Isoscalar and isovector particle densities are derived analytically by using the approximation of a sharp edged nucleus within the local energy density approach with the proton-neutron asymmetry and spin-orbit effects. Equations for the effective nuclear-surface shapes as collective variables are derived up to the higher order corrections in the form of the macroscopic boundary conditions. The analytical expressions for the isoscalar and isovector tension coefficients of the nuclear surface binding energy and the finite-size corrections to the β stability line are obtained.

We present results of microscopic calculations of the strength function, S(E), and α-particle excitation cross sections σ(E) for the isoscalar giant dipole resonance (ISGDR). An accurate and a general method to eliminate the contributions of spurious state mixing is presented and used in the calculations. Our results provide a resolution to the long standing problem that the nuclear matter incompressibility coefficient, K, deduced from σ(E) data for the ISGDR is significantly smaller than that deduced from data for the isoscalar giant monopole resonance (ISGMR).

We use a fully self-consistent Hartree−Fock (HF) based continuum random phase approximation (CRPA) to calculate strength functions S(E) and transition densities ρ t (r) for isoscalar giant resonances with multipolarities L = 0, 1 and 2 in 80 Zr nucleus. In particular, we consider the effects of spurious state mixing (SSM) in the isoscalar giant dipole resonance (ISGDR) and extend the projection method to determine the mixing amplitude of spurious state so that properly normalized S(E) and ρ t (r) having no contribution due to SSM can be obtained. For the calculation to be highly accurate we use a very fine radial mesh (0.04 fm) and zero smearing width in HF−CRPA calculations. We first use our most accurate results as a basis to establish the credibility of the projection method, employed to eliminate the SSM, and then to investigate the consequences of the common violation of self-consistency, in actual implementation of HF based CRPA and discretized RPA (DRPA), as often encountered in the published literature. The HF−DRPA calculations are carried out using a typical box size of 12 fm and a very large box of 72 fm, for different values of particle-hole energy cutoff ranging 1 from 50 to 600 MeV.

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The magnetic susceptibility of electrons confined to a spherical cavity or a circular billiard shows slow oscillations as a function of the number of electrons, which are a new manifestation of the Super Shell Structure found in the free energy of metal clusters. The relationship of the oscillations of the two different quantities is analyzed by means of semiclassical calculations, which are in quantitative agreement with quantal results. The oscillations should be observable for ensembles of circular ballistic quantum dots and metal clusters.

Level density [Formula: see text] is derived for a nuclear system with a given energy [Formula: see text], neutron [Formula: see text], and proton [Formula: see text] particle numbers, within the semiclassical extended Thomas–Fermi and periodic-orbit theory beyond the Fermi-gas saddle-point method. We obtain [Formula: see text], where [Formula: see text] is the modified Bessel function of the entropy [Formula: see text], and [Formula: see text] is related to the number of integrals of motion, except for the energy [Formula: see text]. For small shell structure contribution one obtains within the micro–macroscopic approximation (MMA) the value of [Formula: see text] for [Formula: see text]. In the opposite case of much larger shell structure contributions one finds a larger value of [Formula: see text]. The MMA level density [Formula: see text] reaches the well-known Fermi gas asymptote for large excitation energies, and the finite micro-canonical limit for low excitation energies. Fitting the MMA [Formula: see text] to experimental data on a long isotope chain for low excitation energies, due mainly to the shell effects, one obtains results for the inverse level density parameter [Formula: see text], which differs significantly from that of neutron resonances.

The structure of the 3-dimension pressure-temperature-asymmetry surface of equilibrium of the asymmetric nuclear matter is studied within the thermal Thomas-Fermi approximation. Special attention is paid to the difference of the asymmetry parameter between the boiling sheet and that of the condensation sheet of the surface of equilibrium. We derive the condition of existence of the regime of retrograde condensation at the boiling of the asymmetric nuclear matter. We have performed calculations of the caloric curves in the case of isobaric heating. We have shown the presence of the plateau region in caloric curves at the isobaric heating of the asymmetric nuclear matter. The shape of the caloric curve depends on the pressure and is sensitive to the value of the asymmetry parameter. We point out that the experimental value of the plateau temperature T ≈ 7 MeV corresponds to the pressure P = 10 −2 MeV/fm 3 at the isobaric boiling.