Treatment of the intrinsic Hamiltonian in particle-number nonconserving theories

We discuss the implications of using an intrinsic Hamiltonian in theories without particle-number conservation, e.g., the Hartree–Fock–Bogoliubov approximation, where the Hamiltonian's particle-number dependence leads to discrepancies if one naively replaces the particle-number operator by its expectation value. We develop a systematic expansion that fixes this problem and leads to an a posteriori justification of the widely-used one- plus two-body form of the intrinsic kinetic energy in nuclear self-consistent field methods. The expansion's convergence properties as well as its practical applications are discussed for several sample nuclei.