Projection in the occupation-number space and the canonical transformation

Abstract

A method for projecting the Bardeen-Cooper-Schrieffer states with respect to the particle number is suggested. This method does not involve the Fowler-Darwin integrals which are usually applied for this purpose. Energy matrix elements of an arbitrary single-particle operator and overlap integrals are calculation in the quasi- particle representation and are expressed analytically in terms of the u and v parameters. The volume of calculations according to the method suggested increases linearly with the size of the system in the case of factorizable pairing matrix elements (the weaker the particle number fluctuations, the smaller the quantity of calculations). The method is illustrated by some model systems. In the paper the limiting case of weak correlations is considered and comparison with perturbation theory is carried out.