# Nuclear response in a finite-temperature relativistic framework

## TL;DR

This paper develops a finite-temperature relativistic framework for nuclear response using the Bethe-Salpeter equation and Matsubara Green's functions, enabling analysis of nuclear oscillations at various temperatures.

## Contribution

It introduces a temperature-dependent projection operator to simplify the Bethe-Salpeter equation at finite temperature within a relativistic quantum hadrodynamics model.

## Key findings

- Successfully applied to monopole, dipole, and quadrupole responses of $^{48}$Ca.
- Analyzed the evolution of nuclear collective oscillations with temperature.
- Demonstrated the method's effectiveness in finite-temperature nuclear response studies.

## Abstract

A thermal extension of the relativistic nuclear field theory is formulated for the nuclear response. The Bethe-Salpeter equation (BSE) with the time-dependent kernel for the particle-hole response is treated within the Matsubara Green's function formalism. We show that, with the help of a temperature-dependent projection operator on the subspace of the imaginary time (time blocking), it is possible to reduce the BSE for the nuclear response function to a single frequency variable equation also at finite temperature. The approach is implemented self-consistently in the framework of quantum hadrodynamics based on the meson-nucleon Lagrangian. The method is applied to the monopole, dipole and quadrupole response of $^{48}$Ca and to the dipole response of the tin isotopes $^{100,120,132}$Sn, in particular, to a study of the evolution of nuclear collective oscillations with temperature. The article is dedicated to the memory of Pier Francesco Bortignon and devoted to the developments related to his pioneering ideas.