Giant-dipole Resonance and the Deformation of Hot, Rotating Nuclei

The development of nuclear shapes under the extreme conditions of high spin and/or temperature is examined. Scaling properties are used to demonstrate universal properties of both thermal expectation values of nuclear shapes as well as the minima of the free energy, which can be used to understand the Jacobi transition. A universal correlation between the width of the giant dipole resonance and quadrupole deformation is found, providing a novel probe to measure the nuclear deformation in hot nuclei.Comment: 6 pages including 6 figures. To appear in Phys. Rev. Lett. Revtex

Quantum and semiclassical study of magnetic anti-dots

We study the energy level structure of two-dimensional charged particles in inhomogeneous magnetic fields. In particular, for magnetic anti-dots the magnetic field is zero inside the dot and constant outside. Such a device can be fabricated with present-day technology. We present detailed semiclassical studies of such magnetic anti-dot systems and provide a comparison with exact quantum calculations. In the semiclassical approach we apply the Berry-Tabor formula for the density of states and the Borh-Sommerfeld quantization rules. In both cases we found good agreement with the exact spectrum in the weak magnetic field limit. The energy spectrum for a given missing flux quantum is classified in six possible classes of orbits and summarized in a so-called phase diagram. We also investigate the current flow patterns of different quantum states and show the clear correspondence with classical trajectories.Comment: 14 pages, 13 figure

A Particle number conserving shell-correction method

The shell correction method is revisited. Contrary to the traditional Strutinsky method, the shell energy is evaluated by an averaging over the number of particles and not over the single-particle energies, which is more consistent with the definition of the macroscopic energy. In addition, the smooth background is subtracted before averaging the sum of single-particle energies, which significantly improves the plateau condition and allows to apply the method also for nuclei close to the proton or neutron drip lines. A significant difference between the shell correction energy obtained with the traditional and the new method is found in particular for highly degenerated single-particle spectra (as i.e. in magic nuclei) while for deformed nuclei (where the degeneracy is lifted to a large extent) both estimates are close, except in the region of super or hyper-deformed states.Comment: 11 pages in LaTeX, 7 figure

Uniform approximations for pitchfork bifurcation sequences

In non-integrable Hamiltonian systems with mixed phase space and discrete symmetries, sequences of pitchfork bifurcations of periodic orbits pave the way from integrability to chaos. In extending the semiclassical trace formula for the spectral density, we develop a uniform approximation for the combined contribution of pitchfork bifurcation pairs. For a two-dimensional double-well potential and the familiar H\'enon-Heiles potential, we obtain very good agreement with exact quantum-mechanical calculations. We also consider the integrable limit of the scenario which corresponds to the bifurcation of a torus from an isolated periodic orbit. For the separable version of the H\'enon-Heiles system we give an analytical uniform trace formula, which also yields the correct harmonic-oscillator SU(2) limit at low energies, and obtain excellent agreement with the slightly coarse-grained quantum-mechanical density of states.Comment: LaTeX, 31 pp., 18 figs. Version (v3): correction of several misprint

Semiclassical description of shell effects in finite fermion systems

A short survey of the semiclassical periodic orbit theory, initiated by M. Gutzwiller and generalized by many other authors, is given. Via so-called semiclassical trace formmulae, gross-shell effects in bound fermion systems can be interpreted in terms of a few periodic orbits of the corresponding classical systems. In integrable systems, these are usually the shortest members of the most degenerate families or orbits, but in some systems also less degenerate orbits can determine the gross-shell structure. Applications to nuclei, metal clusters, semiconductor nanostructures, and trapped dilute atom gases are discussed.Comment: LaTeX (revteX4) 6 pages; invited talk at Int. Conference "Finite Fermionic Systems: Nilsson Model 50 Years", Lund, Sweden, June 14-18, 200

Nuclear prolate-shape dominance with the Woods-Saxon potential

We study the prolate-shape predominance of the nuclear ground-state deformation by calculating the masses of more than two thousand even-even nuclei using the Strutinsky method, modified by Kruppa, and improved by us. The influences of the surface thickness of the single-particle potentials, the strength of the spin-orbit potential, and the pairing correlations are investigated by varying the parameters of the Woods-Saxon potential and the pairing interaction. The strong interference between the effects of the surface thickness and the spin-orbit potential is confirmed to persist for six sets of the Woods-Saxon potential parameters. The observed behavior of the ratios of prolate, oblate, and spherical nuclei versus potential parameters are rather different in different mass regions. It is also found that the ratio of spherical nuclei increases for weakly bound unstable nuclei. Differences of the results from the calculations with the Nilsson potential are described in detail.Comment: 16 pages, 17 figure

Periodic-Orbit Bifurcations and Superdeformed Shell Structure

We have derived a semiclassical trace formula for the level density of the three-dimensional spheroidal cavity. To overcome the divergences occurring at bifurcations and in the spherical limit, the trace integrals over the action-angle variables were performed using an improved stationary phase method. The resulting semiclassical level density oscillations and shell-correction energies are in good agreement with quantum-mechanical results. We find that the bifurcations of some dominant short periodic orbits lead to an enhancement of the shell structure for "superdeformed" shapes related to those known from atomic nuclei.Comment: 4 pages including 3 figure

Eigenvalue spectrum for single particle in a spheroidal cavity: A Semiclassical approach

Following the semiclassical formalism of Strutinsky et al., we have obtained the complete eigenvalue spectrum for a particle enclosed in an infinitely high spheroidal cavity. Our spheroidal trace formula also reproduces the results of a spherical billiard in the limit $\eta\to1.0$. Inclusion of repetition of each family of the orbits with reference to the largest one significantly improves the eigenvalues of sphere and an exact comparison with the quantum mechanical results is observed upto the second decimal place for $kR_{0}\geq{7}$. The contributions of the equatorial, the planar (in the axis of symmetry plane) and the non-planar(3-Dimensional) orbits are obtained from the same trace formula by using the appropriate conditions. The resulting eigenvalues compare very well with the quantum mechanical eigenvalues at normal deformation. It is interesting that the partial sum of equatorial orbits leads to eigenvalues with maximum angular momentum projection, while the summing of planar orbits leads to eigenvalues with $L_z=0$ except for L=1. The remaining quantum mechanical eigenvalues are observed to arise from the 3-dimensional(3D) orbits. Very few spurious eigenvalues arise in these partial sums. This result establishes the important role of 3D orbits even at normal deformations.Comment: 17 pages, 7 ps figure

Closed orbits and spatial density oscillations in the circular billiard

We present a case study for the semiclassical calculation of the oscillations in the particle and kinetic-energy densities for the two-dimensional circular billiard. For this system, we can give a complete classification of all closed periodic and non-periodic orbits. We discuss their bifurcations under variation of the starting point r and derive analytical expressions for their properties such as actions, stability determinants, momentum mismatches and Morse indices. We present semiclassical calculations of the spatial density oscillations using a recently developed closed-orbit theory [Roccia J and Brack M 2008 Phys. Rev. Lett. 100 200408], employing standard uniform approximations from perturbation and bifurcation theory, and test the convergence of the closed-orbit sum.Comment: LaTeX, 42 pp., 17 figures (24 *.eps files, 1 *.tex file); final version (v3) to be published in J. Phys.

The contrasting fission potential-energy structure of actinides and mercury isotopes

Fission-fragment mass distributions are asymmetric in fission of typical actinide nuclei for nucleon number $A$ in the range $228 \lnsim A \lnsim 258$ and proton number $Z$ in the range $90\lnsim Z \lnsim 100$. For somewhat lighter systems it has been observed that fission mass distributions are usually symmetric. However, a recent experiment showed that fission of $^{180}$Hg following electron capture on $^{180}$Tl is asymmetric. We calculate potential-energy surfaces for a typical actinide nucleus and for 12 even isotopes in the range $^{178}$Hg--$^{200}$Hg, to investigate the similarities and differences of actinide compared to mercury potential surfaces and to what extent fission-fragment properties, in particular shell structure, relate to the structure of the static potential-energy surfaces. Potential-energy surfaces are calculated in the macroscopic-microscopic approach as functions of fiveshape coordinates for more than five million shapes. The structure of the surfaces are investigated by use of an immersion technique. We determine properties of minima, saddle points, valleys, and ridges between valleys in the 5D shape-coordinate space. Along the mercury isotope chain the barrier heights and the ridge heights and persistence with elongation vary significantly and show no obvious connection to possible fragment shell structure, in contrast to the actinide region, where there is a deep asymmetric valley extending from the saddle point to scission. The mechanism of asymmetric fission must be very different in the lighter proton-rich mercury isotopes compared to the actinide region and is apparently unrelated to fragment shell structure. Isotopes lighter than $^{192}$Hg have the saddle point blocked from a deep symmetric valley by a significant ridge. The ridge vanishes for the heavier Hg isotopes, for which we would expect a qualitatively different asymmetry of the fragments.Comment: 8 pages, 9 figure