Quantum Shell Structure Research Articles

Core electrons and specific heat capacity in the fast electron heating of solids

The accuracy with which the Thomas–Fermi (TF) model can provide electronic specific heat capacities for use in calculations relevant to fast electron transport in laser-irradiated solids is examined. It is argued that the TF model, since it neglects the quantum shell structure, is likely to be significantly inaccurate for low- and intermediate-Z materials. This argument is supported by examining the results of calculations using more sophisticated methods that account for degeneracy, the quantum shell structure, and other non-ideal corrections. It is further shown that the specific heat capacity curve generated by this more advanced treatment leads to substantial (factor of two) changes in fast electron transport simulations relative to similar modeling based upon the TF model.

Interaction effects in quantum dots in a vertical magnetic field

The Hartree-Fock approximation has been used to compute the properties of parabolic two-dimensional quantum dots under a perpendicular magnetic field. The addition energies for vertical quantum dots up to N = 20 electrons is analysed at different strengths of the effective electron-electron interaction. A remarkable agreement between experimental data and results for the addition energy for N = 2,3,4, 5 electrons exhibits an important role of the screening of the effective interaction for interpretation of the ground state transitions in the magnetic field. We suggest a recipe to determine the orbital momenta of the QD ground states. We show that quantum shell structure of quantum dots survives only at small magnetic fields.

Linear optical properties of the semiconductor quantum shell

We present the analysis of a single exciton eigenstate in a spherical quantum shell and its linear optical absorption by using the parabolic band model and a matrix diagonalization method. The result shows that the confinement effect for an exciton in a spherical quantum shell structure is stronger than that in a spherical quantum dot structure, in general. This attributes mainly to the exclusion of $2s$ single particle state in forming an exciton state in a quantum shell. The emission spectra from an exciton in a quantum shell would show blueshifts compared to those in a quantum dot. The eigenlevels of an exciton state in a quantum shell are much denser than those in a quantum dot. We found that the total absorption is proportional to the volume of the structure, as well.

Temperature dependence of density profiles for a cloud of noninteracting fermions moving inside a harmonic trap in one dimension

We extend to finite temperature a Green's-function method that was previously proposed to evaluate ground-state properties of mesoscopic clouds of noninteracting fermions moving under harmonic confinement in one dimension. By calculations of the particle and kinetic-energy density profiles, we illustrate the role of thermal excitations in smoothing out the quantum shell structure of the cloud and in spreading the particle spill out from quantum tunnel at the edges. We also discuss the approach of the exact density profiles to the predictions of a semiclassical model often used in the theory of confined atomic gases at finite temperature.

Regular and chaotic motion in axially deformed nuclei.

The combined effect of an octupole and hexadecapole term, when added to a strongly deformed axial harmonic oscillator potential, is carefully studied. The problem is nonintegrable, which calls for a thorough classical analysis in order to understand the quantum mechanical results. Shell structure which is found for particular combinations of the deformation parameters are explained in terms of dominant classical periodic orbits. Using the ``removal of resonances'' method as an approximation, explicit expressions in terms of the deformation parameters are obtained for effective winding numbers, which in turn generate the quantum shell structure. A mutual cancellation of the octupole and hexadecapole deformation in prolate superdeformed systems has been discovered. Strongly oblate deformed potentials can yield shell structure only when even higher multipoles are added while prolate potentials can support shell structure for arbitrary higher multipoles.

Classical bifurcation and enhancement of quantum shells: Systematic analysis of reflection-asymmetric deformed oscillator

Correspondence between classical periodic orbits and quantum shell structure is investigated for a reflection-asymmetric deformed oscillator model as a function of quadrupole and octupole deformation parameters. Periodic orbit theory reveals several aspects of quantum level structure for this non-integrable system. Good classical- quantum correspondence is obtained in the Fourier transform of the quantum level density, and importance of periodic orbit bifurcation is demonstrated. Systematic survey of the local minima of shell energies in the two-dimensional deformation parameter space shows that prominent shell structures do emerge at finite values of the octupole parameter. Correspondences between the regions exhibiting strong shell effects and the classical bifurcation lines are investigated, and significance of these bifurcations is indicated.

Alkali metal clusters and the jellium model

The application of the jellium model and the resulting quantum shell structure for metal clusters is examined in the light of theoretical calculations and experimental observations. Objections to the jellium model by Kappes, Schar, Rädi and Schumacher appear to be based on misunderstandings of the model and on inadequate experiments.

Constant Energy Differences in Atomic Structure

Constant second-order energy differences for the hydrogen isoelectronic series, as obtained from optical spectra, were examined. A distinct pattern consistent with the quantum shell structure of the Periodic Table of elements was revealed. The relationship between periodicity and atomic structure is discussed. (C.H.)