Semiclassical shell-structure moment of inertia for equilibrium rotation of a simple Fermi system

Semiclassical shell-structure components of the collectivemoment of inertia are derived within the mean-field cranking model in the adiabatic approximation in terms of the free-energy shell corrections through those of a rigid body for the statistically equilibriumrotation of a Fermi system at finite temperature by using the nonperturbative extended Gutzwiller periodic-orbit theory. Their analytical structure in terms of the equatorial and 3-dimensional periodic orbits for the axially symmetric harmonic oscillator potential is in perfect agreement with the quantum results for different critical bifurcation deformations and different temperatures.     

Fermi-liquid relations, large-N expansion and Bethe-ansatz solution for the degenerate Anderson model

The large-N expansion results for the ground-state charge and spin susceptibilities are compared with the exact Bethe-ansatz solution. The agreement is good in the mixed-valence regime and poor in the Kondo limit. The exact Fermi-liquid relation between the T-linear coefficient of the specific heat and the spin and charge susceptibilities is derived and compared with the results within the large-N approximation.     

Semiclassical inertia of nuclear collective dynamics

For the low-lying collective excitations in nuclei, the transport coefficients, such as the stiffness, the inertia, and the friction, are derived within the periodic-orbit theory in the lowest orders of semiclassical expansion corresponding to the extended Thomas—Fermi approach. The multipole vibrations near the spherical shape are described in the mean-field approximation through the infinitely deep square-well potential and Strutinsky averaging of the transport coefficients. Owing to the consistency condition, the collective inertia for sufficiently increased particle numbers and temperatures is substantially larger than that of irrotational flow. The average energies of collective vibrations, reduced friction, and effective damping coefficients are in better agreement with experimental data than those found from the hydrodynamic model. The text was submitted by the authors in English.     

Retardation effects in damping of nuclear collective excitations

We expand the nonmarkovian collision integral in terms of multipolarities of the distortion of the Fermi surface. It is shown that damping of zero-sound is determined by all multipolarities of the Fermi-surface deformation. For large zero-sound velocity with respect to the Fermi velocity the relaxation time is related to the quadrupole deformation of the Fermi surface. The contributions of collisions to the total widths of the giant multipole resonances are calculated in a semiclassical macroscopic nuclear model.     

Inertial parameters in the interacting boson—fermion approximation

The Hartree—Bose—Fermi and the adiabatic approximations are used to derive analytic formulae for the moment of inertia and the decoupling parameter of the interacting boson—fermion approximation for dformed systems. These formulae are applied to the SU(3) dynamical symmetry. In the large N limit we obtain perfect agreement with the exact results.     

Semiclassical treatment of quadrupole shape effects in the elastic scattering of heavy ions below the Coulomb barrier

A perturbative semiclassical approximation for the elastics-matrix is used to derive simple and accurate formulae describing the effects of a nuclear quadrupole deformation on the elastic scattering of aligned nuclei. Expressions are derived for the second rank tensor components of the analysing power, the ratios of which turn out to be simple trigonometric functions of the scattering angle in agreement with experimental observations. The approximations are discussed in some detail and higher order corrections are derived. In an appendix we derive a semiclassical first-order perturbation formula describing the effect of a non-central complex perturbation in the presence of a non-perturbatively treated central term. Our formula is in disagreement with some earlier published formulae which fail to treat the real part of the perturbation correctly.     

Collective gyromagnetic ratio and moment of inertia from density-dependent Hartree-Fock calculations

The collective gyromagnetic ratio and moment of inertia of deformed even-even axially symmetric nuclei are calculated in the cranking approximation using wave functions obtained with the Skyrme force S-III. Good agreement is found for g_R, while the moment of inertia is about 20 % too small. The cranking formula leads to better agreement than the projection method.     

Semiclassical description of isoscalar giant multipole resonances

The scaling approximation in a semiclassical theory of nuclear collective motions based on the Vlasov equation is applied to the study of isoscalar giant resonances. Analytic forms are obtained for the frequencies of any multipolarity, expressed just in terms of local density distributions, using realistic nuclear effective forces. The importance of non local interactions and diffuse surfaces is clearly shown. The limits of the scaling picture in describing high multipolarity resonances are finally discussed.     

The nuclear self-energy and related quantities in the semiclassical approximation

By using our recently developed semiclassical model for the imaginary part of the optical potential, we calculate here the polarization and correlation contributions to the real part via the dispersion relation. As underlying nonlocal mean-field potential, the semiclassical Hartree-Fock potential evaluated with the Gogny D1 effective interaction or the Perey-Buck potential is employed. With this full self-energy or second-order mass operator we calculate consistently depths, radial dependence and volume integrals of the single-particle potential, rearrangement energies and effective masses, the momentum distribution, mean free paths of a nucleon in a nucleus, and single-particle level densities. We obtain depths which are in excellent agreement with experiment including the Fermi anomaly: the effective mass exhibits a strong bump at the Fermi and the nuclear surface and the single-particle level density at the Fermi energy is enhanced by 65% yielding almost the correct average experimental value.     

Spatial correlations of pairing collective states

The properties of the low-energy nuclear spectrum are greatly affected by pairing correlations. We study these effects in the nucleus ²¹⁰Pb which has two particles moving outside closed shells. The configuration-mixed wave functions describe the motion of particles which are on the average closer together than they would be if the particles were confined to particular orbitals. Since the energy associated with pairing correlations is much smaller than the Fermi energy the width of the associated probability distribution is determined by the wavelength of single particles moving close to the Fermi surface. Despite the fact that the amplitudes associated with high-lying configurations are small, their net effect is important, typically changing the collectivity of the states by a factor of about two. The results of the microscopic calculations compare well with a semiclassical pairing transition density calculated on the basis of the Thomas-Fermi approximation.     

The total acoustic impedance of a prolate spheroid performing transverse oscillatory movements

Using the theory of spheroidal wave functions, the total acoustic impedance is determined for a prolate spheroid performing transverse translational and rotational oscillatory movements. Expressions for the radiation resistance, the added mass, and the added moment of inertia are derived. It is shown that, in the lowfrequency approximation, this mass and moment of inertia reach limiting values identical to hydrodynamic ones. The components of the total acoustic impedance are calculated for spheroids of different relative thicknesses at an arbitrary frequency.     

Semiclassical description of reactions at energies near the Coulomb barrier

The modified semiclassical approximation of Coulomb matrix elements is extended to include effects of distorting nuclear potentials in the scattering wave functions. The applicability and efficiency of the proposed semiclassical method are discussed. The advantages of this approximation are shown for a typical heavy-ion transfer reaction.     

Non-Fermi-liquid effects in tunneling

Non-Fermi-liquid tunneling mechanisms in a quantum structure with its own two-dimensional continuum doped with transition metal impurities are considered. New physical realizations of the two-channel Kondo orbital model with mechanisms different from those previously described in literature occur in such quantum structures. The tunneling transparency is anomalously high owing to new channels generated by multiparticle Fermi-liquid resonances near the edge of the two-dimensional energy band in the process of tunneling. The widths of new edge resonances can be much smaller than the width of the “bare” non-Fermi-liquid resonance at the Fermi level in the banks. The additional scattering due to tunneling induces a transition from the non-Fermi-liquid to the Fermi-liquid state as the separation between the Fermi level in the banks and the two-dimensional band edge in the quantum well varies. Zh. éksp. Teor. Fiz. 114, 1466–1486 (October 1998)     

Positive parity states in Er

The positive parity states in ¹⁶⁷Er are described in terms of the rotational model, where the particle-rotation coupling is taken into account. The moment of inertia, the Fermi energy and the coupling strength are determined by fitting the energies. The wave functions thus obtained are used to calculate the (d, p) stripping and (d, t) pick-up cross sections and branching ratios. The results obtained are in agreement with experimental data.     

Density distributions in nuclei

Density distribution across the nuclear surface is obtained in the approximation of relatively sharp nuclear edge. It is used to determine dynamical parts of the density relevant to density vibration resonances. Results of the simple calculations are in close agreement with detailed microscopic theories.     

Multiphonon excitations in heavy ion grazing collisions

A semiclassical model is used to study the excitation of giant resonances in heavy ion grazing collisions. The projectile is described as a moving Woods-Saxon potential with a fixed shape, and the evolution of the target state is calculated by time-dependent perturbation theory. Using random phase approximation wave functions, probabilities to excite various resonances are obtained. Multiple phonon excitations appear as the possible mechanism for the structures observed in heavy ion collisions.     

三体heritage混合相互作用和核转动惯量的变化

讨论了在费米子动力学对称模型中大形变区核转动惯量的变化机制.指出在无I1带和基带交叉的情况下,heritage混合本身也可以引起转动惯量的变化,但引起混合的相互作用形式是重要的,引入某种三体相互作用后能很好地解释实验事实.