Hello everyone,
I am trying to reproduce the calculations from an old article by J.J. Hopfield (J. Phys. Chem. Solids, vol.10, pp.110-119 (1959) - A theory of edge emission phenomena in CdS, ZnS and ZnO -attached here). In the fourth section "The systematics of edge emission", he starts to calculate the probabilities of photon emission with the simultaneous emission of n phonons.
Here he employs an approximation for the thermal spread of the hole in k-space, which I assume comes from the Heisenberg uncertainty principle: k0=(kBT*m/2hbar^2)^1/2, where the spread in real space is given by the fundamental length scale for a polaron r=(hbar/2m*omega)^1/2, and using kBT instead of hbar*omega.
Later, after stating that W1, the transition probability with the emission of 1 phonon is simply W0 multiplied by the Huang-Rhys factor (sum|f(q)|^2, for q smaller than the thermal spread of the hole), there is another approximation which I cannot understand no matter how much I think about it: W1=W0*N(kBT/hbar*omega)^1/2, using a certain approximation for f(q) (which I also don't understand).
To me, it looks as if the sum over |f(q)|^2 is approximated as N(kBT/hbar*omega)^1/2, and I simply can't figure out how that happens.
If anyone has some insight into these approximations, it would help me immensely. Thank you!
Claudiu
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