8
H. Bichsel and H. Schindler
The dimensionless quantity
f n =
2mc 2
3 ( ¯
hc)
2
E n ||n|
Z
j =1
r i |0
2 ,
(2.3)
with the sum extending over the electrons in the target atom, is known as the dipole
oscillator strength (DOS). Similarly, transitions to the continuum are characterised
by the dipole oscillator strength density df/dE, and the photoionisation cross
section σ γ (E) is given by
σ γ (E) =
2π 2 α ( ¯
hc)
2
mc 2
df (E)
dE
.
(2.4)
The dipole oscillator strength satisfies the Thomas-Reiche-Kuhn (TRK) sum rule,
n
f n +
dE
df (E)
dE
= Z.
(2.5)
For most gases, the contribution of excited states (
f n ) to the TRK sum rule is a
few percent of the total, e.g. ∼5% for argon and ∼7% for methane [25, 26].
As can be seen from Fig. 2.2, the photoabsorption cross section reflects the
atomic shell structure. Evaluated atomic and molecular photoabsorption cross
10
4
10
3
10
2
10
–4
10
–3
10
–2
10
2
10
–1
E [eV]
1
10
σ
γ [Mb]
Ar
Ne
Fig. 2.2 Photoabsorption cross sections of argon (solid curve) and neon (dashed curve) as a
function of the photon energy E [25, 26]