Large-scale second RPA calculations with finite-range interactions

TL;DR

This paper performs large-scale second RPA calculations using finite-range interactions, analyzing nuclear responses like giant resonances and collective states without arbitrary truncations, focusing on methodological and physical insights.

Contribution

It introduces a consistent SRPA approach with finite-range interactions, avoiding divergences and validating the diagonal approximation, while addressing stability issues related to ground-state correlations.

Findings

Finite-range interactions prevent divergence problems.

Diagonal approximation is conditionally validated.

Stability issues linked to missing ground-state correlations.

Abstract

Second RPA (SRPA) calculations of nuclear response are performed and analyzed. Unlike in most other SRPA applications, the ground state, approximated by the Hartree-Fock (HF) ground state, and the residual couplings are described by the same Hamiltonian and no arbitrary truncations are imposed on the model space. Finite-range interactions are used and thus divergence problems are not present. We employ a realistic interaction, derived from the Argonne V18 potenial using the unitary correlation operator method (UCOM), as well as the simple Brink-Boeker interaction. Representative results are discussed, mainly on giant resonances and low-lying collective states. The focus of the present work is not on the comparison with data, but rather on technical and physical aspects of the method. We present how the large-scale eigenvalue problem that SRPA entails can be treated, and demonstrate how the method operates in producing self-energy corrections and fragmentation. The so-called diagonal approximation is conditionally validated. Stability problems are traced back to missing ground-state correlations.