Abstract
The photoelectric effect in hydrogen-like atoms has been treated by various authors, and the object of this paper is to co-ordinate the various results and to obtain values of σ, the absorption coefficient, which should be valid for all ranges of
hv
0
, the energy of a quantum of the incident light, and for all values of Z, the atomic number of the atom. To this end we shall develop a method which is applicable in the range not previously examined—where Z is large and
hv
0
~
mc
2
,
m
being the mass of the electron and
c
the velocity of light. The problem may be stated briefly as follows. The nucleus of the atom is a heavy particle and may therefore be regarded as fixed at the origin of co-ordinates. We shall neglect exchange interaction between the atomic electrons, assuming that each K-electron may be treated separately. We may then consider the absorption by a simplified model consisting of a fixed nucleus and one K-electron, so that the results obtained have to be doubled to give the total absorption by the K-shell. The system is then perturbed by a beam of γ-rays travelling along the Z-axis, the perturbing potentials being given by A
y
=
b
0
[
e
2π
iv
0
(
t - z/c
)
+
e
-2π
iv
0
(
t - z/c
)
], A
x
= A
z
= 0, A
0
= 0.
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