Thermal X-ray radiation (PDF) - SRON

3.6.7 Photoionisation
Figure 3.20: Photoionisation cross section in barn (10 −28 m −2 ) for Fei (left) and
Fexvi (right). The p and d states (dashed and dotted) have two lines each because
of splitting into two sublevels with different j.
This process is very similar to direct ionisation. The difference is that in the case
of photoionisation a photon instead of an electron is causing the ionisation. Further,
the effective cross section is in general different from that for direct ionisation. As
an example Fig. 3.20 shows the cross section for neutral iron and Na-like iron. It
is evident that for the more highly ionised iron the so-called ”edges” (ionisation
potentials) are found at higher energies than for neutral iron. Contrary to the case
of direct ionisation, the cross section at threshold for photoionisation is not zero. The
effective cross section just above the edges sometimes changes rapidly (the so-called
Cooper minima and maxima).
Contrary to the direct ionisation, all the inner shells have now the largest cross
section. For the K-shell one can approximate for E > I
σ(E) ≃ σ 0 (I/E) 3 (3.41)
where as before I is the edge energy. For a given ionising spectrum F(E) (photons
per unit volume per unit energy) the total number of photoionsations follows as
C PI = c
For hydrogenlike ions one can write:
∫ ∞
0
n i σ(E)F(E)dE. (3.42)
σ PI = 64πng(E, n)αa2 0
3 √ 3Z 2 ( I E )3 , (3.43)
where n is the principal quantum number, α the fine structure constant and A 0 the
Bohr radius. The gaunt factor g(E, n) is of order unity and varies only slowly. It
has been calculated and tabulated by Karzas & Latter (1961). The above equation
is also applicable to excited states of the atom, and is a good approximation for all
excited atoms or ions where n is larger than the corresponding value for the valence
electron.
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