Collective inertia of Nambu-Goldstone mode from linear response theory

TL;DR

This paper develops a precise and efficient method to calculate the collective inertia of Nambu-Goldstone modes in superfluid nuclei using linear response theory, aiding the understanding of collective motions.

Contribution

The authors derive an analytical expression for the response function of NG modes in terms of coordinate-momentum representation, applicable even with zero-energy symmetry-restoring modes.

Findings

Derived analytical formulas for NG mode inertia and conjugate operators.

Validated the method with translational and pairing rotational modes.

Performed illustrative calculations on Sn isotopes, N=82 isotones, and 130Xe nucleus.

Abstract

Background: Spurious zero-energy Nambu-Goldstone (NG) modes appear when the symmetry of a system is spontaneously broken. The Thouless-Valatin inertia, the collective inertia of the NG mode, contains important information concerning collective motion. Purpose: To establish an efficient and precise method for deriving the collective inertia and the conjugate operator of a NG mode, we derive an expression for the response function in terms of the coordinate-momentum representation of the quasiparticle random-phase approximation which is valid even if a symmetry-restoring zero-energy mode is present. Methods: We use the finite amplitude method for computing the response function of superfluid nuclei with the nuclear density functional theory. Results: We derived analytically the collective inertia and the conjugate coordinate operator of the NG mode from the zero-energy linear response with the momentum operator of the NG mode. The formulation is tested in the cases of translational and pairing rotational modes. Illustrative calculations are performed for the neutron pairing rotation in Sn isotopes, the proton pairing rotation in N = 82 isotones, and the neutron and proton pairing rotations around the 130Xe nucleus. Conclusions: The proposed formulation allows us to compute the collective inertia of the NG mode precisely and efficiently. The conjugate coordinate operator can be utilized to remove spurious contributions to the strength distribution in the finite amplitude method.