Shells, orbit bifurcations, and symmetry restorations in Fermi systems
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NUCLEI Theory
Shells, Orbit Bifurcations, and Symmetry Restorations in Fermi Systems∗ A. G. Magner1)** , M. V. Koliesnik1) , and K. Arita2) Received April 4, 2016
Abstract—The periodic-orbit theory based on the improved stationary-phase method within the phasespace 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. Soloviev. 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. DOI: 10.1134/S1063778816060181
1. INTRODUCTION Semiclassical periodic-orbit theory (POT) is a convenient tool for analytical studies of the shell structure in the single-particle level density of finite fermionic systems near the Fermi surface [1–8]. This theory relates the oscillating level density and shell-correction energy to the sum of periodic orbits and their stability characteristics and, thus, gives the analytical quantum–classical correspondence. According to the shell-correction method (SCM) [9, 10], the oscillating part of the total energy of a finite fermion system, the so-called shell-correction energy, is associated with an inhomogeneity of the singleparticle (s.p.) energy levels near the Fermi surface. The SCM is based on Strutinsky’s smoothing procedure to extract the shell components of the level density and energy, which has to be added to the macroscopic parts, in particular, within the Liquid Drop Model (LDM) [11] or Extended Thomas–Fermi (ETF) approach [12]. Deep foundations of the relation of a quasiparticle spectrum near the Fermi surface to the finite many-body fermionic systems with a strong particles’ interaction, such as atomic nuclei, ∗
The text was submitted by the authors in English. Institute for Nuclear Research, NASU, Kiev, Ukraine. 2) Department of Physics, Nagoya Institute of Technology, Japan. ** E-mail: [email protected] 1)
can be found in [13, 14] which are based on the Landau quasiparticles’ theory of Fermi liquids [15, 16]. Depending on the level density at the Fermi energy—and with it the shell-correction en
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