Microscopic justification of the Equal Filling approximation

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.