Shell-model studies of the astrophysical $\mathit{rp}$ reaction ${}^{29}$P($p,\gamma$)${}^{30}$S

We present results for levels in ${}^{30}$S (the mirror nucleus of ${}^{30}$Si) that are used for the ${}^{29}$P($p$,$\gamma$) $rp$ 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 $\gamma$-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($p$,$\gamma$)${}^{30}$S reaction rates.

Figure 1

$c$ coefficients from the isobaric mass multiplet equation (IMME: $E=a+b{T}_z+c{T}_z^2$) for states in ${}^{30}$S (in order of increasing experimental energy, as in Table ). The coefficients are experimental (closed circles) and theoretical, calculated from USDB-cdpn (open circles) and USDA-cdpn (crosses).

Figure 2

The total $rp$ reaction rate versus temperature T9 (GigaK) (top panel) and the contribution of each of the final states (lower panel) obtained with the data from Table .

Figure 3

The total $rp$ reaction rates of USDA-cdpn, and USD-cdpn compared to USDB-cdpn for ${}^{30}$S.

Figure 4

The USDB-cdpn present rate divided by the rate given in the 2010 evaluation [15]; solid line for the median rate and the dashed lines for the low and high rates as given in Table B.58 of Ref. [15].