Lipkin method of particle-number restoration to higher orders

Background: On the mean-field level, pairing correlations are incorporated through the Bogoliubov-Valatin transformation, whereupon the particle degrees of freedom are replaced by quasiparticles. This approach leads to a spontaneous breaking of the particle-number symmetry and mixing of states with different particle numbers. In order to restore the particle number, various methods have been employed, which are based on projection approaches before or after variation. Approximate variation-after-projection (VAP) schemes, utilizing the Lipkin method, have mostly been used within the Lipkin-Nogami prescription. Purpose: Without recurring to the Lipkin-Nogami prescription, and using instead st…