145 research outputs found
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 and an
Aharonov-Bohm magnetic flux. Numerical results are presented and compared with
known results for models with . 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 . We also discuss
the power parameter 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 U(n,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 U(n,f). Calculations showed that in the first stage of this fission reaction,
the isotopes Ge and 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
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
- …