Correlations in the Sp(1,R) model for the monopole oscillations.

Abstract

In the framework of the Sp(1,R) model for the monopole oscillations, we examine how the ground state correlations affect the monopole operator sum rules ${m}_{l}$, 0\ensuremath{\le}l\ensuremath{\le}3, in $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$. Our way of probing the correlations indicates their importance for the even sum rules, whereas the odd ones practically are not affected by it. Since the scaling incompressibility is proportional to ${m}_{3}$, we also conclude that the scaling incompressibility is not sensitive to ground state correlations. The above conclusions are in agreement with the random-phase approximation results.