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

Energy- and non-energy-weighted sum rules (N and M) were evaluated for the nuclear charge monopole and dipole modes. Sums are given for different intermediate isospins by using the method in which sums are split into isoscalar, vector, and tensor parts. This facilitates the separation of model-dependent quantities; in particular, possible modifications of shell-model evaluations arising from correlations are considered. Four important specific results are the following: (i) The shell-model value of M in the dipole case is carefully calculated for 208Pb, 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 shellmodel 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.