Thermal equilibration ofLu176viaKmixing

Abstract

In astrophysical environments, the long-lived (${T}_{1/2}=37.6$ Gyr) ground state of $^{176}\mathrm{Lu}$ can communicate with a short-lived (${T}_{1/2}=3.664$ h) isomeric level through thermal excitations. Thus, the lifetime of $^{176}\mathrm{Lu}$ in an astrophysical environment can be quite different than in the laboratory. We examine the possibility that the rate of equilibration can be enhanced via $K$ mixing of two levels near ${E}_{x}=725$ keV and estimate the relevant $\ensuremath{\gamma}$-decay rates. We use this result to illustrate the effect of $K$ mixing on the effective stellar half-life. We also present a network calculation that includes the equilibrating transitions allowed by $K$ mixing. Even a small amount of $K$ mixing will decrease the timescale for equilibration during an $s$-process triggered by the $^{22}\mathrm{Ne}$ neutron source.