M1Transitions Among thef72d32−1States ofK40

The three experimentally known $M1\mathrm{}$ transition rates among the $f_{\frac{7}{2}}d_{\frac{3}{2}}^{}{}_{}{}^{-1\mathrm{}}{2}^{-}$, $3^{-}$, $4^{-}$, and $5^{-}$ quartet of ${}_{}{}^{40}{}_{}{}^{}\mathrm{K}$ are calculated to first order using the one-particle, one-hole wave functions of Perez. The calculations are in qualitative agreement with experiment and illustrate that the effective moment method is not valid when used with a zeroth-order (i.e., the pure $f_{\frac{7}{2}}d_{\frac{3}{2}}^{}{}_{}{}^{-1\mathrm{}}$ configuration) calculation. This is expected since the effective moments correct for second-order effects and cannot simulate the first-order correction due to the presence of $f_{\frac{5}{2}}d_{\frac{3}{2}}^{}{}_{}{}^{-1\mathrm{}}$ and $f_{\frac{7}{2}}d_{\frac{5}{2}}^{}{}_{}{}^{-1\mathrm{}}$ impurities.