Unblocking of the Gamow-Teller strength in stellar electron capture on neutron-rich Germanium isotopes

We propose a new model to calculate stellar electron capture rates for neutron-rich nuclei. These nuclei are encountered in the core-collapse of a massive star. Using the Shell Model Monte Carlo approach, we first calculate the finite temperature occupation numbers in the parent nucleus. We then use these occupation numbers as a starting point for calculations using the random phase approximation. Using the RPA approach, we calculate electron capture rates including both allowed and forbidden transitions. Such a hybrid model is particularly useful for nuclei with proton numbers Z<40 and neutron numbers N>40, where allowed Gamow-Teller transitions are only possible due to configuration mixing by the residual interaction and by thermal unblocking of $pf$-shell single-particle states. Using the even germanium isotopes Ge-68 to Ge-76 as examples, we demonstrate that the configuration mixing is strong enough to unblock the Gamow-Teller transitions at all temperatures relevant to core-collapse supernovae.