Neutron stars and the fermionic Casimir effect

The inner crust of neutron stars consists of nuclei of various shapes immersed in a neutron gas and stabilized by the Coulomb interaction in the form of a crystal lattice. The scattering of neutrons on nuclear inhomegeneities leads to the quantum correction to the total energy of the system. This correction resembles the Casimir energy and turns out to have a large influence on the structure of the crust.Comment: 6 pages, 1 figure, presented at the Fifth Workshop on Quantum Field Theory under the Influence of External Conditions, Leipzig, Germany, September 10-15, 2001, to appear in Int. J. Mod. Phys.

Semiclassical Quantization for the Spherically Symmetric Systems under an Aharonov-Bohm magnetic flux

The semiclassical quantization rule is derived for a system with a spherically symmetric potential $V(r) \sim r^{\nu}$ $(-2<\nu <\infty)$ and an Aharonov-Bohm magnetic flux. Numerical results are presented and compared with known results for models with $\nu = -1,0,2,\infty$. It is shown that the results provided by our method are in good agreement with previous results. One expects that the semiclassical quantization rule shown in this paper will provide a good approximation for all principle quantum number even the rule is derived in the large principal quantum number limit $n \gg 1$. We also discuss the power parameter $\nu$ dependence of the energy spectra pattern in this paper.Comment: 13 pages, 4 figures, some typos correcte

Mean-field description of ground-state properties of drip-line nuclei. (I) Shell-correction method

A shell-correction method is applied to nuclei far from the beta stability line and its suitability to describe effects of the particle continuum is discussed. The sensitivity of predicted locations of one- and two-particle drip lines to details of the macroscopic-microscopic model is analyzed.Comment: 22 REVTeX pages, 13 uuencoded postscript figures available upon reques

Semiclassical Trace Formulas for Noninteracting Identical Particles

We extend the Gutzwiller trace formula to systems of noninteracting identical particles. The standard relation for isolated orbits does not apply since the energy of each particle is separately conserved causing the periodic orbits to occur in continuous families. The identical nature of the particles also introduces discrete permutational symmetries. We exploit the formalism of Creagh and Littlejohn [Phys. Rev. A 44, 836 (1991)], who have studied semiclassical dynamics in the presence of continuous symmetries, to derive many-body trace formulas for the full and symmetry-reduced densities of states. Numerical studies of the three-particle cardioid billiard are used to explicitly illustrate and test the results of the theory.Comment: 29 pages, 11 figures, submitted to PR

Group theoretical analysis of symmetry breaking in two-dimensional quantum dots

We present a group theoretical study of the symmetry-broken unrestricted Hartree-Fock orbitals and electron densities in the case of a two-dimensional N-electron single quantum dot (with and without an external magnetic field). The breaking of rotational symmetry results in canonical orbitals that (1) are associated with the eigenvectors of a Hueckel hamiltonian having sites at the positions determined by the equilibrium molecular configuration of the classical N-electron problem, and (2) transform according to the irreducible representations of the point group specified by the discrete symmetries of this classical molecular configuration. Through restoration of the total-spin and rotational symmetries via projection techniques, we show that the point-group discrete symmetry of the unrestricted Hartree-Fock wave function underlies the appearance of magic angular momenta (familiar from exact-diagonalization studies) in the excitation spectra of the quantum dot. Furthermore, this two-step symmetry-breaking/symmetry-restoration method accurately describes the energy spectra associated with the magic angular momenta.Comment: A section VI.B entitled "Quantitative description of the lowest rotational band" has been added. 16 pages. Revtex with 10 EPS figures. A version of the manuscript with high quality figures is available at http://calcite.physics.gatech.edu/~costas/uhf_group.html For related papers, see http://www.prism.gatech.edu/~ph274c

Collinear cluster tripartition as sequential binary fission in the 235^{235}U(nth_{\rm th},f) reaction

The mechanism leading to the formation of the observed products of the collinear cluster tripartition is carried out within the framework of the model based on the dinuclear system concept. The yield of fission products is calculated using the statistical model based on the driving potentials for the fissionable system. The minima of potential energy of the decaying system correspond to the charge numbers of the products which are produced with large probabilities in the sequential fission (partial case of the collinear cluster tripartition) of the compound nucleus. The realization of this mechanism supposes the asymmetric fission channel as the first stage of sequential mechanism. It is shown that only the use of the driving potential calculated by the binding energies with the shell correction allows us to explain the yield of the true ternary fission products. The theoretical model is applied to research collinear cluster tripartition in the reaction $^{235}$U(n$_{\rm th}$,f). Calculations showed that in the first stage of this fission reaction, the isotopes $^{82}$Ge and $^{154}$Nd are formed with relatively large probabilities and in the second stage of sequential fission of the isotope Nd mainly Ni and Ge are formed. This is in agreement with the yield of the isotope $^{68}$Ni which is observed as the product of the collinear cluster tripartition in the experiment.Comment: 20 pages, 9 figure

Enhanced T-odd P-odd Electromagnetic Moments in Reflection Asymmetric Nuclei

Collective P- and T- odd moments produced by parity and time invariance violating forces in reflection asymmetric nuclei are considered. The enhanced collective Schiff, electric dipole and octupole moments appear due to the mixing of rotational levels of opposite parity. These moments can exceed single-particle moments by more than two orders of magnitude. The enhancement is due to the collective nature of the intrinsic moments and the small energy separation between members of parity doublets. In turn these nuclear moments induce enhanced T- and P- odd effects in atoms and molecules. First a simple estimate is given and then a detailed theoretical treatment of the collective T-, P- odd electric moments in reflection asymmetric, odd-mass nuclei is presented and various corrections evaluated. Calculations are performed for octupole deformed long-lived odd-mass isotopes of Rn, Fr, Ra, Ac and Pa and the corresponding atoms. Experiments with such atoms may improve substantially the limits on time reversal violation.Comment: 28 pages, Revte

Energetics, forces, and quantized conductance in jellium modeled metallic nanowires

Energetics and quantized conductance in jellium modeled nanowires are investigated using the local density functional based shell correction method, extending our previous study of uniform in shape wires [C. Yannouleas and U. Landman, J. Phys. Chem. B 101, 5780 (1997)] to wires containing a variable shaped constricted region. The energetics of the wire (sodium) as a function of the length of the volume conserving, adiabatically shaped constriction leads to formation of self selecting magic wire configurations. The variations in the energy result in oscillations in the force required to elongate the wire and are directly correlated with the stepwise variations of the conductance of the nanowire in units of 2e^2/h. The oscillatory patterns in the energetics and forces, and the correlated stepwise variation in the conductance are shown, numerically and through a semiclassical analysis, to be dominated by the quantized spectrum of the transverse states at the narrowmost part of the constriction in the wire.Comment: Latex/Revtex, 11 pages with 5 Postscript figure

Formation and control of electron molecules in artificial atoms: Impurity and magnetic-field effects

Interelectron interactions and correlations in quantum dots can lead to spontaneous symmetry breaking of the self-consistent mean field resulting in formation of Wigner molecules. With the use of spin-and-space unrestricted Hartree-Fock (sS-UHF) calculations, such symmetry breaking is discussed for field-free conditions, as well as under the influence of an external magnetic field. Using as paradigms impurity-doped (as well as the limiting case of clean) two-electron quantum dots (which are analogs to helium-like atoms), it is shown that the interplay between the interelectron repulsion and the electronic zero-point kinetic energy leads, for a broad range of impurity parameters, to formation of a singlet ground-state electron molecule, reminiscent of the molecular picture of doubly-excited helium. Comparative analysis of the conditional probability distributions for the sS-UHF and the exact solutions for the ground state of two interacting electrons in a clean parabolic quantum dot reveals that both of them describe formation of an electron molecule with similar characteristics. The self-consistent field associated with the triplet excited state of the two-electron quantum dot (clean as well as impurity-doped) exhibits symmetry breaking of the Jahn-Teller type, similar to that underlying formation of nonspherical open-shell nuclei and metal clusters. Furthermore, impurity and/or magnetic-field effects can be used to achieve controlled manipulation of the formation and pinning of the discrete orientations of the Wigner molecules. Impurity effects are futher illustrated for the case of a quantum dot with more than two electrons.Comment: Latex/Revtex, 10 pages with 4 gif figures. Small changes to explain the difference between Wigner and Jahn-Teller electron molecules. A complete version of the paper with high quality figures inside the text is available at http://shale.physics.gatech.edu/~costas/qdhelium.html For related papers, see http://www.prism.gatech.edu/~ph274c

Garvey-Kelson Relations for Nuclear Charge Radii

The Garvey-Kelson relations (GKRs) are algebraic expressions originally developed to predict nuclear masses. In this letter we show that the GKRs provide a fruitful framework for the prediction of other physical observables that also display a slowly-varying dynamics. Based on this concept, we extend the GKRs to the study of nuclear charge radii. The GKRs are tested on 455 out of the approximately 800 nuclei whose charge radius is experimentally known. We find a rms deviation between the GK predictions and the experimental values of only 0.01 fm. This should be contrasted against some of the most successful microscopic models that yield rms deviations almost three times as large. Predictions - with reliable uncertainties - are provided for 116 nuclei whose charge radius is presently unknown.Comment: 4 pages and 3 figure