Stellar weak rates of the $rp$-process waiting points: Effects of strong magnetic fields

Incorporating microscopic nuclear-structure information into the discussion of bulk properties of astronomical objects such as neutron stars has always been a challenging issue in interdisciplinary nuclear astrophysics. Using the $rp$-process nucleosynthesis as an example, we studied the effective stellar $\beta^+$ and electron capture (EC) rates of eight waiting-point (WP) nuclei with realistic stellar conditions and presence of strong magnetic fields. The relevant nuclear transition strengths are provided by the projected shell model. We have found that, on average, due to the magnetic field effect, the $\beta^+$ and EC rates can increase by more than an order of magnitude for all combinations of density and temperature, as well as in each of WPs studied. We relate the onset field strength, at which the weak rates begin to increase, to nuclear structure quantities, $Q$ value or electronic chemical potential $\mu_e$. The enhanced weak rates may change considerably the lifetime of WPs, thereby modifying the current understanding of the $rp$-process.