The Impact of the New ${}^{65}$As(p,$\gamma$)${}^{66}$Se Reaction Rate on the Two-Proton Sequential Capture of ${}^{64}$Ge, Weak GeAs Cycles, and Type-I X-Ray Bursts such as the Clocked Burster GS 1826$-$24

Abstract

We re-assess ${}^{65}$As(p,$\gamma$)${}^{66}$Se reaction rates based on a set of proton thresholds of ${}^{66}$Se, $S_{\mathrm{p}}$(${}^{66}$Se), estimated from the experimental mirror nuclear masses, theoretical mirror displacement energies, and full $pf$-model space shell-model calculation. The self-consistent relativistic Hartree-Bogoliubov theory is employed to obtain the mirror displacement energies with much reduced uncertainty, and thus reducing the proton-threshold uncertainty up to 161 keV compared to the AME2020 evaluation. Using the simulation instantiated by the one-dimensional multi-zone hydrodynamic code, KEPLER, that closely reproduces the observed GS 1826$-$24 clocked bursts, the present forward and reverse ${}^{65}$As(p,$\gamma$)${}^{66}$Se reaction rates based on a selected $S_{\mathrm{p}}$(${}^{66}$Se) = 2.469$\pm$0.054 MeV, and the latest ${}^{22}$Mg($\alpha$,p)${}^{25}$Al, ${}^{56}$Ni(p,$\gamma$)${}^{57}$Cu(p,$\gamma$)${}^{58}$Zn, ${}^{55}$Ni(p,$\gamma$)${}^{56}$Cu, and ${}^{64}$Ge(p,$\gamma$)${}^{65}$As reaction rates, we find that though the GeAs cycles is weakly established in the rapid-proton capture process path, the ${}^{65}$As(p,$\gamma$)${}^{66}$Se reaction still strongly characterizes the burst tail end due to the two-proton sequential capture on ${}^{64}$Ge, not found by Cyburt et al. (2016) sensitivity study. The ${}^{65}$As(p,$\gamma$)${}^{66}$Se reaction influences the abundances of nuclei $A$ = 64, 68, 72, 76, and 80 up to a factor of 1.4. The new $S_{\mathrm{p}}$(${}^{66}$Se) and the inclusion of the updated ${}^{22}$Mg($\alpha$,p)${}^{25}$Al reaction rate increases the production of ${}^{12}$C up to a factor of $4.5$ that is not observable and could be the main fuel for superburst. The waiting point status of and two-proton sequential capture on ${}^{64}$Ge, weak-cycle feature of GeAs at region heavier than ${}^{64}$Ge, and impact of other possible $S_{\mathrm{p}}$(${}^{66}$Se) are also discussed.

Comments: 25 pages, 19 figures, 3 tables, accepted by The Astrophysical Journal on 10 January 2022