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Physics of Particles and Nuclei Letters

Thermodynamically Consistent Description of One-Phonon States Fragmentation in Hot Nuclei

Alan A. Dzhioev, A.I. Vdovin

Published Nov 1, 2021• 1 citation
Publisher

Abstract

The fragmentation of one-phonon states in hot nuclei is studied. For this purpose, the quasiparticle-phonon nuclear model is extended to a finite temperature by applying the formalism of thermo field dynamics. It is shown that consistent application of the thermal state condition leads to the realization of the detailed balance principle at each stage of the thermal Hamiltonian diagonalization. The equations describing the coupling between thermal one-phonon and two-phonon states are derived.

DOI
10.1134/s1547477121060054

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The fragmentation of one-phonon states in hot nuclei is studied. For this purpose, the quasiparticle-phonon nuclear model is extended to a finite temperature by applying the formalism of thermo field dynamics. It is shown that consistent application of the thermal state condition leads to the realization of the detailed balance principle at each stage of the thermal Hamiltonian diagonalization. The equations describing the coupling between thermal one-phonon and two-phonon states are derived.
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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 phononphonon 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. 1.
Thermal Bogoliubov transformation is an essential ingredient of the thermo field dynamics—the real time formalism in quantum field and many-body theories at finite temperatures developed by H. Umezawa and coworkers. The approach to study properties of hot nuclei which is based on the extension of the well-known Quasiparticle-Phonon Model to finite temperatures employing the TFD formalism is presented. A distinctive feature of the QPM-TFD combination is a possibility to go beyond the standard approximations like the thermal Hartree-Fock or the thermal RPA ones.
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 the Bogoliubov quasiparticles consisting the phonon but also on the Bose thermal occupation numbers of the phonon. This strongly affects a thermal phonon coupling due to the renormalization 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 co-workers.
To take systematic account of thermal correlation effect on the mean field, the thermal random phase approximation formalism is extended based on the thermofield dynamics scheme. The random phase approximation phonon operator is expressed in terms of the thermofield dynamics quasiparticle operators with a tilde as well as those without a tilde, and the increase of the dimensionality of variational parameter manifold enables us to derive the extended thermal random phase approximation equation from deeper minimum of grand potential. It is shown that the extended thermal random phase approximation equation is justified also from viewpoint of time-dependent formalism. The method of constrained variation applied to the first extended thermal random phase approximation can be straightforwardly generalized to the second, or higher extended thermal random phase approximation. Extended expressions are given also for the stability condition of thermal Hartree-Fock-Bogoliubov approximation and the energy-weighted sum rule.