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arXiv:1909.12053

The collective excitation of nuclear matter in a bosonizated formula of Landau Fermi liquid theory

Bao-Xi Sun

Published Sep 26, 2019• 0 citations
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Abstract

The collective excitation of the nuclear matter is analyzed in a bosonizated formula of Landau Fermi liquid theory. When the nonlinear self-interacting terms of the scalar meson are taken into account in the Walecka model, the collective excitation energies of the nuclear matter can be obtained self-consistently. It shows that the calculation results are consistent with the corresponding experimental data of the nucleus ${}^{208}Pb$ when the quantum number of the orientation of the orbital angular momentum $m$ is zero. Moreover, the cases with the nonzero $m$ values are also studied, it manifests that the collective excitation energy with the fixed nonzero $m$ value are almost invariant when the quantum number of the orbital angular momentum $l$ changes. However, the collective excitation energy of the nuclear matter decreases with the absolute value of $m$ increasing. The direct interaction between two nucleons near the Fermi surface only changes the Fermi velocity, while the exchange interaction causes the collective excitation of the nuclear matter. At this point, it is different from the traditional views in nuclear physics, which announce that the random phase approximation is essential to generate the nuclear collective excitation states.

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The collective excitation of the nuclear matter is analyzed in a bosonizated formula of Landau Fermi liquid theory. When the nonlinear self-interacting terms of the scalar meson are taken into account in the Walecka model, the collective excitation energies of the nuclear matter can be obtained self-consistently. It shows that the calculation results are consistent with the corresponding experimental data of the nucleus 208Pb{}^{208}Pb208Pb when the quantum number of the orientation of the orbital angular momentum mmm is zero. Moreover, the cases with the nonzero mmm values are also studied, it manifests that the collective excitation energy with the fixed nonzero mmm value are almost invariant when the quantum number of the orbital angular momentum lll changes. However, the collective excitation energy of the nuclear matter decreases with the absolute value of mmm increasing. The direct interaction between two nucleons near the Fermi surface only changes the Fermi velocity, while the exchange interaction causes the collective excitation of the nuclear matter. At this point, it is different from the traditional views in nuclear physics, which announce that the random phase approximation is essential to generate the nuclear collective excitation states.
The methods of quantum statistics previously developed by the author are applied to the determination of properties of the ground state of nuclear matter. An expansion in powers of the pair-function of quantum statistics is made and expressions are derived for the momentum distribution, pair-correlation function, binding energy, and effective single-particle energies. The leading terms of these expressions can be interpreted in terms of an effective two-body interaction, and a model of nuclear matter which consists of interacting quasi-particles whose energies are the effective single-particle energies is thereby suggested. The theory is compared with Brueckner's theory and also with Landau's phenomenological theory of the Fermi liquid.
We give a Hamiltonian-based interpretation of microscopic Fermi liquid theory within a renormalization group framework. The Fermi liquid fixed-point Hamiltonian with its leading-order corrections is identified and we show that the mean field calculations for this model correspond to the Landau phenomenological approach. This is illustrated first of all for the Kondo and Anderson models of magnetic impurities which display Fermi liquid behaviour at low temperatures. We then show how these results can be deduced by a reorganization of perturbation theory, in close parallel to that for the renormalized φ4 field theory. The Fermi liquid results follow from the two lowest order diagrams of the renormalized perturbation expansion. The calculations for the impurity models are simpler than for the general case because the self-energy depends on frequency only. We show, however, that a similar renormalized expansion can be derived also for the case of a translationally invariant system. The parameters specifying the Fermi liquid fixed-point Hamiltonian are related to the renormalized vertices appearing in the perturbation theory. The collective zero sound modes appear in the quasiparticle-quasihole ladder sum of the renormalized perturbation expansion. The renormalized perturbation expansion can in principle be used beyond the Fermi liquid regime to higher temperatures. This approach should be particularly useful for heavy fermions and other strongly correlated electron systems, where the renormalization of the single-particle excitations are particularly large. We briefly look at the breakdown of Fermi liquid theory from a renormalized perturbation theory point of view. We show how a modified version of the approach can be used in some situations, such as the spinless Luttinger model, where Fermi liquid theory is not applicable. Other examples of systems where the Fermi liquid theory breaks down are also briefly discussed.
This paper presents the results of investigation of the superfluid states in a two-component Fermi liquid within the framework of the Fermi liquid approach. Particular attention is paid to the superfluid states in nuclear matter which are characterized by the superposition of singlet and triplet types of pairing in spin and isospin spaces. The fundamental principles of the Fermi liquid approach are formulated and further used in the study of superfluidity in nuclear matter with the superposition of singlet and triplet types of pairing. The system of self-consistency equations is derived and its solutions are presented. The conditions of existence of the considered states are determined. These conditions impose certain constraints on the interaction potential and particle density in the system. It is shown that the states with a complete set of nonzero order parameters are realized only in a narrow density range, the width and position of which on the density scale depend on the actual parametrization of the Skyrme potential employed. We considered 18 different parameterizations and indicated for which of them the studied types of superfluid states may appear. The problem of stability of the states with the superposition of singlet and triplet pairing is studied. It is shown that the lowest value of the thermodynamic potential corresponds to purely triplet states. Then, in the order of increasing, follow the thermodynamic potentials of purely singlet states and mixed singlet-triplet states. Separately, we consider the case of unitary states, for which the solutions of the self-consistency equations are also analyzed. It is shown that the density range in which such states can be realized is different from that corresponding to the nonunitary states. The problem of existence of the unitary superfluid states with the superposition of singlet and triplet superfluidity is considered in the case of asymmetrical nuclear matter. It is shown that the appearance of asymmetry in nuclear matter breaks the unitarity of superfluid states in nuclear matter with regard to isospin.
A numerical method has been developed to solve the RPA equation, exchange term included, in nuclear matter. The dynamic form factor S(q, ω) is extracted for several v4 and v6 phenomenological potentials, including the d1-potential of Gogny et al. The limits of validity of the long-wavelength (Landau) approximation and the often adopted local-kernel approximation are discussed. Substantial disagreements with the exact results are found for the latter. The method is then applied to solve a Jastrow-correlated extension of the RPA equation, using the hardcore OMY potential. Results of calculations performed in two-body cluster approximation and Fermi-Hypernetted-Chain (FHNC) approximation are compared. The two-body results predict an instability against density fluctuations, which disappears at the FHNC level. The validity and consequences of employing the FHNC effective potential within the self-consistent HF/RPA framework are discussed. Future developments include applying the method to other Fermi systems such as liquid 3He and the microscopic calculation of Landau parameters.
The spectrum of elementary excitations in the system of interacting Bose- and Fermi-particles was obtained at a temperature of absolute zero (Dose- condensation being taken into account by means of the Bogolyabov canonic transformations. In terms of a model of permeable spheres'' with finite repulsion it(is shown that the boson spectrum omega (p) in a definite region of parameter has the minimum at p = 0. By selecting parameters one succeeds in obtaining a quite satisfactory quantitative agreement of the theoretical and experimental spectra for superfluid helium. In the case when the Fermi energy is considerably higher than the bosorins maximum energy, a gap characterizing bond energy of the copper pairs can appear in the fermion speetrum due to exchange of virtual supercondensate'' bosons. If in this case the interaction between fermions at infinity is of attraction character, then under certain conditions sustained longitudinal collective excitations of Pose-type with a finite gap'' in the energy spectrum may exist in the superfluid fermion subsystem. Possibility of appearance of similar excitations in superfluid nuclear matter of neutron stars (pulsars) due to gravitational interaction between nucleons is discussed. (auth)