https://doi.org/10.1140/epja/s10050-025-01502-y
Regular Article - Theoretical Physics
Elucidating the finite temperature quasiparticle random phase approximation
1
Facility for Rare Isotope Beams, Michigan State University, 48824, East Lansing, MI, USA
2
Department of Physics, Faculty of Science, University of Zagreb, Bijenička c. 32, 10000, Zagreb, Croatia
3
Department of Physics and Astronomy, University of North Carolina, CB 3255, 27599-3255, Chapel Hill, NC, USA
Received:
5
August
2024
Accepted:
27
January
2025
Published online:
26
February
2025
In many astrophysical scenarios, such as core-collapse supernovae and neutron star mergers, as in well as heavy-ion collision experiments, transitions between thermally populated nuclear excited states have been shown to play an important role. Because of its simplicity and ability to extrapolate, the finite-temperature quasiparticle random phase approximation (FT-QRPA) is an efficient method for studying the properties of hot nuclei. The statistical ensembles in the FT-QRPA make the theory much richer than its zero-temperature counterpart, but also obscure the meaning of various physical quantities. In this work, we clarify several aspects of the FT-QRPA, including notation seen in the literature, and demonstrate how to extract physical quantities from the theory. To illustrate the correct treatment of finite-temperature transitions, we place special emphasis on the charge-exchange transitions described by the proton-neutron FT-QRPA (FT-PNQRPA). With the FT-PNQRPA built on the nuclear energy-density functional theory, we obtain solutions in a relativistic matrix approach and also in the non-relativistic finite amplitude method. We show that the proper treatment of de-excitations from thermally populated excited states causes the Ikeda sum rule to be fulfilled. In addition, we demonstrate the impact of these transitions on stellar electron capture (EC) rates in 
Ni. While their inclusion does not affect the EC rates in 
Ni, the rates in 
Ni are dominated by de-excitations for temperatures 
MeV. In systems with a large negative Q-value, the inclusion of de-excitations within the FT-QRPA is necessary for a complete description of reaction rates at finite temperature.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
