Beta Decay in Stellar Interiors

A study is made of the temperature and density dependence of beta-decay rates as they are affected by electron capture from continuum orbits, the absence of atomic binding energies, screening, and the exclusion principle. The rate of allowed electron capture from continuum orbits in a Fermi gas is calculated using the $V-A$ law; Coulomb corrections are included and nuclear matrix elements occur as parameters that can frequently be determined from terrestrial experiments. There is no atomic binding-energy contribution to the total beta-decay energy for completely ionized atoms and this causes a decrease in decay rates for low-energy electron emitters in stars relative to their terrestrial values. Screening will usually not affect beta-decay rates significantly. The exclusion principle inhibits beta decay in stellar interiors because many of the low-momentum states are occupied prior to the decay; the amount by which a decay rate is decreased can be calculated in terms of the known beta spectrum and the temperature and density of the medium surrounding the radioactive nucleus. Beta decay for some normally radioactive nuclei is almost impossible in the interior of very dense stars, such as white dwarfs, since the Fermi energy can equal or exceed the maximum beta-decay energy available. Some applications to the theory of element formation in stars are suggested.