Effect of Two-Body Correlations on Sum Rules for Nuclear Charge Monopole and Dipole Modes

Abstract

We have evaluated energy- and non-energy-weighted sum rules ($N$ and $M$) for the nuclear charge monopole and dipole modes. Sums are given for different intermediate isospins, using the method in which sums are split into isoscalar, vector, and tensor parts. This facilitates the separation of model-dependent quantities, and we particularly consider possible modifications of shell-model evaluations arising from correlations. Four important specific results are: (i) The shell-model value of $M$ in the dipole case is carefully calculated for $^{208}\mathrm{Pb}$, and is 30% larger than the observed value; this difference must arise from correlations. (ii) The previously suggested smallness of the isotensor part of $M$ is not general, but depends on using a shell-model wave function; it is shown theoretically and from experiment that the isotensor part may be large. (iii) The effects of correlations on $M$ can be displayed in a form requiring no new calculations (given published Tamm-Dancoff diagonalizations). (iv) There is a close relation between the charge-exchange part of $N$ in the dipole and monopole problems, so one can use data on the former to evaluate the latter; also, a connection with the effective $M1$ charge and effective mass is shown.