Shell Structure Effects Research Articles

Energetics of small clusters of stabilized jellium: Continuum and shell-structure effects

We evaluate binding energies, ionization energies, and second-order energy differences as functions of valence electron number for small spherical clusters of stabilized jellium, using the Kohn–Sham equations with the local-spin-density (LSD) approximation. Cohesive energies are also reported. A comparison is made with semiclassical formulas (liquid drop model and Padé approximant, with surface and curvature coefficients derived from first principles). These formulas nicely average the shell-structure oscillations of the energy, which are found to be almost the same as for ordinary jellium. Spherical clusters with 1, 7, and 9 electrons have binding energies very close to those of the semiclassical predictions. © 1993 John Wiley & Sons, Inc.

A Spike of 9482Mo in Yields of Uranium Spontaneous Fission An Extension of Shell Structure Effect.

The investigations of the isotopic abundance ratios of molybdenum in zircon have shown that the molybdenum isotopic composition obtained reflects two effects: (1) spontaneous fission of 23892U contained in the zircon and (2) double beta decay of 9640Zr. Interestingly, however, the products due to the spontaneous fission appear to have a strange large excess (spike) of 9842Mo. It intrigues us that 92 minus 42 leaves 50, one of the outstanding magic numbers. It is suggested in the present communication that the strange spike of 9842Mo in question can result from a special type of sontaneous fission having essential bearings on the magic number 50 of protons and the “magical” numbers 58 and 92 of neutrons.

Mesonic weak decays of Λ- and ΛΛ-hypernuclei

Systematic estimates of pionic decays of light-to-heavy hypernuclei are presented with the discussion on the effects of shell-structure, Pauli blocking and pion distortion. For light Λ- and ΛΛ-hypernuclei, a practical method is proposed to calculate realistically the continuum pion spectra for three-body decay modes.

Semiclassical approximation for the isotopic shift of charge radii in Ca isotopes

The peculiar behavior of the rms-charge and mass radii of the Ca isotopes is explained by current approaches. Here these approaches are supplemented by microscopic calculations within the isomorphic shell model. The model verifies the trend of the data correctly, as a result of shell structure (particle–hole) and deformation effects. These results involve two numerical (not adjustable) parameters and are quantitatively at least equally as good as those of the best available theoretical calculations. In the case of 41Ca, however, a further investigation is required.

Liquid-drop model for crystalline metals: Vacancy-formation, cohesive, and face-dependent surface energies.

The energy of a metallic crystal is expressed as a sum of volume, surface, and curvature terms. The fully self-consistent solution of a simplified problem shows that, in the absence of shell-structure effects, this expression can be accurate even for atomic-scale properties. Thus the liquid-drop model, originally developed for finite systems (nuclei), may actually be more appropriate for infinite ones (metals). First applications are made to the face dependence of the surface energy and to monovacancy-formation and cohesive energies. Predictions of the model may be tested by experiment or by fully self-consistent Kohn-Sham calculations.

Thomas-fermi approach to the theory of optical constants in the XUV range

The theory of many-electron atoms and ions and their interaction with XUV radiation is one of the fundamental aspects of X-ray laser physics. The topic of this paper is the theory of optical constants of many-electron atoms in the XUV which define the dielectric susceptibility of materials in this wavelength range. We use the statistical description of atomic electrons and, as a starting point, develop the rigorous theory of the dynamical response of a Thomas-Fermi atom. The equations obtained are used with proper boundary conditions to find the dynamical polarizability and photoabsorption of many-electron atoms. The results are employed for an analysis of existing experimental data on optical constants of Ar and Si. A procedure is suggested to include into the theory the effects of atomic electron shell structure. This leads to more reasonable results and better agreement with experiment. In particular, the effect of the Cooper minimum in the atomic photoionization cross-section can be described.

Shell-dependent level densities in nuclear reaction codes

We review a level density formulation which corrects for shell structure effects via a correction based on the shell correction to the nuclear mass surface. This prescription has been entered into the code ALICE as an option requiring only an input flag to implement. Comparisons are made between calculated 56.54Fe( α, xn yp) excitation functions with this level density option versus use of an uncorrected Fermi gas formula, and with an option using a pure liquid drop mass surface. All results are also compared with the experimental excitation functions for production of 56.57Ni and 56.57Co.

Influence of the Shell Effects on the Charge Distributions of the Heavy-Ion Reaction Products

Various approaches to calculate the coefficient of the transport equation describing the process of multinucleon transfer are analysed. It is shown that the expressions for transition probabilities containing the effects of the nuclear shell structure can be obtained if we do not use averaging of the matrix elements over many shell configurations. On this basis, in the framework of the model with the realistic single-particle scheme of levels the charge distributions of the reaction products in the collisions 52Cr + 181Ta, 51V + 197Au and 20Ne + 197Au are investigated. The role of the Coulomb interaction in a dinuclear system is discussed. It is shown that the Coulomb interaction increases the formation probability for very asymmetric configurations.

Low-energy octupole modes in the A=24-54 region.

When the low-energy octupole state and low-energy octupole resonance are considered as a single composite mode in {ital A}=24--54 even-even nuclei, a regular pattern for the energy centroids is found. The location of the energy centroid as a function of nuclear mass can be explained in terms of the effects of shell structure on collective octupole excitations. It is predicted that the energy of the centroid of the composite mode in the stable isotope {sup 50}Cr, where it has not yet been measured, is 5.7{plus minus}0.4 MeV.

Cranking model of collective rotational motion of atomic electrons.

Collective rotational motion of strongly correlated atomic electrons is investigated by using the self-consistent cranking model. The intrinsic wave function and the moment of inertia are analyzed as a function of angular velocity of rotation. Origin of the ``rotational contraction'' is ascribed to the effect of quantum-mechanical shell structure.

NUCLEAR SHELL STRUCTURE AND CLUSTERED QUARK MATTER

We show that some nuclear shell structure effects may appear if the nucleus is viewed as a drop of clustered quark matter.

Pi-mesonic decay of light Λ-hypernuclei

The π-mesonic decays of all p-shell Λ hypernuclei are studied using the shell model combined with density-dependent Hartree-Fock wavefunctions. The pion distortion is taken into account by using the optical potential. The summed decay rate of π 0 and π − decays decreases with the mass number A, while each decay rate (Γ π 0 , Γ π − ) exhibits a non-trivial and characteristic variation with A, reflecting the shell-structure effects. Among the π-mesonic decay partial rates some strong transition strengths are seen in, for example, π − decays of 9 ΛLi and 9 ΛBe and π 0 decay of 12 ΛC. Large-asymmetric pion angular patterns are predicted in π − decays from the polarized hypernuclei such as 8 ΛLi(1 −), 8 ΛBe(1 −) and 9 ΛBe( 1 2 +) .

Nuclear shell effects on the radial coupling form in collective (N, γ) processes

The effective nucleon-nucleus interaction, responsible for the excitation of giant resonances in fast nucleon radiative capture, is investigated within the framework of the direct-semi-direct model in order to determine the weight of shell structure effects on the particle-vibration coupling. In the 40Ca(n, γ) reaction, it appears that the radial coupling forms obtained on the assumption of finite-range nuclear forces, as well as the reduced transition amplitudes in the energy range of isovectorEl and isoscalarE2 resonances are very sensitive to the nucleon distribution inside the nucleus. The geometrical properties of the differential cross-section are, instead, only slightly affected; therefore, the reliability of the predictions for the angular distributions supplied by the coupling form considered up to now (with nuclear Fermi density) is confirmed.

Effect of shell structure on the nucleon transfer contribution to the imaginary part of the heavy ion optical potential.

We calculate the imaginary part of the heavy ion optical potential at the strong absorption radius assuming that the absorption is essentially given by the depopulation of the entrance channel due to nucleon transfer. The transfer probabilities of individual nucleons between specific quantum states are calculated with a simple formula. The method is applied to several pairs of nuclei and the results are compared to the experiment and other previous calculations.

Electron stripping cross section from multiply charged ions by neutral atoms

Electron stripping cross sections for energetic highly charged C and Ne ions are calculated using the method based on the binary encounter approximation. Electrons of the ion are considered to be stripped by collision with the target nucleus, i.e. the electron screening is ignored. The cross section is written in terms of relative velocity between each electron and the target nucleus. The velocity distribution of electrons of the ions is obtained by the Thomas-Fermi statistical model for the purpose of obtaining the general behavior of projectile and target atomic number dependences. The effect of shell-structure on the cross section is taken into account by considering the average binding energies of electrons that are supposed to exist in each shell.

Probes for electronic and geometrical shell structure effects in alkali-metal clusters. Photoionization measurements on K xLi, K xMg and K xZn( x < 25)

We present photoionization mass spectra for molecular beams containing K x ( x < 40), K x Li( x < 25), K x Mg ( x < 25) and K x Zn ( x < 25). Potassium and potassium/lithium beams manifest abundance maxima at M 2 +, M 8 + and M 20 + (M = alkali), consistent with previous observations for sodium and sodium/potassium expansions. Adding zinc or magnesium to a potassium expansion results in new relative abundance maxima at K 8M′ + and K 18M′ +/K 19M′ +. Vertical ionization potentials were determined for K 6Mg-K 9Mg and K 8Zn. We compare these new results for heteroclusters with predictions of the spherical well jellium model.

Photoionization and shell structure of potassium clusters.

The photoion yields for potassium clusters produced in a supersonic expansion comprising between N=3 and 30 atoms are presented. The measured photoionization thresholds show the effects of electronic shell structure, with associated energy gaps in the range 0.1 to 0.3 eV. Odd-even alternations in the yields and thresholds are observed.

Local behavior of the kinetic energy in density functional theory

AbstractThe local behavior of several approximate kinetic energy functionals is analyzed, for the case of free atoms and ions, by comparison with the local kinetic energy of Hartree–Fock theory. The atomic electron densities used are, in all cases, Hartree–Fock electron densities. The kinetic energy functional obtained by the gradient expansion method (with a small number of terms) is, locally, not very accurate, but its integrated value is fortuitously accurate, due to a strong cancellation of errors. Functionals which have the Weizsäcker term tw = (Δ ρ)2/8ρ as a key ingredient are more accurate locally. The explicit incorporation of the shell structure and nonlocal density effects into the kinetic energy functional leads to the best results. The motivation for this work is that only a kinetic energy functional with an accurate local behavior will give good electron densities on solution of the Euler equation derived from it.

Theory of the aluminum shock equation of state to 10 4 Mbar

A composite theoretical shock equation of state for aluminum is compared with experimental data, including new Soviet data to 4000 Mbar. Overall agreement is good, showing that current theoretical models of hot, dense matter are adequate. Significant electron shell structure effects are predicted by ionization equilibrium and self-consistent field models to occur in the 100 Mbar region, but better experimental precision is needed for testing the models here.

Quasifree scattering of positive pions on carbon

We have studied the reaction $^{12}\mathrm{C}$(${\ensuremath{\pi}}^{+}$,${\ensuremath{\pi}}^{+}p$)$^{11}\mathrm{B}$ in a coincidence experiment that completely determined the kinematics of each event. The energy resolution was sufficient to identify the truly quasifree events, i.e., those that left the residual nucleus in its ground state. A comparison of our data with empirically normalized plane wave impulse approximation calculations shows reasonable agreement as long as only one parameter is varied at a time. Some effects of the nuclear shell structure can be seen. There is an indication that the ($\frac{3}{2}$,$\frac{3}{2}$) resonance may be narrowed inside a nucleus.NUCLEAR REACTIONS $^{12}\mathrm{C}$(${\ensuremath{\pi}}^{+}$,${\ensuremath{\pi}}^{+}p$), $E=130\ensuremath{-}200$ MeV; measured $\ensuremath{\sigma}(E,\ensuremath{\theta},{E}^{\ensuremath{'}})$, PWIA analysis. Resolution \ensuremath{\sim} 1 MeV, ${\ensuremath{\theta}}_{\ensuremath{\pi}}=\ensuremath{-}60\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}130\ifmmode^\circ\else\textdegree\fi{}$, ${\ensuremath{\theta}}_{p}=30\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}45\ifmmode^\circ\else\textdegree\fi{}$.