Deviations from theΔT=0Isotopic Spin Selection Rule in Fermi Transitions

Abstract

Experimental deviations from the $\ensuremath{\Delta}T=0$ isotopic spin selection rule have been observed experimentally in $J\ensuremath{\rightarrow}J$ beta transitions. In the theory of a vector interaction with a conserved current these deviations have to be explained only in terms of isotopic spin impurities, while in the conventional theory exchange mesonic currents may also induce Fermi transitions with $\ensuremath{\Delta}T\ensuremath{\ne}0$. In this paper an attempt is made to estimate the contribution of the isotopic spin impurities arising from the Coulomb interaction between the protons. The $j\ensuremath{-}j$ coupling shell model is used to calculate the relevant Coulomb matrix elements. When all the nucleons outside the core are in the same orbit the main contribution comes from the Coulomb interaction between the protons outside the core. A comparison between the empirical Fermi matrix element ${M}_{\mathrm{F}}$ and the calculated one is performed in the case of ${\mathrm{Mn}}^{52}$, ${\mathrm{Sc}}^{44}$, and ${\mathrm{Na}}^{24}$. The two quantities agree fairly well for the manganese-52. No such an agreement is found in the two other cases; the predicted ${M}_{\mathrm{F}}$ being too large for the sodium-24, too small for the scandium-44 at least by a factor ten. This discrepancy may reflect the inadequacy of the $j\ensuremath{-}j$ shell model to describe the Coulomb effects or the presence of mesonic effects. More experiments are needed to make a choice between these two possibilities.