Influence of Nambu-Goldstone mode on energy-weighted sum of excitation strengths in random-phase approximation

TL;DR

This paper investigates how Nambu-Goldstone modes affect the energy-weighted sum of excitation strengths in RPA, providing a general formula to isolate their contribution, with applications to nuclear excitations.

Contribution

A new general formula is derived to separate Nambu-Goldstone mode contributions to the energy-weighted sum in RPA, enhancing understanding of symmetry breaking effects.

Findings

The formula accurately isolates NG-mode contributions in theoretical models.

Application to nuclear excitations confirms the formula's consistency.

Analysis supports the validity of RPA in describing symmetry-breaking phenomena.

Abstract

Influence of the Nambu-Goldstone (NG) mode on the energy-weighted sum (EWS) of the excitation strengths is analyzed, within the random-phase approximation (RPA). When a certain symmetry is broken at the mean-field level, a NG mode emerges in the RPA, which can be represented by canonical variables forming a two-dimensional Jordan block. A general formula is rederived which separates out the NG-mode contribution to the EWS, via the projection on the subspace directed by the NG mode. As examples, the formula is applied to the $E1$ excitation and the rotational excitations in nuclei, further confirming theoretical consistency of the RPA.