Nuclear response in a finite-temperature relativistic framework

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.

Nuclear Shell Structure in a Finite-Temperature Relativistic Framework

“…The same truncation criteria were applied for all temperature regimes. As in our previous calculations [4,5,54,67], at high temperatures many additional phonon modes appear in the excitation spectra as a consequence of the thermal unblocking, which leads to a significant expansion of the phonon model space with the temperature growth. The single-particle intermediate states k 3 were included in the summation of Eq.…”

“…It has been shown in the previous studies [77,78] that the low-energy collective quadrupole 2 + and octupole 3 − phonons couple most strongly to the single-particle degrees of freedom. This is consistent with our qualitative study discussed in Section IV A, which emphasizes the importance of the low-energy phonons for the fragmentation of singleparticle states.…”

“…As shown in Ref. [67], the relationship (10) is model independent and includes the exact transition densities, while the interaction U is the bare interaction between nucleons in the vacuum. In practice, employing effective interactions and the random phase approximation based on these interactions for the computation of the phonon characteristics provide quite a realistic description of the dynamical self-energy.…”

“…In practice, employing effective interactions and the random phase approximation based on these interactions for the computation of the phonon characteristics provide quite a realistic description of the dynamical self-energy. In this work, we use the effective interaction of the covariant energy density functional (CEDF) [59,60] with the NL3 parametrization [68] and the relativistic random phase approximation [69] adopted to finite temperature in our previous developments for calculations of the phonon modes [4,5,67].…”

Temperature evolution of the nuclear shell structure and the dynamical nucleon effective mass

“…However, numerous models employing effective interactions and the random phase approximation based on these interactions for the computation of the phonon vertices and frequencies typically provide quite realistic approaches to the dynamical self-energy. In this work, we use the effective interaction of the covariant energy density functional (CEDF) [33,34] with the NL3 parametrization [46] and the concept of the 'nosea' relativistic random phase approximation (RRPA) [47] adopted to finite temperature in our previous developments [38,48,49].…”