1. December 20, 2007, Sergey Bastrukov Elastic Vibrations of Atomic Nuclei and Neutron Stars Brief review of elastodynamical approach to the continuum mechanics of nuclear matter

2. Atomic nuclei (heavier than Fe-56) and neutron stars are products of supernova explosion. The identical density and similar nucleonic composition suggest that they can be regarded as small and big samples of one and the same in material properties nucleon condensed matter. Z=114-118 Dubna Z=114-118 Dubna Z=110-112 Darmstadt

3. The current investigations on nuclear physics and pulsar astrophysics suggest that the Fermi-degenerate nucleon condensed matter constituting interior of atomic nuclei and the main body of neutron stars possesses properties of solid-mechanical shear elasticity and shear viscosity. In nuclear physics, the Solid Globe Model has been invoked to explain electric and magnetic giant-resonant excitations in terms of spheroidal and torsional shear vibrations of viscoelastic solid sphere. In pulsar astrophysics, the Solid Star Model is currently utilized to explain the detected millisecond quasi-periodic oscillations in electromagnetic spectra of pulsars and magnetars in terms of torsional elastic vibrations. Continuous Nuclear Matter as Viscoelastic Fermi-solid

4. The empirically established general trends in data on energy centroid of giant resonances throughout periodic table are properly described in terms of shear vibrations of an elastic sphere This implies that Fermi-degenerate nucleon material can be specified as elastic Fermi-solid. Electric giant resonances can be interpreted as spheroidal shear vibrations of femtoparticle of an elastic Fermi-continuum

5. Abstract The nuclear fluid-dynamical Hamiltonian which takes the distortion of the local Fermi surface into account predicts the Twist mode (T=0, J=2 – ) at a finite frequency (about 7.5 MeV for 208 Pb). The application of our non-Newtonian nuclear fluid dynamics to the Twist was initiated by M.Danos, who kindly informed one of the authors (G.H.) about early attempts of J.H.D.Jensen to obtain a nuclear twisting mode within Newtonian hydrodynamics. The nuclear “Twist” Magnetic quadrupole resonance can be thought of as an eigenmode of torsional quadrupole oscillations driven by restoring force of elastic stresses Magnetic giant resonances as eigenmodes of torsional elastic vibrations

7. Viscosity of nuclear matter The widths of resonances carry information about viscosity of nuclear matter

8. Nuclear Solid Globe Model Ring-like distribution of sites about of which the nucleons undergo zero-point oscillations and exchange places. The nucleons are not localized but are in the state of incessant quantum-wave motions which is described as ordered Fermi-motion of independent nucleon-like quasi- particle in the nuclear mean field.

9. Nuclear Solid Globe Model

11. From standpoint of the solid globe model the fast nuclear response by giant electric resonances is associated with irrotational shear deformational oscillations of orbits preserving their closed shape and by giant magnetic resonances differentially – rotational oscillations of orbits with respect each other. In the process of these oscillations the energy order of single-particle states in the potential of nuclear mean field of shell model is unchanged.

12. Fundamental modes of quasi-static nodeless elastic shear vibrations of solid sphere

17. Experimental manifestation of solid-mechanical viscoelasticity of nuclear matter in the electromagnetic response of atomic nuclei by giant resonances

18. Dipole Spheroidal and Dipole Torsional modes emerge when perturbation sets in oscillations peripheral layer whereas internal undisturbed region remains immobilized. This case can be treated as elastic oscillations of peripheral layer against static core

23. Starquake X-ray flare ~ 100-300 sec Quasi-periodic oscillations of x-ray lumioisity

28. Dipole spheroidal and torsional oscillations of the crust against core are Goldstone modes vanishing when the all volume of the star sets in vibrations. The case when h=1.

30. QPOs of lowest frequency are due to dipole spheroidal and torsional elastic shear vibrations of the crust against core