Comparative analysis of formalisms and performances of three different beyond mean-field approaches

TL;DR

This paper compares three beyond mean-field approaches—EMPM, STDA, and SRPA—in nuclear physics, highlighting their similarities, differences, and the EMPM's unique ability to fully eliminate spurious center-of-mass effects.

Contribution

It provides a detailed comparison of EMPM, STDA, and SRPA methods, demonstrating EMPM's capacity to completely remove spurious c.m. admixtures in nuclear calculations.

Findings

EMPM and STDA produce identical results under certain conditions

EMPM uniquely allows complete removal of c.m. admixtures

All methods show similar results when using the same Hamiltonian

Abstract

We investigate the differences and analogies between the equation of motion phonon method (EMPM) and second Tamm-Dancoff and random-phase approximations (STDA and SRPA) paying special attention to the problem of spurious center-of-mass (c.m.) admixtures. In order to compare them on an equal footing, we perform self-consistent calculations of the multipole strength distributions in selected doubly magic nuclei within a space including up to two-particle-two-hole (2p-2h) basis states using the UCOM two-body intrinsic Hamiltonian and we explore the tools each approach supplies for removing the spurious c.m. admixtures. We find that the EMPM and STDA yield exactly the same results when the same intrinsic Hamiltonian is used and the coupling of the Hartree-Fock state with the 2p-2h space is neglected, but, unlike STDA and SRPA, the EMPM offers the possibility to completely remove c.m. admixtures.