First-Forbidden Matrix Elements inβDecay

Abstract

An assumed form for the linear combination in $\ensuremath{\beta}$ decay ($S\ensuremath{-}T+{\ensuremath{\lambda}}_{P}P$), is used as a tool to explore the features of nuclear structure revealed by first-forbidden matrix elements. The assumptions made are sufficient to account for the observed fact that most first-forbidden transitions have $log\mathrm{ft}$ values centering around 6.5, 7.5, and 8.5, according as $\ensuremath{\Delta}I=0, 1, or 2$. The squared matrix elements are reduced by an order of magnitude (i) when configuration mixing occurs, as in the usual, "unfavored" transitions, in contrast to the "favored" transitions around $A=208$; (ii) when the single-particle spin change $\ensuremath{\Delta}j$ predicted by the shell model exceeds the nuclear spin change $\ensuremath{\Delta}I$. From (i) and (ii) it is concluded that the elementary form of the shell model specifies individual particle orbitals with good accuracy but that configuration mixing is also of major importance, although it is not encompassed by the simple shell model. The ${2}^{\ensuremath{-}}$\ensuremath{\rightarrow}${2}^{+}$ transitions can be classified under (ii); their apparently straight spectra should average on the order of 10 percent $\ensuremath{\alpha}$ type. The only consistent interpretation of the RaE decay is as a ${1}^{\ensuremath{-}}$\ensuremath{\rightarrow}${0}^{+}$ transition; it is possible to predict that this kind of spectrum is unlikely to occur at any other mass number $A$. Evidence for the presence of the pseudoscalar interaction $P$ in the linear combination is then provided by the low $\mathrm{ft}$ values of $\ensuremath{\Delta}I=0$ transitions.