Norm operator method for boson expansions

TL;DR

This paper introduces a novel boson expansion theory that avoids the traditional closed-algebra approximation, improving the accuracy and faithfulness of mapping fermion systems onto boson representations in nuclear physics.

Contribution

It develops a boson expansion method that does not rely on the closed-algebra approximation, enhancing the fidelity of fermion-to-boson mapping and elucidating the construction of the fermion subspace.

Findings

Reveals the mechanism for constructing the fermion subspace in boson expansions.

Shows that conventional methods improperly apply the closed-algebra approximation.

Provides a more faithful reproduction of fermion subspace onto boson subspace.

Abstract

We propose a new boson expansion theory that does not premise the closed-algebra approximation, indispensable for formulation until now, as an extension of the conventional practical boson expansion methods that have tried to elucidate nuclear collective motion, which is a method that allows the closed-algebra approximation not to be used or to be used appropriately, enables us to obtain the boson expansion easier, and reproduces the fermion subspace onto the boson subspace more faithfully than the conventional practical methods. The two-phonon norm matrix composed of all the phonon excitation modes is investigated in detail, which reveals the mechanism, essential for the boson expansion methods, of how we should construct the fermion subspace to be mapped from the whole fermion space. The conventional practical boson expansion methods have applied the closed-algebra approximation improperly to strengthen the effect of the Pauli principle inappropriately, which should be replaced by those that do not use that approximation or use it properly.