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