Single-particle Level Spacing Research Articles

Magnetic dipole absorption of radiation in small conducting particles

We give a theoretical treatment of magnetic dipole absorption of electromagnetic radiation in small conducting particles, at photon energies which are large compared to the single-particle level spacing, and small compared to the plasma frequency. We discuss both diffusive and ballistic electron dynamics for particles of arbitrary shape. The conductivity becomes non-local when the frequency is smaller than the frequency characterizing the transit of electrons from one side of the particle to the other, but in the diffusive case plays no role in determining the absorption coefficient. In the ballistic case, the absorption coefficient is proportional to for , but is a decreasing function of for .

Quasiatomic Fine Structure and Selection Rules in Quantum Dots

We probe the electronic shell structure of quasiatomic systems, realized in GaAs-AlGaAs quantum dots, by resonant Raman spectroscopy. We observe a series of discrete spin-density excitations, whose energies are very close to single-particle level spacings in a quantum dot. The combined information from experiments at different wave vectors in the lateral direction and from investigations with applied magnetic fields reveals a distinct set of Raman allowed transitions $(\ensuremath{\Delta}n,\ensuremath{\Delta}m)$, where changes $\ensuremath{\Delta}n$ and $\ensuremath{\Delta}m$ are changes in radial and angular momentum quantum numbers, respectively.

Co-tunneling of the charge through a 2-D electron island

A double barrier Single Electron Transistor is realized in two dimensions by confining the 2-D electron gas of a GaAs/GaAlAs heterojunction to a small island by means of Schottky gates. Two gates provide adjustable tunnel barriers and a central gate controls the electron number in the island. The island has small single-particle energy level spacing and forms a metallic island. Periodic conductance oscillations characteristic of Coulomb blockade are observed when the central gate voltage is varied. The ability to vary the tunnel conductance allows us to study the basic physics of the Coulomb blockade: our results show that the quantum charge fluctuation mechanism which limits the tunneling blockade at low temperature is of second order in tunnel barrier transparencies in agreement with the charge Macroscopic Quantum Tunneling (q-MQT) or co-tunneling model.

Tb147and proton single particle states nearZ=64

Proton single particle level spacings near $Z=64$ are deduced from an analysis of low-lying levels in $^{145}\mathrm{Eu}$, using a pairing force as the residual interaction. Two forms for the pairing force are explored. Using this spectrum, high spin states in $^{144}\mathrm{Sm}$, $^{146}\mathrm{Gd}$, and $^{148}\mathrm{Dy}$ are calculated and compared with known experimental values when possible. The low-lying states in $^{143}\mathrm{Pm}$ and $^{147}\mathrm{Tb}$ are also calculated. The need for experimental data on $^{147}\mathrm{Tb}$ is emphasized.NUCLEAR STRUCTURE $Z\ensuremath{\approx}64$, proton single particle states, pairing force, high spin states.

Isospin mixing inF19

Isospin mixing in the yrast $I=\frac{5}{{2}^{+}}$ $T=\frac{1}{2}$ level has been calculated assuming an isoscalar nucleonnucleon interaction and the single-particle level spacings observed in $^{17}\mathrm{O}$ and $^{17}\mathrm{F}$. Results are presented for both the (${d}_{\frac{5}{2}}$,${s}_{\frac{1}{2}}$) and two variants of the (${d}_{\frac{5}{2}}$,${s}_{\frac{1}{2}}$,${d}_{\frac{3}{2}}$) model spaces. The experimental value does not require the introduction of a charge symmetry or charge independence breaking nucleon-nucleon interaction.NUCLEAR STRUCTURE Isospin mixing in $^{19}\mathrm{F}$ calculated.

Exponential model with pairing attenuation and the backbending phenomenon

Rotational energy calculations with an exponential dependence of the nuclear moment of inertia on pairing correlations coupled with an explicit spin dependence of the effective pairing gap analogous to that used in superconductivity give an excellent fit to the experimental data on excitation energies of yrast band levels in well-deformed even-even nuclei and also reproduce the backbending feature satisfactorily. The variation of the pairing gap parameter with spin is found to be gradual and smooth as compared to the abrupt variation evidenced in the pairing collapse treatment. Variations of the limiting moments of inertia parameter with mass number derived from our model exactly match with those coming out of the cranking model calculations for neutrons and are in no way related to the proton results; for lighter rare earth nuclei also the fluctuations in the values of the moment of inertia are found to correspond to those of the neutron single particle level spacings in this region.

Level Density Based on the Degenerate Single Particle Levels

Level density for the equidistant level scheme is derived with keeping the degeneracy of the single particle levels. The derivation is sufficiently accurate within the framework of the model, and the only approximation introduced is the saddle point approximation in the Darwin-Fowler integral. The results are discussed in comparison with those by the Rosenzweig approximation and those of the continuous approximations. It is found that the Rosenzweig approximation is accurate for a rather broad range of the nuclear temperature in the case of large systems. The deviation from the more accurate calculation appears only below the excitation energy of a few times the single particle level spacing. Discussion is presented on the quantitative relationship among the continuous approximation, the Rosenzweig model and the present method, in the light of the result of the level counting.

Analytical Approximation of the Combinatorial Calculation of Nuclear Level Densities

An exact numerical solution of the spin-dependent level-density problem for a spherical shell-model nucleus with realistic single-particle level spacings is used to investigate the validity of analytical expressions based on approximate treatments of the model. With parameters chosen by reference to the numerical values, at least one of the analytical expressions proposed in the literature results in adequate fits to these values. Fitted parameters for the region $Z=25 \mathrm{to} 59$ and $N=25 \mathrm{to} 91$ are presented, and their physical interpretation is discussed. The dependence of the parameters on the number of nucleons of either kind is strongly affected by the shell structure of the nucleus. The level-density parameter $a$ is not simply proportional to the mass number $A$, and the spin distribution parameter can not be represented by the rigid-body moment of inertia, nor by any other monotonic function of $A$. Both parameters vary smoothly across the major proton and neutron shells, and the contributions of the two types of nucleons are additive.

Interpretation of isomer ratios in nuclear reactions with Fermi-gas and superconductor models

Nuclear temperatures and isomer ratios are calculated on the basis of a recent semi-quantitative theory for a Fermi gas with pairing correlations analogous to those of a superconducting metal. Although the superconductor model predicts only a slight energy dependence of the nuclear temperature at low-excitation energies, in agreement with some, but not all experimental results, the single-particle level spacings required to reproduce the absolute values of the experimental nuclear temperatures are considerably smaller than expected. The superconductor model predicts a reduction from the rigid-body moment of inertia which is consistent with isomer ratios for nuclei with an odd number of nucleons. However, some evidence is presented to show that the superconductor model overestimates the reduction in the moment of inertia for odd nuclei †††. Nuclear temperatures and isomer ratios are calculated also with a shifted Fermi gas model. In this model the Fermi gas predictions are modified to compensate for pairing interactions by simply re-defining excitation energies relative to a characteristic level. In the present calculations we assume the characteristic level of an odd nucleus is identical with its ground state. For odd nuclei the experimental isomer ratios are in good agreement with predictions of the Fermi gas theory with a rigid body moment of inertia. The shifted Fermi gas model gives better agreement with nuclear temperatures than the superconductor model, but gives too large a moment of inertia for odd-mass nuclei. The degree of agreement between the predictions of the above superconductor theory and the various experimental data for all types of nuclei is unimproved over the simpler Fermi gas theory.

Neutron evaporation and level densities in excited nuclei

The theory of a cascade neutron evaporation process is derived in detail in a form suited to the treatment of highly excited nuclei which have a continuous distribution of excitation energies following a primary direct interaction. The results are found to give good agreement with neutron spectra of nuclei following bombardment with 190 MeV protons observed by Gross. Data from medium energy neutron reactions, thermal energy neutron resonances, and heavy ion reaction experiments are compared. Formulae are derived in an appendix for the effect on the level density of a gap in the single particle level spacing at the Fermi level.

Experimental Single-Particle Level Spacings in the Region of the1f72Shell

A review is presented of experimental information about the relative position of single-particle states in odd-$A$ nuclei in the region of the $1{f}_{\frac{7}{2}}$ shell. In Appendix I a discussion of the assignments is given for all the included level schemes. Some striking empirical regularities in nuclei with odd nucleon numbers g28 are mentioned in Appendix II.