Hartree-Fock calculations of the ratio of bound-state to continuumbetadecay of187Re, the chronometric partner of187Os

Since the β decay of ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$ is first-forbidden unique, the ratio ρ of bound-state to continuum β decay of ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$ reduces to a problem in atomic physics. A knowledge of ρ is required if one is to connect the experimentally determined value of the rate of continuum decay to a value of the half-life $T_{1/2}$ for the β decay of ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$. The value of $T_{1/2}$ plays a significant role in the use of the geochemically determined ratio of ${}_{}{}^{187}{}_{}{}^{}\mathrm{Os}$ to ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$ in the estimation of the age of our galaxy. Our results for ρ, based on the Hartree-Fock-Dirac single-configuration and the multiconfiguration Dirac-Fock approximations strengthen the conclusion of Williams, Fowler, and Koonin [Astrophys. J. 281, 363 (1984)] based on a modified Thomas-Fermi model, that ρ is only of the order of 1%. We also include a few values of the rate for a process first considered by Perrone [Ph.D. thesis, Rice University (1971)], the bound-state β decay of a bare ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$ nucleus. (Since the mass of the ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$ nucleus is less than the sum of the masses of its daughter nucleus ${}_{}{}^{187}{}_{}{}^{}\mathrm{Os}$ and of an electron, continuum decay of a bare ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$ nucleus is forbidden; neutral ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$ can β decay only because of the greater binding energy of the electrons of ${}_{}{}^{187}{}_{}{}^{}\mathrm{Os}$ than of ${}_{}{}^{187}{}_{}{}^{}$Re.)