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207
INELASTIC-SCATTERING CROSS SECTIONS OF
FAST CHARGED PARTICLES BY Li *
Y.-K. Kim and Mitio Tnokutt
TABLE 70. Paramerers ror tir BETHE
Cross SECTIONS oF Lit
The eross sections for some important discrete excitations
and for the total inelastic scattering of fast charged particles
by Lit are evaluated directly from correlated wave functions
and other data in the literature according to the Bethe procedure and related sum rules. Cross sections for other discrete excitations are determined by extrapolating their dependence on the effective quantum numbers, The ionization
cross section is then obiained by subtracting the sum ofall
discrete excitation cross sections from the total inelastic
scattering cross section, thus avoiding the direct use of any
continuum wave functions. The resulting ionization cross
section is reliable, and agrees very well with the experiment
by Peart and Dolder.
The total inelastic-scattering cross section ot for
sufficiently fast charged particles of charge ze and
.
se
1, 2)
velocity v is given by‘
_ a| 4 Cos) a)
Stor = Sais (Mn jin (#,)
where dp is the Bohr radius, m the electron mass, R the
Rydberg energy, and 8 = v/c, c being the speed oflight.
The constants Mio. and Ciot can be evaluated from the
ground-state wave function and the optical (dipole)
oscillator strength distribution of the target system.”
The ground-state wave function of Li” computed by
Weiss” leads to Jfj.1 = 0.2860, in complete agreement
with a more accurate result of Pekeris.“’ The value
ZT, — I, = 0.6280 (in the notation of Reference 2) obtained from the Weiss wave function should, therefore,
be very reliable. Furthermore, a value of £(--1)
0.526 + 0.015 [see Reference 2 for the definition of
L(~1)] was adopted on the basis of the oscillatorstrength distribution in the literature.” The value of
Cor = —2L(-1) th -ht+ Mice In (2me"/R) is
given in Table 70.
The Bethe cross sections for discrete excitations are
also given by”
In
=
Cc
Total
0.2860
2.787
Discrete excitation
0.1414
1.224
Tonization
0. 1446
1.563
ean be calculated from wave functions directly (sce
Sec. 5 of Reference 8).
Weiss” calculated for Lit very accurate wave func-
tions not only for the ground state but also for the 2’S,
2'P, 3'S, 3'P and 3'D states, and Perkins” computed
correlated wave functions for the 4.5, 5S, 64S and 7148
states with similar accuracy. From these wave functions one can evaluate accurate Bethe cross sections for
the excitations to the above-mentioned discrete states
and eventually to higher discrete states by extrapola-
tion.
The values of Jf;,, C,, and b, are listed in Table 71.
The sum ofall discrete (single) excitation cross sections
Sexe CaN be expressed in the form similar to Eq. (1) with
two constants M2,, and Coxe. These constants are
defined as
(4)
IM. = > (discrete) AZ%, ,
and
(5)
Coxe => (diserete) [Ci + 5,],
respectively. The results thus obtained are given in
Table 70.
Once the values of Af’ and C are knownfor oto: and
Fexe, Ole can evaluate the “‘counting” ionization cross
section gion by subtraction:
Fion = Ttot —
Tex G
_ Srapz"
a
2
| “+
mv/R {Ata In (43) — 8
Srazz"
mit/R iat |s (*,) — | ++ Cs) (2)
for an (optically) allowed transition, and
22
CG,
=
Sraoz
mv/R
Dn
(3)
for a forbidden transition. The constants 177,,C,, and 6,
* Principal results of this work presented at the VIth International Conference on the Physies of Electronic and Atomic
Collisions (VI ICPEAC), Cambridge, Massachusetts, July
28-Aug. 2, 1969.
MW
,
Cu .
(6)
This method leads to an accurate ionization cross section without calculating the continuum wave functions
directly. The same method was applied successfully to
Heas explained elsewhere in this report."” The values
of Mion and Cion are listed in Table 70.
The uncertainty in gexe is about the same as that in
Stot-| When appropriate values of the constants are
substituted, one gets
t The generalized oscillator strengths of Lit computed from
the Weiss and Perkins wave functions in the length andvelocity
formulas agree with each other within 1%or better.
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