Nuclear structure and pairing correlations for the heavy elements

Abstract

The advent of BCS calculations for deformed nuclei has brought extensive progress in understanding many nuclear properties. With the aid of fast and versatile computer facilities a number of previously-made simplifying assumptions have been tested. (1) By use of delta- force matrix elements between Nilsson eigenfunctions, instead of a constant- G pairing force, some feeling for the nature of fluctuations in δ ν values and their variation as the systems are filled is gained. (2) By carrying the usually-neglected G vv′ matrix elements of Belyaev a generally uniform lowering of Nilsson levels is observed as the system is filled. (3) The systematic effects on variational energies and average configuration mixing caused by projecting fixed-particle terms from BCS wave functions (PBCS) is studied. (4) The variation has been performed on the fixed-particle expression (FBCS). The FBCS method gives the lowest possible energies for a variational solution of the projected BCS form. The FBCS method is found always to lead to non-trivial solutions no matter how weak the residual force strength; the abrupt transition between superfluid and normal states of the nuclear fluid, predicted by the BCS method, is thus found to be a spurious result. The FBCS method always gives more configuration mixing than PBCS. The PBCS energies are close to FBCS in the region of high pairing correlation but are worse where pairing correlation is lower. This tendency is reflected strikingly in the odd-even mass differences, where the PBCS method gives differences much too large in the region of low pairing correlation. Most of the simpler methods are found to predict too-high level densities for odd-proton systems, relative to the FBCS method.