  Semiconductor excitons are commonly seen as hydrogen atom. This analogy
requires a unique hole mass. In reality, this is not so due to the complexity
of the semiconductor band structure. The precise consequences on the exciton
physics of the Coulomb coupling between heavy and light holes remain a tricky
open problem. Through an ``optimized perturbative'' approach that uses excitons
with a flexible hole mass as a basis, we show that for zero exciton wave
vector, the heavy-light hole mass difference does not split the $(2\times4)$
exciton degeneracy in zinc-blende-like semiconductors, the hole mass for
binding energy being close to the average mass inverse. By contrast, for
nonzero exciton wave vector, that physically breaks the crystal symmetry, the
exciton degeneracy splits into two branches quantized along the exciton wave
vector, with nontrivial center-of-mass dependence not only on the heavy and
light hole masses, but also on the electron mass.
