Single-particle Energy Levels Research Articles

Mean single-particle potentials and single-particle energies in a microscopic model of the nucleus

A method for calculating mean single-particle potentials and the corresponding single-particle energy levels in nuclei is presented. Specific formulas for these quantities are written for Slater determinant wave functions in the case of polarized orbitals and a central exchange nucleon-nucleon potential featuring a Gaussian radial dependence. The resulting theoretical estimates of single-particle properties of the nuclei considered in the present study are in satisfactory agreement with relevant experimental data.

N-P pairing in nuclei

Variational wavefunctions for treating N-P pairing in the T=1 and T=0 channels are presented. Alpha-like correlations are explicitly included in the wavefunctions and arbitrary single-particle energy level spacings are allowed. A triple projection before variation procedure is used to obtain these wavefunctions. Taking a model system with equally spaced single-particle levels, several features of nuclei near the N=Z line are calculated. A new type of multiple degeneracy is found in nuclei near the N=Z line.

Pairing Correlation Effect on the Zero-Bias Tunneling Spectra of Ultrasmall Superconducting Grains

We study the superconducting pairing correlation (SPC) effect on the resonant tunneling through an ultrasmall metallic grain with a gate electrode. The resonant conductance peaks appearing with an increase or decrease of the gate voltage are accompanied by the transition of the total electron number N on the grain, such as N ↔ N ±1. We focus our attention on the tunneling resonance associated with an odd- N state. In the absence of the SPC effect, the structure of the zero-bias resonant conductance peak for N ↔ N - 1 is equivalent to that for N ↔ N + 1. It is shown that due to the interplay between the SPC effect and the nonuniform spacings of single-particle energy levels, we expect a notable difference between the two peak structures.

Shell-Tunneling Spectroscopy of the Single-Particle Energy Levels of Insulating Quantum Dots

The energy levels of CdSe quantum dots are studied by scanning tunneling spectroscopy. By varying the tip-dot distance, we switch from “shell-filling” spectroscopy (where electrons accumulate in the dot and experience mutual repulsion) to “shell-tunneling” spectroscopy (where electrons tunnel, one at a time, through the dot). Shell-tunneling spectroscopy provides the single-particle energy levels of the CdSe quantum dot. The results of both types of tunneling spectroscopy are compared with pseudopotential many-body calculations.

Transmission through a Quantum Dot with Two Orbitals

Transmission coefficient through a quantum dot, which contains two orbitals, is calculated in the weak-tunneling regime, taking into account the Coulomb interaction within the dot. Transmitted waves through these orbitals acquire phase shifts which differ by π from each other in the present model. The transmission coefficient as a function of gate voltage exhibits symmetric and asymmetric line shapes, depending on temperature T. A nearly symmetric line shape appears in the temperature region of 0.05 \\lesssimkBT/δ\\lesssim0.25, where δ is the single-particle energy level separation in the dot. This behavior is understood by a combined action of the above-mentioned phase difference and the Coulomb interaction. A possibility that this mechanism explains the recent experiment is suggested.

Pseudo spin-orbit potential in relativistic self-consistent models

Physik-Department der Technischen Universitat Munchen, D-85747 Garching, Germany~Received 6 December 1999; published 10 October 2000!The properties of the pseudo spin-orbit potential, in particular those related to its singularity structure, areinvestigated in the relativistic Hartree formalism. The validity of sufficient conditions for the pseudospinsymmetry are also analyzed. We have found a strong influence of the scalar meson mass and the compress-ibility modulus on the single-particle energy level ordering of the pseudospin doublet.PACS number~s!: 24.10.Jv, 21.60.Cs, 21.10.Pc, 24.80.1yI. INTRODUCTION

Chemical potential quantization and Bose-Einstein condensation

In this paper, first of all, we proved if the ideal Bose gas with a finite volume and number of particles has a non-degenerate single-particle energy level n, the chemical potential μ can take the value μn = n and there is a phase transition temperature Tp,n, where n = 0,1,2 Taking 0 ≤ n Tp,n+1. When the temperature T > Tp,n or T ≤ Tp,n+1, μ # n and the most probable occupation number Nn = 0. In the temperature interval Tp,n ≥ T > Tp,n+1, μ = n and 0 ≤ Nn = N - NjsupNn, where Nj is the most probable occupation number in the degenerate level j. Thus, if the finite ideal Bose gas has some non-degenerate single-particle levels, there exists a characteristic temperature Tp = Tp,0. The chemical potential μ is quantized when T ≤ Tp, and this leads to the creation of a macroscopic quantum state (pure state) or Bose-Einstein condensation phase. Tp = Tp,0 is a first-order phase transition point, Tp,n#0 is a zero-order phase transition point. Next, we obtained a new expression of the most probable distribution of the finite ideal Bose gas. In this expression Nj is directly proportional to gj - 1, where gj and Nj are, respectively, the degeneracy and the most probable occupation number in the degenerate level j. This property agrees with what chemical potential can be quantized if there is a non-degenerate level for the finite ideal Bose gas. Finally, using this expression, we defined a micro-partition function M, obtained the statistical expressions of some thermodynamical quantities.

Bose-Einstein condensation of excitons in two dimensions

Bose-Einstein condensation (BEC) is shown to exist for a noninteracting system in two dimensions, provided that the single-particle energy levels have a discrete spectrum below the continuum of extended states. This BEC, unlike that for three-dimensional Bose gases, possesses off-diagonal order only of finite range, and is thus not in violation of the Hohenberg theorem. The observation of such a BEC in the transport properties of excitons moving on the heterointerface of a type-II semiconductor superlattice is suggested, bearing in mind the fact that the random potential fluctuations would give rise to localized states on such surfaces.

Light scattering from self-assembled quantum disks

We present results of calculations and experiments probing the electronic structure of self-assembled Ga 0.8In 0.2As semiconductor quantum dots by inelastic light scattering. The inelastic light scattering signal is strongly enhanced when the energy of the incident light is resonant with the first excited subband. Both the optical phonon and the low frequency scattering spectra exhibit a strong effect of optical alignment, i.e., when the exciting and the scattered light have the same linear polarization. To understand the results of measurements we calculate both the single particle energy levels and excitonic states in the disk. The calculations of the resonant light scattering cross section are interepreted in terms of the one-phonon resonant Raman process involving bulk acoustical phonons interacting with excited subband excitons of the quantum dot.

Quantum chaotic motion of a single particle in heavy nuclei

In the framework of the two-center shell model we calculate the nearest neighbor level spacing distribution and spectral rigidity of single-particle energy levels of heavy nuclei when the shape parameters are changed systematically. In the two cases of the single-particle Hamiltonian with and without the spin-orbit coupling l · s and square angular momentum l 2 terms, the shape parameter regions are determined respectively, in which both of the spacing distribution and spectral rigidity approach the predictions of the Gaussian orthogonal ensemble of random matrix theory. In both cases it is shown that a considerable octupole-like deformation is necessary to induce the chaotic single-particle motion. Moreover, the occurrence of the chaotic motion not only appears in the heavy nuclei with oblate shapes but also in prolate ones with a proper neck. The neck appreciably influences the occurrence of the chaotic motion when the separation between the two centers is medium or larger. It is exhibited that the level repulsion which is strongly related to the nuclear deformation governs the regularity (chaoticity) of the single-particle motion. We find that the l · s term obviously favors the chaotic motion, however, the l 2 term only slightly affects the chaotic motion. In addition, it is implied that when the two terms are taken into account, the chaotic motion occurs even in very elongated nuclei.

The single-particle spectrum and its spacing and curvature distributions in rotating heavy nuclei

For the heavy nucleus 92 238U, the influence of the shape parameters and cranking frequency on single-particle energy levels in a rotating system is examined. It has been found that the level spacing distribution and the two kinds of curvature distributions (with respect to the separation distance and cranking frequency, respectively) of levels individually approach those of the Gaussian unitary ensemble (GUE) in different regions of separation distance and cranking frequency. They, however, share a common parameter region in which they are all close to those of GUE. Furthermore, it is suggested that the chaotic motion in a heavy nucleus is possibly realized under the condition of superdeformation and high spin.

The statistical properties of single-particle levels in rotating heavy nuclei

The single particle-energy levels of U92238 as a function of cranked frequency are given in rotating two-centre shell model. It is found that the curvature distribution approaches the prediction of Gaussian unitary ensemble (GUE) [14] for a certain range of separations between two centers at some cranked frequencies, which is the first support to the prediction in the realistic and complex system like heavy nuclei. Meanwhile, we find that the spacing distributions for various separations have a similar structure when the frequency is high, for which a formulae is suggested to describe this kind of spacing distributions. In addition, we compute the spectral rigidity characterizing the long range correlation of a spectrum.

Fission of metal clusters: A comparison of jellium model calculations and shell correction method calculations

We investigate the fission process Ag2+23 → Ag+12 + Ag+11 in order to compare total energies that calculated by the shell correction method and jellium models. A cavity potential and a Woods-Saxon-type potential are used as the shell potential for the shell correction method, with which the single-particle energy levels are calculated. Shell corrections are obtained by using the Balian-Bloch formula and by smoothing the discrete energy levels in the shell potentials. The jellium model calculations are performed in the framework of the local spin density functional approximation. The conventional jellium model and stabilized jellium model are used. Although the qualitative agreement between the shell correction method calculations and the stabilized jellium calculations is very good, an improvement of the liquid drop energy will be necessary for the satisfactory quantitative agreement. © 1996 John Wiley & Sons, Inc.

Fission of metal clusters: A comparison of jellium model calculations and shell correction method calculations

We investigate the fission process Ag2+23 Ag+12 + Ag+11 in order to compare total energies that calculated by the shell correction method and jellium models. A cavity potential and a Woods-Saxon-type potential are used as the shell potential for the shell correction method, with which the single-particle energy levels are calculated. Shell corrections are obtained by using the Balian-Bloch formula and by smoothing the discrete energy levels in the shell potentials. The jellium model calculations are performed in the framework of the local spin density functional approximation. The conventional jellium model and stabilized jellium model are used. Although the qualitative agreement between the shell correction method calculations and the stabilized jellium calculations is very good, an improvement of the liquid drop energy will be necessary for the satisfactory quantitative agreement. © 1996 John Wiley & Sons, Inc.

Carrier Tunneling in High Magnetic Fields

Proceedings of the XXIV International School of Semiconducting Coinpounds, Jaszowiec 1995. A magnetic field induced coupling is observed between the Landau levels with different quantum number of two GaAs quantum wells separated by a thin (Ga,Al)As tunnel barrier using magneto-photoluminescence-excitation spectroscopy. This coupling cannot be due to a resonance between single particle energy levels, and therefore an explanation is proposed in terms of the Coulomb interaction of magneto-excitons across the thin barrier.

Two-neutrino double-beta decay transition to a 2+ excited state

The Gamow-Teller matrix elements of 2 nu beta beta transitions to a 21+ final excited state has been calculated within the QRPA formalism for 76Ge and 136Xe. The relative stability of the calculation with respect to the particle-particle interaction strength is confirmed; on the other hand, the results are strongly dependent on the choice of the single-particle energy levels. A plausible explanation of such behaviour, originating in the interference of the individual contributions due to the third power of the energy denominator, has been proposed.

Electron states in a quasi-one-dimensional charge channel over liquid helium in the presence of a transverse magnetic field.

Calculations are carried out for single-particle energy levels and wave functions for electrons in a quasi-one-dimensional charge channel formed on the surface of liquid helium. The expressions for the spectrum are obtained for two different orientations of the magnetic field perpendicular to the channel. The conditions for the applicability of the formulas derived are established and they can be used in experimental studies of spectroscopic transitions between

HTSC anomalies as result of the special electron spectrum I. The nature of hole carriers; dc and optical conductivities

The distinctive feature of HTSC electron spectrum is supposed to be the localized pair orbital with single-particle energy level lying at the top of oxygen valence band. The pair level origin is connected with initiation of “negative-U centers” on oxygen atoms at certain sites of HTSC unit cell. Hole carriers in valence band result from thermal excitations of electrons to pair level. Due to pinning of chemical potential at the pair level the hole carriers distribution turns out to be nondegenerated at all concentrations that results in predominance of hole-hole scattering in relaxation processes. The experimental temperature and frequency dependencies of dc and optical conductivities may be explained on such approach.

Stabilized-jellium description of neutral and multiply charged fullerenes C x± 60

A description of neutral and multiply charged fullerenes is proposed based on a stabilized jellium (structureless pseudopotential) approximation for the ionic background and the local density approximation for the σ and π valence electrons. A recently developed shell-correction method is used to calculate total energies and properties of both the neutral and multiply charged anionic and cationic fullerenes. The effect of the icosahedral symmetry is included perturbatively. The calculated single-particle energy level spectrum of C 60 is in good correspondence with experimentally measured ones and previous self-consistent local-density-approximation calculations. For the multiply charged fullerenes, we calculate microscopically the charging energies of C x± 60 for up to x=12 excess charges. A semiclassical interpretation of these results is developed, which views the fullerenes as Coulomb islands possessing a classical capacitance. The calculated values for the first ionization potential and the first electron affinity agree well with the experimental ones. For the second and third ionization potentials, there exist substantial discrepancies in the experimental measurements. Our calculations support the results from charge transfer bracketing experiments and from direct ionization experiments through electron impact. The doubly charged negative ion is found to be very long-lived metastable species, in agreement with observations.

Coulomb blockade and off-resonance tunneling in small electronic systems

The minima of the oscillations of the tunnel conductance through a small electronic system present a rich variety of quantum conduction mechanisms when the charging energy E c and the electrochemical potential difference eV between the resevoirs compete with the single particle energy level separation Δ. We emphasize the strong relation between off-resonance tunneling and elastic co-tunneling in the linear conductance regime while, in the non-linear regime, inelastic co-tunneling has no equivalent for the case of resonant tunneling. We also review the recent experimental results which clearly identify this latter regime and we discuss the intermediate regime, valid for few electron systems, where E c ⋍ Δ.