The Information-theoretic Studies Of One-and Two-electron Atoms

The study of plasma screening effect on atomic structure properties and collision processes is one of the major subjects in the interdisciplinary area of atomic physics and plasma physics.The electrostatic screened Coulomb potential represents the collective effect of correlated charged particles on test atom in plasmas.Its explicit form,however,depends on vastly varied plasma parameters.In the past decades,extensive studies have been performed by many authors on the plasma screening effects on atomic spectral properties and collisional dynamics.The shift of bound state energies for hydrogen atom immersed in Debye plasmas have long been investigated theoretically and the critical screening parameters beyond which the bound states transform into continuum states have been calculated in very high accuracy.The relativistic effect and fine structures of the energy levels for hydrogen-like ions with large nuclear charge have also been available in recent years.The two-electron atoms,such as He and H-,and exotic three-body systems in Debye plasmas attract considerable interest due to their abundant electronic structures including bound,metastable-bound,and doubly-excited quasi-bound(resonance)states.Latter ones are fundamentally important not only in investigating the electron correlation effects in multielectron systems but also in revealing the drastic changes in photoionization,electron-impact excitation and ionization processes.In addition,Hulthén potential is very important short-range potential in many fields.we present a systematic study of characteristic of the hydrogen and helium,in position,momentum,and their product spaces,for hydrogen-like ions and helium atom interacting with weakly-coupled Debye plasmas and Hulthén potential.One-and two-electron systems have been widely studied in atomic and molecular physics,two-electron atoms have much richer physical propertiescompared with one-electron systems,e.g.entanglement,resonance and so on,these properties have very important using in physics.We apply L?wdin's canonical orthogonalization method to get wave function of atomic systems using Slater-type orbital configuration-interaction(STO-CI)basis functions.In classical information theory,Shannon entropy is a basic quantity measuring the average amount of information contained in a probabilistic message distributed discretely.When applying it into quantum systems,it is associated with the continuously changed electronic densities and gives a global measure of the overall randomness or delocalization of electron in corresponding density distribution,due to the logarithmic function in the definition.The Fisher information,which is a gradient functional of the quantum mechanical probability density,is a local measure about the intrinsic accuracy or localization of electron density distribution.It is therefore the combination of these two density-dependent quantities gives,in a complementary manner,a complete description of the localization-delocalization characters of atomic system.The application of these two information-theoretic quantities together with other entropic quantities,such as Rényi entropy,Tsallis entropy,and Onicescu information energy in position,momentum,and their product spaces have been extensively discussed in many quantum systems.More recently,the composite information-theoretic measures,such as the two-component Fisher-Shannon(FS),Crámer-Rao,López Ruiz-Mancini-Calvet(LMC),and LMC-Rényi complexity have been introduced into atomic systems to jointly grasps two different characters of the electron density distribution(spreading,smoothing,irregularity,oscillation,fluctuation,etc.).Such character is especially useful in refining the fundamental uncertainty properties of quantum system.The complexity measures are density-dependent quantities and,therefore,can be considered as intrinsic properties of quantum systems.The Fisher-Shannon one which has been shown to be the most appropriate measure to describe the intuitive complexity of atoms will be considered in this work.These researches present an alternative view of structural informations implied in different systems,such as the dimension-dependence characters of hydrogen atom and harmonic oscillator in arbitrary D-dimension,the non-linear avoid-crossing phenomena for atoms in external electric and magnetic fields,theshell-filling structures for atoms across the periodic table,the scaling properties for atoms confined in different potentials,and the rigorous bounds of information quantities in a variety of atomic systems.we also introduce in detail the methods used in calculating the system energies and wave functions,the formula in calculating the information-theoretic measures,and the scaling laws of these measures with respect to nuclear charge and screening parameter in this work.