On the TFD treatment of collective vibrations in hot nuclei

TL;DR

This paper reexamines the formalism of collective excitations in hot nuclei using thermo field dynamics, revealing that thermal phonon wave functions depend on both Fermi-Dirac and Bose thermal occupation numbers, affecting phonon interactions.

Contribution

It introduces a revised understanding of thermal phonon wave functions and interactions, emphasizing the importance of Bose thermal occupation numbers and the appropriate conjugation rule for fermions.

Findings

Thermal phonon wave functions depend on both Fermi-Dirac and Bose occupation numbers.

Renormalization of phonon-phonon interactions enlarges the configuration space.

The double tilde conjugation rule by I.Ojima is more suitable for this context.

Abstract

The approach in a theory of collective excitations in hot nuclei exploring the formalism of thermo field dynamics and the model Hamiltonian consisting of a mean field, the BCS paring interaction and long-range particle-hole effective forces is reexamined. In contrast with earlier studies it is found that a wave function of a thermal phonon is depended not only on the Fermi-Dirac thermal occupation numbers of Bogoliubov quasiparticles consisting the phonon but on the Bose thermal occupation numbers of the phonon as well. This strongly affects a thermal phonon couplings due to renormalizing of a phonon-phonon interaction and enlarging the number of thermal two-phonon configurations coupled with one-phonon ones. Moreover, it is shown that the formulation of the double tilde conjugation rule for fermions proposed by I.Ojima is more appropriate in the context of the present study than the original one by H.Umezawa and coworkers.