  Weak decay rates under stellar density and temperature conditions holding at
the rapid proton capture process are studied in neutron-deficient medium-mass
waiting point nuclei extending from Ni up to Sn. Neighboring isotopes to these
waiting point nuclei are also included in the analysis. The nuclear structure
part of the problem is described within a deformed Skyrme Hartree-Fock + BCS +
QRPA approach, which reproduces not only the beta-decay half-lives but also the
available Gamow-Teller strength distributions, measured under terrestrial
conditions. The various sensitivities of the decay rates to both density and
temperature are discussed. In particular, we study the impact of contributions
coming from thermally populated excited states in the parent nucleus, as well
as the competition between beta decays and continuum electron captures.
