Self-consistent Semiclassical Calculation Research Articles

JACOBI SHAPE TRANSITIONS WITHIN THE LSD MODEL AND THE SKYRME-ETF APPROACH

The "Modified Funny-Hills parametrisation" is used together with the Lublin-Strasbourg Drop Model to evaluate the stability of rotating nuclei. The Jacobi transition into triaxial shapes is studied. By a comparison with selfconsistent semiclassical calculations in the framework of the Extended Thomas-Fermi method, the validity of the present approach is demonstrated and possible improvements are indicated.

Nuclear mean fields through self-consistent semiclassical calculations

Semiclassical expansions derived in the framework of the Extended Thomas-Fermi approach for the kinetic energy density τ( r) and the spin-orbit density J( r) as functions of the local density ρ( r) are used to determine the central nuclear potentials V n( r) and V p( r) of the neutron and proton distribution for effective interactions of the Skyrme type. We demonstrate that the convergence of the resulting semiclassical expansions for these potentials is fast and that they reproduce quite accurately the corresponding Hartree-Fock average fields.

Bulk properties of rotating nuclei and the validity of the liquid drop model at finite angular momenta

Out of self-consistent semi-classical calculations performed within the so-called Extended Thomas-Fermi approach for 212 nuclei at all even angular momentum values I ranging between 0 and 80 ħ and using the Skyrme SkM ∗ effective force, the I-dependence of associated liquid drop model parameters has been studied. The latter have been obtained trough separate fits of the calculated values of the strong interaction as well as direct and exchange Coulomb energies. The theoretical data basis so obtained, has allowed to make a rough quantative assessment of the variation with I of the usual volume and surface energy parameters up to spin of ∼ 30–40ħ. As a result of the combined variation of the surface and Coulomb energies, it has been shown that this I-dependence results in a significant enhancement of the fission stability of very heavy nuclei, balancing thus partially the well-known instability due to centrifugal forces.

Semiclassical Approach for Static and Dynamical Properties of Nuclei11The project supported by National Natural Science Foundation of China through Grant No. 18905002.

This article summarizes recent progress in the semiclassical treatment of nuclear static and dynamical problems. We first give a short outline of fundamental concepts adopted in the semiclassical approximations, including -expansion, Bloch density matrix and Wigner-Kirkwood transformation. Then we proceed to discuss two major types of semiclassical approaches: self-consistent semiclassical calculation and its extended forms for deformed and hot nuclei for static properties of nuclei, and Vlasov equation, including its extension Vlasov-Uehling-Uhlenbeck equation, for dynamical properties, especially the collisional problems, of nuclei.

Optical potential and the fusion barrier of two hot nuclei.

The finite-temperature self-consistent semiclassical calculation is carried out to determine the nucleon densities of some hot nuclei at thermal equilibrium with temperature T. These densities are applied, in the energy density formalism, to calculate the nucleus-nucleus optical potential and the corresponding fusion barrier between two hot nuclei. A moderate temperature dependence is found for the optical potential and fusion barrier.

Hartree–Fock and Self-Consistent Semiclassical Approaches to the Properties of 208Pb11This work was supported partly by the National Natural Science Foundation of China.

Based on the extended Skyrme force SKa and GS2, the Hartree–Fock and self-consistent semiclassical calculations are carried out to investigate the static properties of 208Pb. The present results are compared with each other and with the experiments. A good agreement is obtained between two theoretical approaches and between theories and experiments.

Self-consistent semiclassical calculation of nucleus-nucleus optical potentials and fusion barriers

The nucleus-nucleus optical potentials of a series of spherical nuclei and the corresponding fusion barriers are evaluated in the energy density formalism with sudden approximation. The nucleon densities of both target and projectile nuclei are determined by a self-consistent semi-classical calculation. The resulting fusion barriers are in good agreement with experimental ones for medium-heavy systems but systematically smaller for heavy systems, although the spin-orbit contribution to and the exchange effect on the potentials have been taken into consideration.

Self-consistent semiclassical calculation of the spin-orbit contribution to the nucleus-nucleus optical potential

The spin-orbit contribution to the nucleus-nucleus optical potentials is calculated in an energy density formalism with nuclear density profiles determined by a self-consistent semiclassical approach. The sudden approximation is adopted in our calculation. Results both with and without exchange effects are presented and discussed.

Self-consistent semiclassical calculation with extended Skyrme forces and the properties of giant resonances

Using the semiclassical approach to the Skyrme-HF energy density, one obtains the energy density functional H ( rho n, rho p) for a nucleon system. The variational calculation of this functional, under the condition of fixed nucleon number, results in a self-consistently determined nuclear ground state from which the nuclear giant resonances (GR) are studied using a sum rule approach. The moment of strength function, the centroid energy and the isospin properties of GR are calculated. All the results are in good agreement with experimental results and detailed HF+RPA ones.

Fission barriers of excited nuclei

The 240Pu fission barrier is calculated in the finite temperature Hartree-Fock approximation with Skyrme effective forces for temperatures ranging from 0 to 3 MeV. The disappearance of the double hump barrier structure and of the underlying liquid drop barrier, when increasing the excitation energy, is shown. The latter is quantitatively related to an increase of the fissility parameter through self-consistent semi-classical calculations. The results of our calculations are shown to be compatible with experimental (p. f) cross sections in rare-earth nuclei.

Selfconsistent semiclassical calculations using the partial [formula omitted] resummation method

Selfconsistent semiclassical calculations using the partial resummation technique have been performed for a number of spherical nuclei. The results are found in very good agreement with those obtained in the more lengthy selfconsistently Strutinsky averaged Hartree-Fock approach. Our method has also been applied to the determination of liquid drop parameters associated with effective forces of the Skyrme type.