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arXiv:nucl-th/9810042 · Physical Review C

Finite temperature nuclear response in the extended random phase approximation

Denis Lacroix A, Ph. Chomaz, Sakir Ayik B

Published Oct 1, 1998• 37 citations
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Abstract

The nuclear collective response at finite temperature is investigated for the first time in the quantum framework of the small amplitude limit of the extended time-dependent Hartree-Fock approach, including a non-Markovian collision term. It is shown that the collision width satisfies a secular equation. By employing a Skyrme force, the isoscalar monopole, isovector dipole, and isoscalar quadrupole excitations in ${}^{40}\mathrm{Ca}$ are calculated and important quantum features are pointed out. The collisional damping due to decay into incoherent two-particle--two-hole states is small at low temperatures but increases rapidly at higher temperatures.

DOI
10.1103/physrevc.58.2154

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The nuclear collective response at finite temperature is investigated for the first time in the quantum framework of the small amplitude limit of the extended time-dependent Hartree-Fock approach, including a non-Markovian collision term. It is shown that the collision width satisfies a secular equation. By employing a Skyrme force, the isoscalar monopole, isovector dipole, and isoscalar quadrupole excitations in 40Ca{}^{40}\mathrm{Ca}40Ca are calculated and important quantum features are pointed out. The collisional damping due to decay into incoherent two-particle--two-hole states is small at low temperatures but increases rapidly at higher temperatures.
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.
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A linear response framework is set up for the evaluation of collective excitations in a confined vapour of interacting Bose atoms at finite temperature. Focusing on the currently relevant case of contact interactions between the atoms, the theory is developed within a random-phase approximation with exchange. This approach is naturally introduced in a two-fluid description by expressing the density response of both the condensate and the non-condensate in terms of the response of a Hartree - Fock reference gas to the self-consistent Hartree - Fock potentials. Such an approximate account of correlations (i) preserves an interplay between the condensate and the non-condensate through off-diagonal components of the response, which instead vanish in the Hartree - Fock - Bogoliubov approximation; and (ii) yields a common resonant structure for the four partial response functions. The theory reduces to the temperature-dependent Hartree - Fock - Bogoliubov - Popov approximation for the fluctuations of the condensate when its coupling with the density fluctuations of the non-condensate is neglected. Analytic results are presented which are amenable to numerical calculations and to inclusion of damping rates.
We present a detailed study of the low-lying collective excitations of a spherically trapped Bose-Fermi mixture at finite temperature in the collisionless regime. The excitation frequencies of the condensate are calculated self-consistently using the static Hartree-Fock-Bogoliubov theory within the Popov approximation. The frequency shifts and damping rates due to the coupled dynamics of the condensate, noncondensate, and degenerate Fermi gas are also taken into account by means of the random-phase approximation and linear-response theory. In our treatment, the dipole excitation remains close to the bare trapping frequency for all temperatures considered, and thus is consistent with the generalized Kohn theorem. We discuss in some detail the behavior of monopole and quadrupole excitations as a function of the Bose-Fermi coupling. At nonzero temperatures we find that, as the mixture moves towards spatial separation with increasing Bose-Fermi coupling, the damping rate of the monopole (quadrupole) excitation increases (decreases). This provides us a useful signature to identify the phase transition of spatial separation.