Treatment of the Intrinsic Hamiltonian in Particle-Number Nonconserving Theories

TL;DR

This paper addresses the challenges of using an intrinsic Hamiltonian in particle-number nonconserving theories, proposing a systematic expansion to improve accuracy in nuclear self-consistent methods.

Contribution

It introduces a systematic expansion to correct particle-number dependence issues, justifying the common one- plus two-body intrinsic kinetic energy approximation.

Findings

The expansion converges well for sample nuclei.

The method improves the consistency of intrinsic Hamiltonian treatments.

Practical applications demonstrate enhanced accuracy in nuclear calculations.

Abstract

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.