The past three decades of investigation on nuclear physics and pulsar astrophysics have seen gradual recognition that elastodynamic approach to the continuum mechanics of nuclear matter provides proper account of macroscopic motions of degenerate Fermi-matter constituting interior of the nuclear material objects, the densest of all known today. This paper focuses on one theoretical issue of this development which is concerned with oscillatory behavior of a viscoelastic solid globe in the regime of quasistatic, force-free, non-compressional oscillations less investigated in the literature compared to oscillations in the regime of standing shear waves. We show that in this case the problem of computing frequency and lifetime of spheroidal and torsional modes of non-radial shear vibrations damped by viscosity can be unambiguously resolved by working from the energy balance equation and taking advantage of the Rayleigh's variational method. The efficiency of this method is demonstrated by solid globe models of nuclear physics and pulsar astrophysics dealing with oscillations of a spherical mass of a viscoelastic Fermi-solid with homogeneous and non-homogeneous profiles of the bulk density, the shear modulus, and the shear viscosity.

Spheroidal and torsional modes of quasistatic shear oscillations in the solid globe models of nuclear physics and pulsar astrophysics

The past three decades of investigation on nuclear physics and pulsar astrophysics have seen gradual recognition that elastodynamic approach to the continuum mechanics of nuclear matter provides proper account of macroscopic motions of degenerate Fermi-matter constituting interior of the nuclear material objects, the densest of all known today. This paper focuses on one theoretical issue of this development which is concerned with oscillatory behavior of a viscoelastic solid globe in the regime of quasistatic, force-free, noncompressional oscillations less investigated in the literature compared to oscillations in the regime of standing shear waves. We show that in this case the problem of computing frequency and lifetime of spheroidal and torsional modes of nonradial shear vibrations damped by viscosity can be unambiguously resolved by working from the energy balance equation and taking advantage of the Rayleigh's variational method. The efficiency of this method is demonstrated by solid globe models of nuclear physics and pulsar astrophysics dealing with oscillations of a spherical mass of a viscoelastic Fermi-solid with homogeneous and nonhomogeneous profiles of the bulk density, the shear modulus, and the shear viscosity.

The Landau equation with an energy- and momentumconserving collision term is solved for longitudinal and transverse fluid-dynamical and hydrodynamical collective modes. Depending on the value of the mean free collision time, complex longitudinal poles are found for negative Landau parameterF0 and transverse ones forF1<6.

Complex solutions of the Landau equation with collisional damping

It is shown that for a consistent description of the evolution of tensor Fi1 . . .in= integral rho Xi1Xi2. . .Xind3X by means of the kinetic equation it is necessary to take into account the Fermi surface deformation (FSD) with multipolarity up to rank n. Inclusion of the octupole FSD considerably influences the estimate of the energy of the giant octupole resonance and allows one to describe the low-lying octupole excitations.

Closure of the chain of the kinetic equation moments and description of the negative-parity collective excitations

The long-mean-free-path nuclear fluid dynamics is extended to include damping. First the damping stress is derived from the solution of the Boltzmann equation for a breathing spherical container filled with a Fermi gas. Then the corresponding damping force is incorporated into Euler equations of motion and energies and widths of low lying collective resonances are computed as eigenfrequencies of a vibrating nucleus under surface tension and Coulomb potential as well as the high lying isoscalar giant resonances as eigenfrequencies of an elastic nucleus. Maximum damping is obtained if the particle frequency approximately resonates with the wall frequency. Theoretical results are compared with experimental data and future improvements are indicated.

Nuclear fluid dynamics with long-mean-free-path dissipation: Multipole vibrations and isoscalar giant resonance widths

The collisionless Vlasov equation is solved by a moment expansion and truncated after the fourth moments. This scheme yields fluid dynamical equations for the eigenvibrations of a nucleus which are beyond the usual elastic equations. These Euler equations are solved exactly and also approximately for the normal parity (electric, surface) modes 2/sup +/, first excited 2/sup +/, 3/sup -/, 4/sup +/, the abnormal parity (magnetic, twist) modes 1/sup +/, 2/sup -/, and the compression (breathing and squeezing) modes 0/sup +/, 1/sup -/. Without adjustable parameters, agreement of the resulting giant resonance energies with experimental data, where available, is reasonably good. Since the corrections due to the inclusion of the third and fourth moments enhance the energies by up to 35%, the moment expansion converges only slowly.

Isoscalar giant-resonance energies and long-mean-free path nuclear fluid dynamics

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Isoscalar giant-resonance energies and long-mean-free path nuclear fluid dynamics