Geoscience Reference

In-Depth Information

method applicable to high-energy electrons was proposed by Lisitsa and Savel'ev

(
1987
). The scope of that study was limited by the condition (5). The theory

was extended to
1 and f
1 by Klinskikh and Rapoport (
1987
), where

a general expression was obtained for the
n
-photon differential cross section. In

the alternative approach to the same problem used by Golovinskii (
1988
), the

semiclassical wavefunction was found for an electron scattered by the finite-

range potential in an electromagnetic field. Moreover, the resulting expression for

the potential scattering cross section allows transitions to the limit of the Born

approximation and the case of classical scattering.

It should be noted here that the phenomena described by the time-independent

theory of radiative collisions developed in several studies (Ivanov et al.
1988
,

1995
,
1997b
,
c
,
1999
; Vartazaryan et al.
1989
; Golubkov et al.
1993
,
1999a
,
b
;

Golubkov and Ivanov
1993
,
1994
,
1997
) occur in the near-threshold energy region

of
E
p
! (! is the oscillation frequency of the molecular ion), where the Born

approximation and semiclassical description are strongly inapplicable. According

to (5), the electron quiver amplitude satisfies the relationship

f

!
f

e
n
2
;

a
f
Š

(2.10)

where the electron wavelength
e
is comparable with the dimensions of the Rydberg

XY
** complex. Because of the multichannel Rydberg electron dynamics, electron

energy is not conserved during the complex formation stage. The ponderomotive

energy (cycle-averaged quiver energy) of the slow electron in a laser focal region

is E
D h
f
i

2
.
4!
f
(Collins and Csanak
1991
). If the energy and momentum

of the incident electron are E
p
E, p
e
p
h
f
i
ı
!
f
, and the transit time

L
f
=p through a beam with size L
f
is much longer than the laser pulse duration

l
, then the limitation on the field strength becomes

h
f
i
L
f
!
f
=
l
:

(2.11)

The conditions depicted by Eqs.
2.6
,
2.7
,
2.8
,
2.9
,
2.10
,and
2.11
allow

ignoring the ponderomotive interaction, which would be significant for relatively

fast electrons (Kibble
1966
; Corkum et al.
1989
,
1992
;Reiss
1990
; Salamin and

Faisal
1997
; Salamin
1997
). Indeed, as a result of the analytical properties of

the Coulomb wave functions, the corresponding ponderomotive contributions to

matrix elements, resulting from the electric field inhomogeneity across the laser

focal region, are independent of
E
p
and the scattering channel characteristics. The

resulting general shift of all energy levels in the “electron
C
molecular ion” system

can easily be eliminated by introducing a phase factor. For example, in the case of

a typical laboratory laser with !
f
10
1
, L
f
10
8
,and
l
10
7
, it takes place

when the incident electron energy and the average field strength are E
p

10
1
,

and
h
f
i
1, respectively.