Nuclear many-body problem at zero and finite temperature

Elena Litvinova^1,2,3

¹Department of Physics, Western Michigan University, Kalamazoo, MI 49008-5252, USA

²National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA

³GANIL, CEA/DRF-CNRS/IN2P3, F-14076 Caen, France

Recent developments of the relativistic nuclear field theory (NFT) on the fermionic correlation functions will be presented. The general non-perturbative equation of motion framework is formulated in terms of a closed system of non-linear equations for onebody and two-body propagators. The present formulation provides a direct link to abinitio theories and extends the explicit treatment of many-body correlations beyond the standard NFT level. The novel approach to the nuclear response, which includes configurations with two quasiparticles coupled to two phonons (2q⊗2phonon), is discussed in detail for electromagnetic excitations in medium-mass nuclei. The proposed developments are implemented numerically on the basis of the relativistic effective meson-nucleon Lagrangian and compared to the models confined by 2q and 2q⊗phonon configurations, which are considered the state-of-the-art for the response theory in nuclear structure calculations. The results obtained for the dipole response of 42,48Ca and 68Ni nuclei in comparison to available experimental data show that the higher-complexity configurations are necessary for a successful description of both gross and fine details of the spectra in both high-energy and low-energy sectors. The approach confined by the 2q⊗phonon configurations has been extended recently to the case of finite temperature for both neutral and charge-exchange nuclear response. Within this approach, we investigate the temperature dependence of nuclear spectra in various channels, such as the monopole, dipole, quadrupole and spin-isospin ones, for even-even medium-heavy nuclei. The special focus is put on the giant dipole resonance’s width problem, the low-energy strength distributions and the influence of temperature on the equation of state. The temperature dependence of the GamowTeller and spin dipole excitations will be discussed in the context of its potential impact on the astrophysical modeling of supernovae and neutron-star mergers.