0030-400X/00/8803- $20.00 © 2000 MAIK “Nauka/Interperiodica” 0365
Optics and Spectroscopy, Vol. 88, No. 3, 2000, pp. 365–367. Translated from Optika i Spektroskopiya, Vol. 88, No. 3, 2000, pp. 412–414.
Original Russian Text Copyright © 2000 by Khoperskiœ, Yavna, Nadolinskiœ, Timoshevskaya.
INTRODUCTION
In measurements of spectral characteristics of
many-electron systems without the spherical symmetry
in the ground state, which were preliminary oriented
with respect to the polarization vector of the incident
photon, one should expect the manifestation of strong
orientation effects. This general result of the theory of
atomic [1] and molecular [2] spectra is studied in this
paper by the example of the development of a theory
and method for calculating the differential cross section
for anomalous elastic scattering of polarized X-rays by
a free linear molecule oriented in space.
RESULTS AND DISCUSSION
Consider a case when X-rays are linearly polarized
and vectors of the incident and scattered photons are
perpendicular to the scattering plane. The scattering
plane is defined as a plane passing through the wave
vectors of the incident (k
1
) and scattered (k
2
) photons.
We represent the wave function of the |a〉-orbital of a
linear molecule in the form of the nonrelativistic one-
center expansion
(1)
where, (r) and (ϑ, ϕ) are the radial and spheri-
cal parts of the base wave function of the l
1
symmetry
with a fixed value of the projection m
a
of the angular
momentum on the quantization axis OZ (molecular
axis) and r, ϑ and ϕ are spherical coordinates.
The expression for the differential cross section for
elastic scattering of a photon by a many-electron sys-
a |〉
1
r
-- P
al
1
r (29 Y
l
1
m
a
ϑϕ , ( 29 ,
l
1
∑
=
P
al
1
Y
l
1
m
a
tem [3] in the case of a molecule can be reduced to the
form:
(2)
where atomic units are used and r
0
is the classical
radius of an electron.
The analytic expression for the form factor of a lin-
ear molecule
using the expansion of the exponential over spherical
functions of the rank t ≥ 0 (q = –t, …, t) and the rep-
resentation (1), takes the form:
(3)
where, N is the number of electrons in a molecule, r
j
is
the radius vector of the jth electron, |O〉 is the ground
state of the molecule, θ is the scattering angle between
the vectors k
1
and k
2
, Ω is the solid angle, θ
k
is the
angle between the scattering vector k and the axes OZ,
Ò is the speed of light, ϖ is the energy of the scattered
d σ
1
d Ω ∕ r
0
2
F Q
aq
ϖ ( 29
aq ,
∑
+
2
, =
F O i k r
j
⋅ ( 29 { } exp
j 1 =
N
∑
O , =
O | 〉 det a =
C
q
t (29
F i
t
2 t 1 + ( ) al
1
j
t
kr ( ) al
2
〈 〉 C
12
taa
P
t
θ
k
cos ( ),
l
1
l
2
,
∑
t
∑
a
∑
=
al
1
j
t
kr ( 29 al
2
〈 〉 P
al
1
r (29 P
al
2
r (29 j
t
kr ( 29 r , d
0
∞
∫
=
C
12
ta γ
1 – ( 29
l
1
m
a
–
l
1
C
t (29
l
2
( 29
l
1
t l
2
m
a
– qm
γ
, =
k k k
1
k
2
– 2 ϖ c ∕ ( 29 θ 2 ∕ ( 29 , sin = = =
Orientation Effects in Anomalous Elastic Scattering
of Polarized X-rays by a Linear Molecule
A. N. Khoperskiœ, V. A. Yavna, A. M. Nadolinskiœ, and V. V. Timoshevskaya
Rostov University of Communication Means, Rostov-on-Don, 344038, Russia
Received July 13, 1999
Abstract—A strong orientation effect is theoretically predicted in a suggested modified experiment on anoma-
lous elastic scattering of linearly polarized X-rays by free oriented in space HF and HCl molecules near the ion-
ization threshold of the 1σ molecular orbital. The analytic expression for the form factor of a linear molecule is
determined for the case of one-center nonrelativistic representation of the wave functions of molecular orbitals.
© 2000 MAIK “Nauka/Interperiodica”.
MOLECULAR
SPECTROSCOPY