Thermal X-ray radiation (PDF) - SRON

3.6.2 Collisional de-excitation
A collision between an ion and a free electron can either bring an electron into a
higher orbit or into a lower orbit. When a bound electron ends up in a lower energy
orbit, the process is called collisional de-excitation. Of course, de-excitation can
only occur when the ion is already in an excited state. Therefore, de-excitation is
in practice important only for high density plasmas, where due to collisions higher
levels are populated, or for so-called metastable levels (levels that have only a small
probability to decay radiatively to a lower level).
The rate coefficient S ′ ji of de-excitation j → i is related to S ij, the rate coefficient
of the inverse excitation process i → j. The relation can be derived from the
principles of detailed balance, and is given by:
S ′ ji = w i
w j
e E ij/kT Sij . (3.17)
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