2 A Be ME te a
Be
211
TABLE 75.
Aromic Form Factor, INCOHERENT ScaTTERING
Function, anp Evnastie ELECTRON SCATTERING FACTOR OF
Li-, Compurep rrom THE 53-TERM
Weiss Wave Fouxcrion’)
(Kap)?
F(R)
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
1.998511)
1.99703D
1.99555)
1.994061
1.99258D
1.99111D
1,98963D
1.98816D
1.98668D
0.10
0.20
0.30
0. 40
0.50
0.60
0.70
0.80
0.90
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
100.00
|
2Siac(K)
[3 — F{A)j/(Kas)?
00
00
00
00
00
00
00
00
00
2.857381)-03
5.70916 D-08
8.55538 1-03
1. 13960D -02
1.423111 -02
1.706071) -02
1.988481)-02
2.27034D-02
2.551641 -02
1.001491D 02
5.01486D 01
3.34818D O1
2.514841) O1
2.01483) 01
1.68149) 01
1.44339D 01
1.26481D OL
1.12591D 01
1.98521D
1.97060D
1.95615D
1.94188D
1.92777D
1.91382D
1,90003D
1.88640D
1.87293D
00
00
00
00
00
00
00
00
00
2. 83240D -02
5.610201 -02
8.33466 D -02
1.100711D-01
1.36288D-01
1.620101 -Of
1.87248D4A)1 |
2.12014D-01
2.36319D-01 |
1.01479D
5.147011)
3.47949D
2.64530])
2.14446D
1.81030D
1.57138)
1.39199D
1.25230D
1.85961D
1.73480D
1.62191D
1.52069D
1.42914D
1.34605D
1.27037D
1.20122D
1.13784D
00
00
00
00
00
00
00
00
00
2.60174D-01
4.761561) -01
6.570741 -01
8.09871D-01
9,398911)-01
1.05129D 00
1.14735D 00
1. 23065D 00
1.30329D 00
1.140391) 00
6.328521) -01
4.59363D-01
3.69829 1)-01
3.14171D-01
2.75658 D-01
2.470901 -01
2.248481 -01
2.06907D -01
1.07959D 00
6.86344D-01
4.78842D-01
3.54802) -01
2.74256D-01
2.18770D-01
1.78812D-01
1.49023D -01
1.26190D-01
1.08283D-01
1.36695]
1.720021)
1.8525315
-1.91336D
1.945081)
1.96316D
1.97417D
1.981241
1.98597D
1.989251)
00
00
00
00
00
00
00
00
00
00
tion in Reference 2 by about one third.
O01
00
00
00
00
00
00
00
00
He
As ean be seen from the expectation values of He in
Table 72, the 53-term Weiss wave function for He is,
for all practical purposes, as good as the 1078-term
Pekeris wave function.”
The data in Table 74 agree very well (-~0.1% or
better) with those (see Tables I-III of Reference 1)
computed from the 20-term Hylleraas wave function by
Hart and Herzberg.” The reliability of the data in
Table 74 is expected to be of the order of 0.1%. The
integrals (Table 76) from the Weiss wave function are
only slightly
Reference 3.
different
from
the
values
used
in
Lim
The Li” ion is more hydrogenic than H” and He,
and one expects F(K) and Sin.(K) of Li® to be less
sensitive to the choice of wave functions. The 53-term
Weiss wave function for Li” is, as can be seen from
Table 72, almost as precise as the 444-term wave func-
tion by Pekeris,“” and the data in Table 75 are expected
to be correspondingly accurate. The values of F(K)
TABLE 76. Vaxuues or J, anp J. > CompcuTrep
FROM VaRIOovus Wave FUNCTIONS
=
A
The 39-term Weiss wave function for H” is somewhat
less accurate than the 444-term Pekeris wave function’, judging from the expectation values (Table 72),
and the reliability of the data in Table 73 is expected
to be of the order of 1%.
SotSEITENtt Sey se eee a
results in a zero-minimumin do. For H7, however,
the minimum occursin the forward direction where the
Born approximation may not be applicable because of
the large polarization effect when the incident electron
energy is moderate. The present values of J, und Je
confirm the extrapolated value of J, — J». used in Reference 2. The present result also agrees very well with
slightly more accurate values of the integrals computed
by Rotenberg and Stein.The newresult reduces the
uncertainty of the total inelastic-seattering cross sec-
1,920411D-01
1. 156831)-01
8.40386 D-02
6.61299D -02
5.45149) -02
4.635381) -02
4.03027 1) -02
3.56372D -02
3. 19312D-02
2.891721 -02
(2) See Eqs. (1)-(3) of text for definitions.
) FORTRAN notation is used, ie., 1.08283D-01
1.08283 = 1071.
ture in f.i(A} of H™ is the node near (Ka,)” = 0.6. In
the Born approximation, this type of node should be
present in foi(K) of all negative ions, and the node
The data in Table 73 agree well (~1% or better)
with those presented in Appendix I of Reference 2,
which were computed from the 20-term Hylleraas wave
function by Hart and Herzberg.’ An interesting fea-
H-
f,
[;
Present work
From 20-term Hylleraas® ®)
1.787
He
Lit
1.0811
0.6549
0.0269
1.788 1.0811 ;
Present wark
12.386
0.1850
From 20-term Hylleraas
11.153
0.1849
—10.598
0.8961
I, — Ts
Present work
From 20-term Hylleraas
Extrapolation’ ®
Rotenberg and Stein‘?
—9.365 0.8962
—10.5
| 0.8962
— 10.665
() Defined by Eqs. (18) and (19) of Reference 3.
0.6280
|