Effect of Configuration Mixing on Magnetic Multipole Radiation

Abstract

Expressions for the matrix element governing the emission of magnetic multipole radiation are given. The effect of weak configuration mixing and the small additional contribution to proton matrix elements (\ensuremath{\sim}5%) arising from the nuclear spin-orbit interaction are considered. For $M4$ transitions, even in nuclei near closed shells, the theoretical matrix elements derived from pure configurations are too large by a factor of two. The effect of configuration mixing reduces these. Choosing a $\ensuremath{\delta}$-function interaction of reasonable strength leads to a reduction of \ensuremath{\sim}25% in the matrix element for $1{g}_{\frac{9}{2}}\ensuremath{\rightarrow}2{p}_{\frac{1}{2}}$ transition in $_{39}\mathrm{Y}_{50}^{89}$. The ${(2{p}_{\frac{1}{2}})}^{\ensuremath{-}1}\ensuremath{\rightarrow}{(1{g}_{\frac{9}{2}})}^{\ensuremath{-}1}$ transition in $_{38}\mathrm{Sr}_{49}^{87}$ is reduced close to the required 50%. The $1{h}_{\frac{11}{2}}\ensuremath{\rightarrow}2{d}_{\frac{3}{2}}$ matrix element becomes \ensuremath{\sim}25% smaller. However, there are no data available for the nucleus $_{50}\mathrm{Sn}_{65}^{115}$, with which one would like to make comparison. Finally, the ${(1{i}_{\frac{13}{2}})}^{\ensuremath{-}1}\ensuremath{\rightarrow}{(2{f}_{\frac{5}{2}})}^{\ensuremath{-}1}$ transition in $_{82}\mathrm{Pb}_{125}^{207}$ has its matrix element reduced by only \ensuremath{\sim}6%. Although the reduction in $_{39}\mathrm{Y}_{50}^{89}$ is somewhat too small, one cannot make a positive statement that configuration mixing is incapable of explaining the experimental result since a two-body force of a more realistic type may close the gap between theory and experiment. However, for $_{82}\mathrm{Pb}_{125}^{207}$ there seems no doubt that other effects, for example, meson currents, must be incorporated.