Poo eb oe oa,
onthe
209
There are four sets of experimental ionization cross
sections of Li’, all measured by crossed beam
methods.“”"These experiments measure the absolute
cross section for single ionization only, but the double
ionization cross section is negligible.* Figure 163 shows
that the theory and experiment agree very well in the
asymptotic region {incident electron energy 25 keV).
A more detailed account of this work is being prepared for publication elsewhere.
The authors would like to express their gratitude to
Dr. A. W. Weiss of the National Bureau of Standards
and to Dr. J. F. Perkins of the Redstone Arsenal for
providing the wave functions. The authors are also
indebted to Dr. K. Dolder of the University of Newcastle upon Tyne for communicating prior to publication the experimental data quoted in References 14
and 15.
*The cross section for double ionization is at least two
orders of magnitude smaller than the single ionization cross
section for the incident electron energy of 2500 eV.“
REFERENCES
1. Bethe, H. Ann. Phystk 6, 325 (1930).
2. Inokuti, M., Kim, ¥.-K., and Platzman, R. L. Phys. Rev.
164, 55 (1967).
3. Weiss, A. W. J. Res. Natl. Bur. Std. TLA, 163 (1967).
4. Pekeris, C. L. Phys. Rev. 126, 143 (1962).
5. Stewart, A. L. and Webb, T. G. Proc. Phys. Soc. (Londen)
82, 532 (1963).
6. Bell, K. L., and Kingston, A. E. Proc. Phys. Soc. (London) 90, 337 (1967).
7. Dalgarno, A, and Parkinson, E. M. Prac. Roy. Soc. (London) A301, 253 (1967).
8. Kim, Y.-K., and Inokuti, M. Phys. Rev. 176, 176 (1968).
9. Perkins, J. F. Phys. Rev. 151, 80 (1966).
10. Inokuti, M., and Kim, Y.-K. Total Cross Sections for
Inelastic Scattering of Charged Particles by Atoms and
Molecules. III. Accurate Bethe Cross Section for Ionization of Helium. This report.
11. Lineberger, W. C., Hooper, J. W., and McDaniel, E. W.
Phys. Rev. 141, 151 (1966).
12. Wareing, J. B., and Dolder, K. T. Proc. Phys. Soc. (London)
91, 887 (1967).
13. Peart, B., and Dolder, K. T. J. Phys. Bi, 872 (1968).
14. Peart, B., and Dolder, K.T. Private communication (1969).
15. Peart, B., and Dolder, K. T. Private communication (1969).
FORM FACTORS OF H-, He, AND Lit
Y.-K. Kim
Atomic form factors and incoherent scattering functions
are necessary in evaluating the cross sections for the coherent
and incoherent scattering of photons as well as those for the
elastic and inelastic scattering of charged particles by atoms
and molecules. Accurate atomic form factors, incoherent
scattering functions, and the Born elastic electron scattering
factors for the ground states of H-, He, and Li* have been
computed from correlated wave functions. The data presented
are in good agreement with those evaluated from less accurate wave functions, and confirm the expectation that the
electron correlation affects the values of incoherent scattering functions more than those of atomic form factors. Values of some integrals which are used in the sum rule for the
Bethe cross sections are also tabulated.
TABLE 72.
2
Pexerts Wave Functions In Atomic Units
.
:
:
1,2
This report is an extension of earlier ones’’” on the
atomic form factors F(K) and incoherent-scattering
functions S;,.(K) of H” and He. Similar data on Li”
are also presented.
The functions F(A) and Sj.,(K) for an atom or ion
with N electrons are defined as
N
F(K) = >. (exp (iK-r;)),
(1)
j=l
and
Sine(K) = N™ Pa (exp [7 -(1; — 1)])
Atom
Property
Total energy
Weiss ‘4
Pekeris(°?
(ri)
Weiss
Pekeris
(rie)
.
Tota. ENERGIES AND EXPECTATION VALUES
oF ri AND 72, COMPUTED FROM THE WEISS AND
Weiss
Pekeris
H-
He
Lit
—0.5277475
—0.5277510
—7.279913
—7.279913
11.928
11.914
—2.903724
—2.903724
,
1.19348
1.19348
25. 239
25. 202
2.51643
2.51644
(2)
0.927065
0.927065
respectively, where () denotes an expectation value in
the ground state, KR the momentum transfer, and 1;
the coordinate vector of the jth electron from the
nucleus. Furthermore, in the Born approximation, the
elastic electron scattering factor fa(K), which is
defined by
fal K) = [24 —- F(K)]/(Kao)’,
\
0. 446279
0. 446279
(3)
where ad) is the Bohr radius, is closely related to the
differential cross section de, for the elastic scattering
of electrons by an atom of nuclear charge Ze. [See