Impact of ${}^{68}\mathrm{Se}$ and ${}^{72}\mathrm{Kr}$ stellar weak interaction rates on $rp$-process nucleosynthesis and energetics

The impact of beyond-mean-field predictions of stellar weak interaction rates of ${}^{68}\mathrm{Se}$ and ${}^{72}\mathrm{Kr}$ waiting point nuclei on the $rp$-process in type-I x-ray bursts is investigated including the contribution of thermally populated low-lying states for both ${\beta }^{+}$ decay and continuum electron capture. The realistic description of the effects of shape coexistence and mixing in the structure of parent and daughter nuclei on the stellar weak rates is obtained within the complex excited Vampir model. We performed a series of post-processing calculations revealing significant effects on the energy generation, reaction flow, and final composition of the burst ashes.

Figure 1

The complex excited Vampir decay rates (${\mathrm{s}}^{-1}$) for the ground state and yrast $2^{+}$ state of ${}^{68}\mathrm{Se}$ (left) and the ground state, first excited $0^{+}$ state, and yrast $2^{+}$ state of ${}^{72}\mathrm{Kr}$ (right) decomposed into the corresponding ${\beta }^{+}$ and cEC components for selected densities $\rho Y_e$ ($\mathrm{mol}/{\mathrm{cm}}^3$) as a function of temperature T (GK).

Figure 2

The evolution of complex excited Vampir cEC rates of ${}^{68}\mathrm{Se}$ as a function of temperature $T$ (GK) and density $\rho Y_e$ ($\mathrm{mol}/{\mathrm{cm}}^3$).

Figure 3

${}^{68}\mathrm{Se}$ weak decay flow (computed as the total ${}^{68}\mathrm{Se}$ weak decay rate times the abundance of ${}^{68}\mathrm{Se}$ per nucleon) as a function of time during an x-ray burst obtained using the ${}^{68}\mathrm{Se}$ EXVAM weak interaction rates (dotted-dashed line) compared to that based on standard rates (full line) for hhez1 conditions.

Figure 4

The abundances of hydrogen and helium as a function of time during an x-ray burst obtained using the ${}^{68}\mathrm{Se}$ and ${}^{72}\mathrm{Kr}$ EXVAM weak interaction rates (dotted line) compared to that based on standard rates (full line) (left - hhez1, right - hhez3 composition).

Figure 5

Energy generation rate curve as a function of time during an x-ray burst obtained using the ${}^{68}\mathrm{Se}$ and ${}^{72}\mathrm{Kr}$ EXVAM weak interaction rates (dotted-dashed line) compared to that based on standard rates (full line) (left - hhez2, right - hhez3 composition).

Figure 6

Integrated reaction currents above Ge during an x-ray burst ($\approx 210$ s from the ignition) for the hhez1 composition [2] using the EXVAM results for the temperature dependence of ${\beta }^{+}$-decay and temperature and density variation of cEC rates for ${}^{68}\mathrm{Se}$ and ${}^{72}\mathrm{Kr}$ (see text for details). In the online version stable nuclei are yellow while in the print version are grey.

Figure 7

The evolution of waiting point nuclei and ${}^{103–106}\mathrm{Sn}$ isotope abundances using the EXVAM weak rates (dotted-dashed lines) are compared to the results obtained using standard values (full lines) (hhez1 composition [2]).

Figure 8

The abundances of waiting point nuclei and Sn isotopes as a function of time during an x-ray burst obtained using the ${}^{68}\mathrm{Se}$ and ${}^{72}\mathrm{Kr}$ EXVAM weak interaction rates (dotted-dashed line) compared to that based on standard rates (full line) (left - hhez2; right - hhez3 composition).