Improved microscopic-macroscopic approach incorporating the effects of continuum states

TL;DR

This paper enhances the microscopic-macroscopic nuclear modeling approach by integrating Kruppa's prescription and refining the smoothing procedure, enabling more accurate calculations of binding energies for neutron-rich nuclei.

Contribution

It introduces a new interpretation of the Strutinsky smoothing as a low-pass filter and modifies the BCS equations for Kruppa's spectrum, improving the method's reliability for unstable nuclei.

Findings

The plateau condition is explained via a low-pass filter interpretation.

The method reduces dependence on smoothing width.

Reliable binding energy calculations for nuclei far from stability are achieved.

Abstract

The Woods-Saxon-Strutinsky method (the microscopic-macroscopic method) combined with Kruppa's prescription for positive energy levels, which is necessary to treat neutron rich nuclei, is studied to clarify the reason for its success and to propose improvements for its shortcomings. The reason why the plateau condition is met for the Nilsson model but not for the Woods-Saxon model is understood in a new interpretation of the Strutinsky smoothing procedure as a low-pass filter. Essential features of Kruppa's level density is extracted in terms of the Thomas-Fermi approximation modified to describe spectra obtained from diagonalization in truncated oscillator bases. A method is proposed which weakens the dependence on the smoothing width by applying the Strutinsky smoothing only to the deviations from a reference level density. The BCS equations are modified for the Kruppa's spectrum, which is necessary to treat the pairing correlation properly in the presence of continuum. The potential depth is adjusted for the consistency between the microscopic and macroscopic Fermi energies. It is shown, with these improvements, that the microscopic-macroscopic method is now capable to reliably calculate binding energies of nuclei far from stability.