Up: Electron impact excitation of
The formulas for computing the generalized oscillator strengths (GOS)
are based on the first Born approximation and the LSCoupling scheme,
and may be found in earlier work by the present author
([Ganas 1998]). The following notation appears in the subsequent
discussion. The quantity x = K^{2}a_{0}^{2}, where K is the momentum
tranfer. Also where W is the excitation energy in eV and
R is the Rydberg energy. The quantity .
Plots of the GOS are shown in Fig. 1. As increases, the GOS for
the transitions 3p  ns decrease in oscillatory fashion, while the GOS
for 3p  nd decrease monotonically. The GOS for 3p  np also decrease
monotonically, but pass through a maximum first.

Figure 1:
GOS for 3p  ns, 3p  np, 3p  nd transitions in Si I as
functions of reduced square of momentum transfer. The curves are the
result of the present work. The solid dots, open circles,
and triangles are representative fits
using Eqs. (2) and (3). Values of the GOS below 10^{5} have been
multiplied by 10^{5} 
The calculation of cross sections can be facilitated by parametrizing
the GOS with simple analytic forms:
 
(2) 
 
(3) 
The quantities A, , , in Eqs. (2) and (3) are
adjustable parameters which are varied so as to obtain the best fit
to the numerically generated GOS. The quantity A in Eq. (2) is the
oscillator strength, which is the limit of the GOS as
. When using Eq. (2), A is set equal to the value
of the oscillator strength, and threeparameter fits are
obtained. Fourparameter fits are obtained when using Eq. (3). The
values of the four parameters which yield the best fits are given in
Table 1. Sample fits are shown in Fig. 1. Equations (2) and (3) actually
only reproduce the GOS when it is significantly large.
Table 1:
Values of the dimensionless parameters
A, , , in Eqs. (2) and (3)


Figure 2:
Integrated cross sections for 3p  ns, 3p  np, and 3p  nd
excitations in Si I versus electron impact energy 
Up: Electron impact excitation of
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