Microscopic justification of the Equal Filling approximation

TL;DR

This paper justifies the Equal Filling Approximation used in mean field calculations for odd nuclei through a variational principle, employing ideas from Statistical Quantum Mechanics, and demonstrates its application on Radium isotopes.

Contribution

It provides a theoretical justification for the Equal Filling Approximation using a variational approach based on statistical quantum mechanics.

Findings

Justification of the Equal Filling Approximation as a variational principle.

Application to octupole deformed Radium isotopes.

Accurate computation of ground and low-lying states.

Abstract

The Equal Filling Approximation, a procedure widely used in mean field calculations to treat the dynamics of odd nuclei in a time reversal invariant way, is justified as the consequence of a variational principle over an average energy functional. The ideas of Statistical Quantum Mechanics are employed in the justification. As an illustration of the method, the ground and lowest lying states of some octupole deformed Radium isotopes are computed.