A phenomenological effective two-body interaction for calcium isotopes

Abstract

The 1]~-2pg shell has long been one of the most studied nuclear regions. Recently there has been an extensive effective-interaction calculation on calcium isotopes by F~I)~MAN~ and PITTnL (1). The single set of matrix elements given by them has a good convergence and appears to reproduce the energy spectra, (t,p) strengths and single-neutron spectroscopic factors with reasonable agreement. Moreover, the /~pg matrix elements have the desh'ed feature of repulsion on the average. This is in agreement with the findings obtained by analysing the data from (3He, d) and (d, p) measurements in this shell (~). These matrix elements, derived from Hamada-Johnston potential (a), are, however, attractive on the average. The effective-interaction method in the framework of the shell model has the disadvantage that one cannot use a large configuration space in such calculations. Then the number of variable two-particle matrix elements increases drastically and the method fails. Even in a reasonable configuration space, the two-particle matrix elements obtained from the least-squares fit to the experimental binding energies and level energies of calcium isotopes have large statistical errors (a-e), when all the required two-particle matrix elements are allowed to vary. On the other hand, a large configuration space can be used with a phenomenological effective two-body interaction with a few adjustable parameters. The wave functions thus obtained, in view of greater configurational freedom, are more realistic than those obtained by the effective-interaction method. But it is difficult to get detailed quanti tat ive fit to the binding energies and level energies like the effective-interaction method because there are only a few adjustable parameters in a phenomenological force. So an initial test of a phenomenological residual twobody interaction is to reproduce the matrix elements obtained by the effective-interaction method to get a good description of the experimental data.