Magnetic Moment ofK40in Intermediate Coupling

Abstract

The ${\mathrm{K}}^{40}$ nucleus is of interest since its spin $I=4$ forms a notable exception to Nordheim's rule while the observed value $\ensuremath{\mu}=\ensuremath{-}1.29{\ensuremath{\mu}}_{N}$ for the magnetic moment seems to favor the $j\ensuremath{-}j$ coupling. The theory of intermediate coupling is applied to the configuration ${d}^{\ensuremath{-}1}f$ with the view of accounting for the spin and the observed magnetic moment. It is found that a small spin-orbit interaction will lead to a negative magnetic moment. A central nucleon-nucleon interaction of the form $(mP+nQ)V({r}_{12})$, where $P$ denotes the Majorana and $Q$ the Bartlett operator, is assumed and calculations have been carried out for the exponential, Yukawa and Gaussian types of potential $V({r}_{12})$ with various "ranges." For a suitable choice of the spin-orbit interaction parameter $\ensuremath{\zeta}$, the observed magnetic moment can be obtained, the exact value of $\ensuremath{\zeta}$ depending on the type of potential and range used.