On the absorption of light by crystals

P = ve-w>kT,
where v is of th e order of th e atom ic frequency, 1013 sec.-1.
(б) The electron an d positive hole m ay recom bine, w ith th e emission of 
radiation; we denote th e p ro b ab ility th a t this occurs per tim e dt by Adt; A  
will be of th e same order as for an atom , nam ely, ab o u t 108 sec.-1, and will be 
approxim ately independent of tem p eratu re. I f process (b) happens w ith 
appreciable probability, th e crystal will show luminescence. The frequency 
of th e re-em itted rad iatio n will in general be less th a n th a t of th e absorbed 
radiation, because, as pointed ou t by F renkel (1936) and others, th e atom s 
move into new positions of equilibrium a fter th e absorption act, an d some 
energy is dissipated as heat. This is discussed below.
(c) The electron and positive hole m ay recom bine, giving up th eir energy 
in the form of heat. This process has been investigated from th e theoretical 
point of view in a num ber of papers (Peierls 1932; Frenkel 1936). No 
estim ate has, however, been m ade of th e p robability of this process and of 
its variation w ith tem perature. We shall therefore give a discussion of this 
for halide crystals, following a scheme for th e excited levels due to Seitz
( 1 9 3 8 ) .
W hen a halide crystal absorbs a q u an tu m of radiation, th e electron is 
removed from a halogen ion into an “ o r b it” in which it revolves round th e 
“ hole” so formed.*
Suppose now th a t either before or after th e absorption a ct we displace the 
ion or atom of th e halogen a distance d in any direction and plot in fig. 1 the 
energies of the norm al and excited states of th e crystal as a function of d. 
Clearly it will require more energy to displace the large halogen negative
* Various authors (de Boer 1935; H ilsch and Pohl 1931; von H ippel 1936) have