Shells, orbit bifurcations and symmetry restorations in Fermi systems

Abstract

The periodic-orbit theory based on the improved stationary-phase method within the phase-space path integral approach is presented for the semiclassical description of the nuclear shell structure, concerning the main topics of the fruitful activity of V. G. Solovjov. We apply this theory to study bifurcations and symmetry breaking phenomena in a radial power-law potential which is close to the realistic Woods-Saxon one up to about the Fermi energy. Using the realistic parametrization of nuclear shapes we explain the origin of the double-humped fission barrier and the asymmetry in the fission isomer shapes by the bifurcations of periodic orbits. The semiclassical origin of the oblate-prolate shape asymmetry and tetrahedral shapes is also suggested within the improved periodic-orbit approach. The enhancement of shell structures at some surface diffuseness and deformation parameters of such shapes are explained by existence of the simple local bifurcations and new non-local bridge-orbit bifurcations in integrable and partially integrable Fermi systems. We obtained good agreement between the semiclassical and quantum shell-structure components of the level density and energy for several surface diffuseness and deformation parameters of the potentials, including their symmetry breaking and bifurcation values.

57 pages, 34 figures

References in corpus (10)

• A further look at prolate dominance in nuclear deformation
• Semiclassical origin of anomalous shell effect for tetrahedral deformation in radial power-law potential model
• Transcritical bifurcations in non-integrable Hamiltonian systems
• Normal forms and uniform approximations for bridge orbit bifurcations
• Asymmetry and Spin-Orbit Effects in Binding Energy in the Effective Nuclear Surface Approximation
• Slope-dependent nuclear-symmetry energy within the effective surface approximation
• Isovector dipole-resonance structure within the effective surface approximation
• Analytic approach to bifurcation cascades in a class of generalized Hénon-Heiles potentials
• Semiclassical treatment of symmetry breaking and bifurcations in a non-integrable potential
• Surface corrections to the moment of inertia and shell structure in finite Fermi systems

Cited by in corpus (4)

• Semiclassical catastrophe theory of simple bifurcations
• Microscopic-macroscopic level densities for low excitation energies
• Semiclassical approaches to nuclear dynamics
• Particle-number fluctuations near the critical point of nuclear matter