Statistical measures and magic numbers in metal clusters

In this work, a shell model for metal clusters up to 220 valence electrons is used to obtain the fractional occupation probabilities of the electronic orbitals. Then, the calculation of a statistical measure of complexity and the Fisher-Shannon information is carried out. An increase of both magnitudes with the number of valence electrons is observed. The shell structure is reflected by the behavior of the statistical complexity. The magic numbers are indicated by the Fisher-Shannon information. So, as in the case of atomic nuclei, the study of statistical indicators also unveil the existence of magic numbers in metal clusters.     

The Fisher-Shannon information plane for atoms

The Fisher-Shannon information product and plane for atoms are presented analytically assuming Thomas-Fermi-Gáspár statistical model. A comparison with the Hartree-Fock densities reveals that the atomic shell structure is inadequately expressed information theoretically in the statistical model. The shape complexity measure of Lopez et al. is found to have a better large Z dependence than the one obtained from non-relativistic Hartree-Fock densities.     

Statistical complexity and Fisher-Shannon information in the H-atom

The Fisher-Shannon information and a statistical measure of complexity are calculated in the position and momentum spaces for the wave functions of the H-atom. For each level of energy, it is found that these two indicators take their minimum values on the orbitals that correspond to the highest orbital angular momentum.     

Fisher-Shannon plane and statistical complexity of atoms

Using the Hartree-Fock non-relativistic wave functions in the position and momentum spaces, the statistical measure of complexity C, due to López-Ruiz, Mancini, and Calbet for the neutral atoms as well as their monopositive and mononegative ions with atomic number Z=1-54 are reported. In C, given by the product of exponential power Shannon entropy and the average density, the latter is then replaced by the Fisher measure to obtain the Fisher-Shannon plane. Our numerical results suggest that in overall the Fisher-Shannon plane reproduces the trends given by C, with significantly enhanced sensitivity in the position, momentum and the product spaces in all neutral atoms and ions considered.     

Statistical complexity and Fisher-Shannon information measure of H2

Using the simple Coulson molecular wave function for the ground state H⁺₂ molecule as a function of internuclear distance, the first molecular calculations of (a) the statistical complexity measure due to López-Ruiz, Mancini, and Calbet and (b) the Fisher-Shannon information measure in the position and momentum spaces are reported. It is found that the two measures exhibit the molecular bonding in the form of a characteristic minimum around the equilibrium internuclear distance in the product space.     

Atomic analogue of photonuclear configurational splitting

It is shown that the polarized bremsstrahlung (PB) emitted upon the scattering of a relativistic charged particle’s Coulomb field by atomic electrons yields direct information on the electronic structure of a medium. Indeed, in the X-ray photon energy range 1–10 keV, PB exhibits collective features and the PB intensity sharply increases. At higher photon energies, the coherence of shell electrons rapidly collapses, which is accompanied by a drastic decrease in the PB intensity; hence, the position of the PB spectrum kink allows estimation of the atomic size.     

Spectral fine structure of the atomic ground states based on full relativistic theory

We focus on the full relativistic quantum mechanical calculations from boron to fluorine atoms with electronic configuration of 1s2 2s2 2p n(n =1,2,3,4,and 5),where 1s2 2s2 is the closed shell and 2p n is the open shell.Their active electrons in the open shell occupy all the six spinors as far as possible.Therefore,we suggest a new rule called "maximum probability" for the full symmetry group relativistic theory.Furthermore,the spectral fine structure of the atomic ground states based on the full relativistic theory and their intervals of L-S splitting are all reasonable.It is impossible to calculate the L-S splitting through non-relativistic quantum mechanics.The relativistic effect of atomic mass is increased significantly by about 12 folds from boron atom to fluorine atom.     

用屏蔽法计算较轻元素原子的高次电离能

考虑到离子的相对论效应,依据屏蔽方法,给出了原子第2、1壳层电子电离能的一种表达式.依据较轻元素原子低次(小于13)电离能实验数据,总结出原子(离子)电离第2、1壳层不同电子态电子时,相应的屏蔽系数与电子态及原子序数的函数关系,根据该函数关系,可求出相应原子的高次电离电子的屏蔽系数.计算了原子序数13至23的元素高电荷态离子基态电离能,计算结果与文献可提供的实验数据相符合.     

Configuration complexities of hydrogenic atoms

The Fisher-Shannon and Cramer-Rao information measures, and the LMC-like or shape complexity (i.e., the disequilibrium times the Shannon entropic power) of hydrogenic stationary states are investigated in both position and momentum spaces. First, it is shown that not only the Fisher information and the variance (then, the Cramer-Rao measure) but also the disequilibrium associated to the quantum-mechanical probability density can be explicitly expressed in terms of the three quantum numbers (n,l,m) of the corresponding state. Second, the three composite measures mentioned above are analytically, numerically and physically discussed for both ground and excited states. It is observed, in particular, that these configuration complexities do not depend on the nuclear charge Z. Moreover, the Fisher-Shannon measure is shown to quadratically depend on the principal quantum number n. Finally, sharp upper bounds to the Fisher-Shannon measure and the shape complexity of a general hydrogenic orbital are given in terms of the quantum numbers.     

d Electron momentum densities for position annihilation in transition metals

The relative contribution of 3d electrons to the momentum densities for positron annihilation in the iron series transition metals are calculated, using the atomic Hartree-Fock-Slater orbitals. A discussion is given of the observed systematics. The per electron contribution to the angular correlations is found to decrease with the filling up of the d shell. The high momentum components are found to be relatively enhanced in case of higher Z metals. The built in spin dependence of the electron HFS wavefunction is reflected in the calculated curves.     

Rényi information of atoms

Position and momentum space Rényi information of order α has been studied within a Hartree-Fock framework for 103 neutral atoms, 54 singly charged cations and 43 anions in their ground state. The values of α?1 (α?1) stress the shell structure for position-space (momentum-space) Rényi information. The relationship between the complexity and Rényi information is also studied.     

Interference between electric and magnetic amplitudes for K shell excitation of high-Z H-like projectiles

We report an investigation of projectile K shell excitation for high-Z ions in relativistic ion-atom collisions. For the case of H-like Bi, the excitation process is unambiguously identified by observing the radiative decay of the excited levels to the vacant 1s shell, in coincidence with ions that did not undergo any charge exchange in the reaction target. The results are compared with detailed relativistic calculations, showing that the magnetic interaction is of considerable importance for the K shell excitation process in high-Z ions. For excitation to the L shell sublevels, the experimental data confirm that the magnetic part of the Liénard-Wiechert interaction must be added coherently with the electric part leading to a significant reduction of the K shell excitation cross section.     

Thomas-Fermi theory for atomic nuclei revisited

The recently developed semiclassical variational Wigner-Kirkwood (VWK) approach is applied to finite nuclei using external potentials and self-consistent mean fields derived from Skyrme interactions and from relativistic mean field theory. VWK consists of the Thomas-Fermi part plus a pure, perturbative ?² correction. In external potentials, VWK passes through the average of the quantal values of the accumulated level density and total energy as a function of the Fermi energy. However, there is a problem of overbinding when the energy per particle is displayed as a function of the particle number. The situation is analyzed comparing spherical and deformed harmonic oscillator potentials. In the self-consistent case, we show for Skyrme forces that VWK binding energies are very close to those obtained from extended Thomas-Fermi functionals of ?⁴ order, pointing to the rapid convergence of the VWK theory. This satisfying result, however, does not cure the overbinding problem, i.e., the semiclassical energies show more binding than they should. This feature is more pronounced in the case of Skyrme forces than with the relativistic mean field approach. However, even in the latter case the shell correction energy for e.g., ²⁰⁸Pb turns out to be only ∼−6 MeV what is about a factor two or three off the generally accepted value. As an ad hoc remedy, increasing the kinetic energy by 2.5%, leads to shell correction energies well acceptable throughout the periodic table. The general importance of the present studies for other finite Fermi systems, self-bound or in external potentials, is pointed out.     

等离子体屏蔽效应对Ar~(16+)基态和激发态能级的影响

基于Rayleigh-Ritz变分原理,发展了一套处理弱耦合等离子体环境中多电子原子(离子)非相对论能量及其相对论修正的解析方法.通过考虑电子间交换相互作用以及内外壳层电子的屏蔽效应,计算了Ar~(16+)基态1s~2~1S、单激发态1sns~(1,3)S (n=2—5), 1snp~(1,3)P (n=2—5)和双激发态2snp~1P (n=2—5)非相对论能量及其相对论修正值(包括质量修正、单体和双体达尔文修正以及自旋-自旋接触相互作用项),讨论了等离子体屏蔽效应对能级的影响.结果表明:相对论质量修正和第一类达尔文修正占主导,比其他相对论修正项高出三个数量级.此外,等离子体屏蔽效应具有明显的态选择性,屏蔽效应对外壳层电子的影响大于内壳层电子,随着等离子体屏蔽参数的增加,外壳层电子轨道向外延展,激发态越高,延展程度越大.     

Spin-polarized relativistic calculations on highly ionized molybdenum

The energies of K_α X-ray satellite lines of molybdenum ionized to different degrees in the L shell with closed and open outer shells (n=3,4 and 5) are reported in this work. The calculations have been carried out using Xα method with spin-polarized single configuration relativistic Dirac-Fock wavefunctions. Calculations have also been carried out with un-polarized relativistic wavefunctions. The effect of relativistic spin exchange potential on the total energies of the various states ionized to different degrees in the inner and outer shells are analyzed. As the transition assignments in the spin-polarized treatment of atomic orbitals take into account the spin orientations of the electrons in the initial and final states, the present calculations elucidate the significance of this technique in giving unique spin-dependent transition assignments to experimental energies.     

Study of parameters of the angular distribution of photoelectrons in the relativistic quadrupole approximation

Relativistic calculations of differential cross sections for photoionization are performed and the behavior of parameters β, γ, and δ describing the angular distribution of photoelectrons in the quadrupole approximation is studied. The calculations were carried out for a number of atoms for kinetic energies of photoelectrons E _k ≈50 000 eV. The electronic wave functions of the initial and final states are calculated by the Dirac-Fock method taking into account the exchange interaction and a hole produced in the atomic shell upon photoionization. The dependence of parameters β, γ, and δ on the physical assumptions used in the calculations is studied. Comparison with nonrelativistic calculations shows that relativistic values of the nondipole parameters γ and δ can be substantially different even at low energies of photoelectrons. Our calculations of nondipole parameters γ and δ for the 2p-shell of the Kr atom better agree with the recent experimental data than nonrelativistic calculations performed earlier taking approximately into account the exchange interaction and neglecting a hole.     

Internal conversion in hydrogen-like ions

The probability of internal gamma-ray conversion is theoretically investigated for hydrogen-like ions versus the corresponding neutral atoms. The relevant calculations are performed by the relativistic Dirac-Fock method. The results reveal that the effect of multiple ionization on the coefficients of internal conversion in the K shell is maximal near the ionization threshold and for transitions of high multipole order, where this effect can be as great as a few orders of magnitude. The distinction between the coefficient of internal conversion in the K shell of a neutral atom and that in the respective hydrogen-like ion decreases with increasing transition energy, but it remains sizable for transitions of practical importance. It is found that the ionization of an atom to a hydrogen-like ion with allowance for conversion in external atomic shells may change significantly (by up to eight orders of magnitude) the lifetime of the nucleus being considered. The predicted effects can be observed in experiments with beams of relativistic heavy ions.     

Helical Shell Structures of Ni-A1 Alloy Nanowires and Their Electronic Transport Properties

Six kinds of Ni-A1 alloy nanowires are optimized by means of simulated annealing. The optimized structures show that the Ni-A1 alloy nanowires are helical shell structures that are wound by three atomic strands, which is very similar to the case with pure metallic nanowires. The densities of states （DOS）, transmission function T（ E）, current-voltage （I - V） curves, and the conductance spectra of these alloy nanowires are also investigated. Our results indicate that the conductance spectra depend on the geometric structure properties and the ingredients of the alloy nanowires. We observe and study the nonlinear contribution to the I-V characteristics that are due to the quantum size effect and the impurity effect. The addition of Ni atoms decreases the conductance of the Ni-A1 alloy nanowire because the doping atom Ni change the electronic band structures and the charge density distribution. The interesting statistical results shed light on the physics of quantum transport at the nano-scale.     

Self-consistent electronic structure and ground state properties of TlCl

We present the first self-consistent, relativistic, ab initio calculation of the electronic structure, equilibrium lattice constant, cohesive energy and compressibility of TlCl, as an example of a semiconductor with high atomic number and high ionicity. The theoretical approach is based on the local density-formalism. Our results explain the salient features of recent photoemission measurements and describe the ground-state properties with good accuracy.     

Entropy and complexity analysis of Dirac-delta-like quantum potentials

The Dirac-delta-like quantum-mechanical potentials are frequently used to describe and interpret numerous phenomena in many scientific fields including atomic and molecular physics, condensed matter and quantum computation. The entropy and complexity properties of potentials with one and two Dirac-delta functions are here analytically calculated and numerically discussed in both position and momentum spaces. We have studied the information-theoretic lengths of Fisher, Rényi and Shannon types as well as the Cramér-Rao, Fisher-Shannon and LMC shape complexities of the lowest-lying stationary states of one-delta and twin-delta. They allow us to grasp and quantify different facets of the spreading of the charge and momentum of the system far beyond the celebrated standard deviation.