Influence of Nambu-Goldstone mode on energy-weighted sum of excitation strengths in random-phase approximation
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 excitation and the rotational excitations in nuclei, further confirming theoretical consistency of the RPA.