and S Trajmar a. Phys. B 17 251 '_ (1884).
31



Elastic scattering of e- and e+ from Rb and Cd

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