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Anharmonic effects in nuclei in the quantum hydrodynamic description

VICTOR A. KHODEL

Published Oct 1, 1976• 1 citation
OpenAlex

Abstract

Anharmonic effects in the capillary branch of excitations of a Fermi-liquid drop are considered. The limiting transition to classical hydrodynamics is found. It exists when the orbital angular momenta L/sub i/ of the collective excitations are large. The situation of the classical conservation law for the volume of the system is analyzed in the quantum case. It is found that when the frequency of a collective oscillation is small compared with the characteristic single-particle frequencies, the results obtained on the basis of the phenomenological scheme with a phonon-phonon Hamiltonian are reproduced. It is shown that no new parameters are required to calculate the constants of this Hamiltonian in the theory of finite Fermi systems.

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arXiv:1502.04333•Physical Review B•Jul 15, 2015•1 citation
Anharmonic effects in the capillary branch of excitations of a Fermi-liquid drop are considered. The limiting transition to classical hydrodynamics is found. It exists when the orbital angular momenta L/sub i/ of the collective excitations are large. The situation of the classical conservation law for the volume of the system is analyzed in the quantum case. It is found that when the frequency of a collective oscillation is small compared with the characteristic single-particle frequencies, the results obtained on the basis of the phenomenological scheme with a phonon-phonon Hamiltonian are reproduced. It is shown that no new parameters are required to calculate the constants of this Hamiltonian in the theory of finite Fermi systems.
The nature of low-lying collective nuclear states is analyzed in the framework of the Fermi-liquid approach. It is shown that in a drop of Fermi liquid one has not only the ordinary zero-sound branch but also a new collective mode resulting from the spontaneous breaking of the translational invariance. These are quantum capillary waves that have much in common with ordinary surface excitations of a classical drop. Numerical calculations show that the first collective levels of nuclei belong to this branch.
Some results obtained by E.E. Saperstein and his coauthors in the theory of the ground state and low-lying excited states of magic and semimagic nuclei are discussed briefly. Corrections to the creation amplitude ggg for one low-lying phonon are considered for the first time. These corrections, treated on the basis of the existence of a small parameter, include the tadpole-induced coupling of the amplitudes for the creation of one and two phonons.
A new method which enables us to transcribe the dynamics of the system of even number of fermions into that of the boson system is developed, with the purpose of analysing the “anharmonic effects” on the collective oscillations in spherical even nuclei from the standpoint of the microscopic theory of the collective excitations. In the “harmonic approximation”, a pair of bound quasi-particles is replaced by the “phonon” as an ideal boson. This replacement inevitably leads to neglecting two main effects; the dynamical effect due to the residual interactions omitted under the “harmonic approximation” and the effect of the Pauli-principle among the quasi-particles composing the different pairs. According to our theory, the two effects which cause “anharmonic effects” can be evaluated correctly, in principle. It is not our purpose to go into detailed quantitative calculations, but rather to develop the basic idea.
In the present paper, we consider the theory, describing both spiral magnetics and superfluid Fermi-liquid with a triplet pairing. Previously this method was used in the description of a superfluid Fermi-liquid in the singlet case. This approach is a generalization of the classical theory of Fermi-liquid. This semiphenomenological study combines the advantages of both the microscopic and phenomenological description. The method permits the spectra of collective excitations of the system to be obtained taking into account the Fermi-liquid effects.
The quantum theory of third order anharmonic effects in the photon production amplitude developed by V.A. Khodel has been generalized for nuclei with pairing and for a more accurate description of low-energy collective phonons. An expression for the transition amplitude between two- and one-phonon states has been obtained. This expression has been compared to the solution of a similar problem considered within the quasiparticle–phonon model. It has been shown that this approach describes a number of new effects, including three- and four-quasiparticle correlations in the ground state ( backward-going graphs ).
We develop a hydrodynamic description of the collective modes of interacting liquids in a quasi-one-dimensional confining potential. By solving Navier-Stokes equation we determine analytically the excitation spectrum of sloshing oscillations. For parabolic confinement, the lowest frequency eigenmode is not renormalized by interactions and is protected from decay by the Kohn theorem, which states that center of mass motion decouples from internal dynamics. We find that the combined effect of potential anharmonicity and interactions results in a frequency shift and final lifetime of the Kohn mode. All other excited modes of sloshing oscillations thermalize with the parametrically faster rate. Our results are significant for the interpretation of recent experiments with trapped Fermi gases that observed a weak violation of the Kohn theorem.