Isospin Decomposition of Nuclear Multipole Matrix Elements fromγDecay Rates of Mirror Transitions: Test of Values Obtained with Hadronic Probes

The electromagnetic decay rates of mirror states are used to decompose the multipole electromagnetic matrix elements into isoscalar and isovector or equivalently proton and neutron matrix elements. This method is sensitive to the neutron matrix element because it is measured directly, and it is accurate since it depends only on electromagnetic interactions; it therefore can be used to test methods using inelastic hadron scattering. There is agreement with the results for ($\alpha$,${\alpha }^{\prime }$) on ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ but disagreement with the recent ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$($\pi$,${\pi }^{\prime }$) experiments.