Random-phase-approximation ground-state correlations and the isotope effect in theCa40andCa48

Ellis's method of constructing the random-phase-approximation ground-state wave function which avoids the earlier dubious and incorrect quasiboson approximation is extended to the $N\ne Z$ nuclei. The most important effects arise from the appropriate treatment of the isospin quantum number. In application to the calcium isotopes we find that the calculated relative shift of the proton rms radius from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ to ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ $R=-0.35\%$ for the first time agrees with the high energy electron scattering result $R=-0.31\%$. Excellent agreement is also obtained for the difference of the neutron and proton rms radii in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$. It should be emphasized, however, that our conclusions concerning the magnitude of the effects on the rms radii due to ground state correlations are more significant than the detailed comparison with experiment.