Semiclassical moment of inertia shell-structure within the phase-space approach

Gorpinchenko, D. V.; Magner, A. G.; Bartel, J.; Błocki, J.

doi:10.1088/0031-8949/90/11/114008

Cited by 5 publications

(42 citation statements)

References 31 publications

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“…(The particular choice of a Gaussian form of the averaging function is immaterial and guided only by mathematical simplicity.) Applying this procedure to the semiclassical level density (32), one obtains (16) for the averaged level-density shell correction δg Γ,scl (E) [3,7,8].…”

Section: Discussion Of Resultsmentioning

confidence: 99%

“…The shell-correction energy δU , i.e., the oscillating part of the total energy U of a system of N fermions occupying the lowest quantum levels in a given potential, can be expressed in terms of the oscillating components δg PO (E) at the Fermi energy E = E F of the semiclassical level density (32) and (9), as in [3,5,7,8], see also (18) for the shell-correction energy δU . We are taking into account the spin degeneracy factor 2 in (18).…”

Section: Discussion Of Resultsmentioning

confidence: 99%

“…The coefficients ǫ(E) and a(E) in (33) are also continuous functions of the energy E through all stationary points (POs). Note also that our ISPM expression (32) for the shell correction to the level density is a sum of separate contributions of all involved POs, and a coarse-graining over the energy E (cf. below) may therefore be performed analytically.…”

Section: Trace Formulae Symmetry Breaking and Bifurcationsmentioning

confidence: 99%

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Shells, orbit bifurcations, and symmetry restorations in Fermi systems

2016

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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 oblateprolate shape asymmetry and tetrahedral shapes is also suggested within the improved periodicorbit 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 nonlocal 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.

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Section: Discussion Of Resultsmentioning

confidence: 99%

Section: Discussion Of Resultsmentioning

confidence: 99%

Section: Trace Formulae Symmetry Breaking and Bifurcationsmentioning

confidence: 99%

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Shells, orbit bifurcations, and symmetry restorations in Fermi systems

2016

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“…The small relatively surface and curvature corrections can be taken into account in the vibration energies (114) and sum rules (117)…”

Section: Vibration Energies and Sum Rulesmentioning

confidence: 99%

Semiclassical approaches to nuclear dynamics

2017

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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

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“…This density g can be written, like traditionally done, as [12][13][14] g scl (r, p; ε) = g ETF (r, p; ε) + δg(r, p; ε) , (3) where g ETF (r, p; ε) is the ETF component and δg(r, p; ε) the shell correction (see Ref. [13] for the relation of g scl (r, p; ε) to the Gutzwiller Green's function expansion over classical trajectories).…”

Section: Cranking Model and Shell-structurementioning

confidence: 99%

Surface corrections to the moment of inertia and shell structure in finite Fermi systems

et al. 2016

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The moment of inertia for nuclear collective rotations is derived within a semiclassical approach based on the Inglis cranking and Strutinsky shell-correction methods, improved by surface corrections within the nonperturbative periodic-orbit theory.For adiabatic (statistical-equilibrium) rotations it was approximated by the generalized rigid-body moment of inertia accounting for the shell corrections of the particle density. An improved phase-space trace formula allows to express the shell components of the moment of inertia more accurately in terms of the free-energy shell correction. Evaluating their ratio within the extended Thomas-Fermi effective-surface approximation, one finds good agreement with the quantum calculations.

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Semiclassical moment of inertia shell-structure within the phase-space approach

Cited by 5 publications

References 31 publications

Shells, orbit bifurcations, and symmetry restorations in Fermi systems

Shells, orbit bifurcations, and symmetry restorations in Fermi systems

Semiclassical approaches to nuclear dynamics

Surface corrections to the moment of inertia and shell structure in finite Fermi systems

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