Shell-model studies of the astrophysical mirror rp-reactions $^{34}$S (p,y) $^{35}$ C1 and $^{34g,m}$ C1(py)$^{35}Ar

The two mirror rp-reactions $^{34}$S (p,y) $^{35}$ C1 and $^{34g,m}$ C1(py)$^{35}$Ar were studied via a shell-model approach. At energies in the resonance region near the proton- emission threshold many negative-parity states appear. We present results of calculations in a full (0+1)hω model space which addresses this problem. Energies, spectroscopic factors and proton-decay widths are calculated for input into the reaction rates. Comparisons are also made with a recent experimental determination of the reaction rate for the first reaction. The thermonuclear $^{34g,m}$C1(py)$^{35}$Ar reaction rates are unknown because of a lack of experimental data. The rates for transitions from the ground state of $^{34}$C1 as well as from the isomeric first excited state of $^{34}$C1 are explicitly calculated taking into account the relative populations of the two states.