Shell-model studies of the astrophysicalrpreaction29P(p,γ)30S

Abstract

We present results for levels in ${}^{30}$S (the mirror nucleus of ${}^{30}$Si) that are used for the ${}^{29}$P($p$,$\ensuremath{\gamma}$) $rp$ reaction rate calculations. The resonance energies used in the reaction rate calculations are based on recent measurements which extend the excitation energy spectrum. The levels are checked against results from the isobaric mass multiplet equation and the binding energies of the $T=1$ analog states. Where the analog states are not known the levels are calculated with two-body interactions that use the $sd$-shell interactions USDA and USDB as the charge-independent parts, with a Coulomb, charge-dependent, and charge-asymmetric Hamiltonian added. The $\ensuremath{\gamma}$-decay lifetimes and ${}^{29}$P to ${}^{30}$S spectroscopic factors are also calculated with the same interactions, and together with experimental information on the levels of excited states are used to determine the ${}^{29}$P($p$,$\ensuremath{\gamma}$)${}^{30}$S reaction rates.