Semiclassical approaches to nuclear dynamics

Abstract

The extended Gutzwiller trajectory approach is presented for the semiclassical description of nuclear collective dynamics, in line with the main topics of the fruitful activity of V.G. Solovjov. Within the Fermi-liquid droplet model, the leptodermous effective surface approximation was applied to calculations of energies, sum rules and transition densities for the neutron-proton asymmetry of the isovector giant-dipole resonance and found to be in good agreement with the experimental data. By using the Strutinsky shell correction method, the semiclassical collective transport coefficients such as nuclear inertia, friction, stiffness, and moments of inertia can be derived beyond the quantum perturbation approximation of the response function theory and the cranking model.The averaged particle-number dependence of the low-lying collective vibrational states are described in good agreement with basic experimental data, mainly due to an enhancement of the collective inertia as compared to its irrotational flow value. Shell components of the moment of inertia are derived in terms of the periodic-orbit free-energy shell corrections. A good agreement between the semiclassical extended Thomas-Fermi moments of inertia with shell corrections and the quantum results is obtained for different nuclear deformations and particle numbers. Shell effects are shown to be exponentially dampted out with increasing temperature in all the transport coefficients.Comment: 83 pages, 39 figures, 4 tables, corrected typos and improved Englis

Semiclassical and quantum shell-structure calculations of the moment of inertia

“…This approach was extended by Pashkevich and Frauendorf [8,9] to the description of collective rotational bands. For a deeper understanding of the correspondence between the classical and the quantum approach and their applications to high-spin physics, it is worthwhile to analyze the shell components of the moment of inertia (MI) within the semiclassical periodic-orbit theory (POT) [10][11][12][13][14][15][16][17][18][19][20]. The cranking model is, to some extent, of semiclassical nature because the collective rotation of the nuclear manybody systems is described as a classical transformation from the laboratory to the body-fixed coordinate system, rotating around the former with fixed angular velocity [4,5].…”

“…One could, however, consider another perturbation approach based on the concept of a statistical equilibrium rotation with a generalized rigid-body (GRB) moment of inertia Θ GRB [21] (see Refs. [19,[22][23][24][25][26]), Θ ≈ Θ GRB = m dr r 2 ⊥ ρ(r) , (1) * Email: magner@kinr.kiev.ua…”

“…The nonperturbative Gutzwiller POT, extended to the bifurcation phenomena at large deformations [20,[29][30][31], on the other hand, was applied [25] within the cranking model and a harmonic-oscillator mean field to describe collective rotations (around an axis perpendicular to the symmetry axis). For adiabatic collective rotations (rotations at statistical equilibrium) the MI is then described as the sum of a smooth Extended Thomas-Fermi (ETF) MI Θ ETF [22,32] and shell corrections δΘ [19,[22][23][24]. In a more realistic description of the MI for collective rotations, the ETF approach has already been successful, as in the case of the nuclear energy [33], by including selfconsistency and spin effects into the calculations [22,32].…”

“…As shown in Refs. [19,[22][23][24], one can obtain, through a semiclassical phase-space trace formula, with a good approximation, analytical expressions for MI shell components δΘ in terms of the energy shell corrections δE, for an arbitrary potential well,…”

“…a relation which has been worked out for integrable Hamiltonians, such as for a harmonic oscillator [22,25] or a spheroidal-cavity [19,23,24] mean field. Corrections accounting for a finite surface diffuseness and finite temperature effects of the nuclear system can also been taken into account as demonstrated in Refs.…”