Magnetic Moment ofK40in Intermediate Coupling

The ${\mathrm{K}}^{40}$ nucleus is of interest since its spin $I=4\mathrm{}$ forms a notable exception to Nordheim's rule while the observed value $\mu =-1.29\mathrm{}{\mu }_N$ for the magnetic moment seems to favor the $j-j$ coupling. The theory of intermediate coupling is applied to the configuration $d^{-1\mathrm{}}f$ 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 $\mathrm{}(mP+nQ)V\left(r_{12}\right)$, 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 $V\left(r_{12}\right)$ with various "ranges." For a suitable choice of the spin-orbit interaction parameter $\zeta$, the observed magnetic moment can be obtained, the exact value of $\zeta$ depending on the type of potential and range used.