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Semiconductor valence holes are known to have heavy and light effectivemasses; but the consequence of this mass difference on Coulomb scatterings hasbeen considered intractable and thus ignored up to now. The reason is that theheavy/light index is quantized along the hole momentum that changes in aCoulomb scattering; so, a heavy hole can turn light, depending on thescattering angle. This mass change has never been taken into account inmany-body problems, and a single ``average'' hole mass has been used instead.In order to study the missed consequences of this crude approximation, thefirst necessary step is to determine the Coulomb scatterings with valence holesin a precise way. We here derive these scatterings from scratch, starting fromthe threefold valence-electron spatial level, all the way through thespin-orbit splitting, the Kohn-Luttinger effective Hamiltonian, its sphericalapproximation, and the phase factors that appear when turning from valenceelectron to hole operators, that is, all the points of semiconductor physicsthat render valence holes so different from a na\"{i}ve positive charge.

Exploring the change of semiconductor hole mass under Coulomb scattering