The total cross sections for positron and electron collisions with potassium, sodium, lithium and rubidium are calculated, employing the modified Glauber approximation. The Modified Glauber cross sections for positron collision with potassium and sodium at low intermediate energies are found to agree reasonably well with existing experimental data

Gien, T. T.

English

NASA Technical Reports Server

N90-18962
Positron collisions with alkali-metal atoms
T. T. Gien
Department of Physics, Memorial University of Newfoundland,
St. John's, Newfoundland, Canada AIB 3X7
The total cross sections for positron and electron collisions
with potassium, sodium, lithium and rubidium are calculated,
employing the modified Glauber approximation. The MG cross
sections for positron collision with potassium and sodium at low
intermediate energies are found to agree reasonably well with
existing experimental data.
Measurements of total cross sections for collision of
positron with potassium have been performed only very recently I.
The experimental results of total cross sections for positron
collision by sodium and rubidium have been reported only at this
Workshop 2. In view of the success of the modified Glauber
approximation 3 in producing good agreement with experimental data
of total cross section in the case of e+-He, we have performed
the calculation of total cross sections for positron (and
electron) collisions with potassium, sodium and lithium, again
employing the modified Glauber approximation (MG). The model-
potential approach 4 will also be used in this calculation to
enable the "exact" inclusion of the scattering effects of the
core of the alkali atoms. The total cross sections are
calculated via the optical theorem.
In alkali atoms, the energy of the first p states of the
valence electron is only about 2 eV above its loosely bound s
ground state. This results in a strong coupling between these
two states and, thus, a very large dipole polarizability for the
alkali atoms. Therefore, care must be taken in handling the
effect of this particularly strong coupling between these s and p
states. In the modified Glauber approximation, the effect of
this strong coupling is seen to reflect in the large contribution
to the second Born term of the valence-electron-atom scattering
from the first p states, especially in the forward direction
where the imaginary part of the scattering amplitude is used to
calculate the total cross sections. To obtain a greater accuracy
for our MG results, we feel that in this particular case of
scattering by alkali-metal atoms, the contribution to the second
Born term from the intermediate first p states should be
evaluated exactly.
The MG total cross sections of positron (and electron)
scattering from potassium, sodium and lithium were calculated for
scattering energies ranging from about 10 eV to I000 eV. The MG
positron collision with potassium 5 are found to be in good
agreement with experimental data available at low intermediate
energies at present I, if one takes into consideration the
uncertainty existing in the experimental data due to the
inability of discriminating against the elastically scattered
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positrons (electrons) near the forward direction. At higher
scattering energies (60 - 102.5 eV), the MG values tend to be
somewhat smaller than the experimental values, while at lower
energies, the MG values tend to be somewhat greater. We have
also evaluated exactly the contribution to the second-Born term
from the next higher intermediate state (5s for K, 4s for Na and
3s for Li) and we have found that the new values of total cross
section only change minutely in comparison to the values obtained
with the consideration of the closure approximation for this
term. Therefore, we believe that the accuracy of the MG results
will not be seriously affected by the employment of the closure
approximation for the calculation of the contributions to the
second-Born term from other higher excited intermediate states.
The MG values of e+-K collision are found to be consistent also
with those obtained by Ward et al. 6 in the 5-state close-coupling
calculation.
The MG values of total cross section for electron collision
with potassium 5 are also in fair agreement with experimental data
at energies higher than 50 eV. The MG electron cross sections
are, however, found to be somewhat higher than the positron cross
sections. The merging of the two sets of data above 30 eV, as
was observed in experimental data I, does not seem to materialize
in our MG calculation. In our opinion, since the difference
between the electron and positron MG cross sections above 30 eV
is only within 15%, this non-merging of the theoretical data is
still acceptable, in view of the possible uncertainty of the
experimental data mentioned above. It is worth stressing that in
the modified Glauber approximation, the non-merging of the
electron and positron cross sections may be understood as to
originate from the different contribution in positron and
electron scattering to the cross sections from the core
scattering.
For collision with sodium, we found that the positron total
cross sections are also consistently lower than the electron
cross sections for about i0 to 15 percent. The two cross
sections did not merge with each other even at an energy as high
as i000 eV_ The absolute difference between the electron and
positron cross sections now seems to become smaller somewhat,
because sodium is lighter than potassium, and therefore, the
effectS=of its less "cumbersome" core would influence the cross
sections somewhat less. For collision by lithium, w_os9 core
effect is much weaker, our calculation in the MG approximation
_does:=_ndeed provide_ a m_ging-(w_thin iess _=than i to 3 per cent
of difference) of the positron and electron cross sections at a
rather low energy. It would, therefore, be interesting to also
measure the total cross sections for collision by lithium, which
have not been available in the literature. We also found that
for all three of the alkali targets (K, Na, and Li), the total
cross sections for positron and electron collisions, at least
within the modified Glauber approximation, did not deviate from
•_each _ other at some scattering energy above I00 eV and then re-
merge_at a much higher energy. The MG total cross sections for
38 !
positron (electron) scatterings from sodium 5 are found to be in
reasonably good agreement with experimental datal, 2 in the range
of I0 - I00 eV, and to be consistent with the results of close-
coupling calculation 7 at energies lower than 50 eV. Our values
of e ÷ - Li collision are also consistent with the close-coupling
values 7. Our preliminary results of total cross section for e +-
Rb collision seem to also be consisten$ with those calculated in
the close-coupling approximations" below 30 eV, and with
experimental data z below 50 eV.
Table i MG total cross sections in_a2 for e-K, e-Na and e-Li
K Na Li
Energy e + e- Energy e + e- e + e-
(eV) (eV)
38
48
51
76
102
150
200
300
400
500
800
i000
11 O0
18 20
21 10
28 20
31 20
40
6O
6O
75
5O
O0
O0
O0
O0
O0
O0
O0
105 85
9O O8
84 96
74 52
70 75
62 85
53 97
51 78
38.61
30.76
22.57
17.76
12.60
9.86
8.14
5.40
4.45
102.19
98 85
94 97
85 12
80 98
71 72
61 27
58 75
44 28
36 01
27 44
22 32
16 63
13 48
II 43
8.04
6.78
10 0
15 0
20 0
3O 0
4O 0
50 0
54 4
6O 0
80 0
100 0
150 0
200.0
300.0
400.0
500.0
800.0
i000.0
60 20 72.59
61 37 70.08
56 49 63.37
46 85 51.88
39 72 43.79
34 51 38.01
32 65 35 96
30 57 33 68
25 O0 27 64
21 25 23 60
15 65 17 56
12 50 14 16
9.06 10 39
7.18 8 31
5.99 6 98
4.06 4 79
3.37 3 99
76 50
68 60
60 19
47 83
39 72
34 06
32 08
29 89
24 14
20 33
14 74
ii 66
8 32
6 52
5 38
3 57
2 93
80.90
71.63
62.50
49.40
40.92
35 04
32 99
30 71
24 77
20 85
15 i0
ii 93
8 51
6 66
5 49
3 64
2 99
References
I) T. S. Stein, M. S. Dababneh, W. E. Kaupilla, C. K. Wan and Y.
J. Yan, in Atomic Physics with Positrons ed J. W. Humbertson
and E. A. Armour (New York: Plenum, 1988), p 251
2) T. S. Stein, Scattering of Positrons and Electrons by Alkali
Atoms. Invited paper given at the Workshop (1989, this
Proceedings).
3) T. T. Gien, Phys. Repts. 160, 123-87 (1988)
4) T. T. Gien, Chem. Phys. Lett. 127, 253 (1986)
5) T. T. Gien, J. Phys. B: At. Mol. Opt. Phys. 2__2_,L129 (1989);
J. Phys. B: At. Mol. Phys. 222 (1989, Letter section, in
press)
6) S. J. Ward, M. Hortbatsch, R. P. McEachran and A. D.
Stauffer, J. Phys. B: At. Mol. Phys. _!, L611 (1988).
7) R.P. McEachran, M. Horbatsch, A.D. Stauffer and S.J. Ward,
Positron-Alkali Atom Scattering, Invited paper given at the
Workshop (1989, this Proceedings); see also J. Phys. B: At.
Mol. Phys. 2__22,1845-1861 (1989).
39



Positron collisions with alkali-metal atoms

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