Atomic Effect on β-Decay

Factors leading to the dependence of the β-decay half-life on the atomic electron environment are discussed. An expression for the rate of allowed β-decay of a nucleus embedded in a multielectron atom having an arbitrary electronic configuration is derived. This is then used to obtain a new expression for the ratio of decay constants for bound and continuum decays from a general electron state. This expression fully incorporates exchange of the β-electron with the other bound electrons. It also includes the inhibition of the decay rate, which originates from the total or partial occupation of orbitals by electrons in the initial state. Specific expressions are presented for bound-state decay of an initial-state atomic system having open or closed s-shell configurations. The magnitudes of chemical effects on low-energy β-decays are demonstrated by calculations on ¹⁰⁶Ru. This isotope appears to represent a particularly favourable case for experimental study of chemical effects. Two main chemical effects are found. One arises from the change in bound-state decays, which, although they constitute a small fraction (less than 1%) of total decays, are very sensitive to chemical effects. The other factor arises from the effect on continuum decays of chemically induced changes in the end-point energy. For ¹⁰⁶Ru both effects lead to changes of order 0.1% in the total decay half-life when the ionicity is changed by one unit. However, both effects tend to partially cancel one another, with the result that the net difference in half-life is in the range 0.01-0.1%.