High-precision Calculation Of Multipole Polarizabilities And Hyperpolarizability Of Free Or Confined Hydrogen-like Ions With Plasma Screening Potentials

In the study of complex atomic,the screening effect caused by the interaction between electrons and ions has always been a key problem.As an effective model to explain this process,plasma screening potentials have attracted much attention in various physical and chemical systems.The plasma screening effect changes the structure and dynamics of the system to a great extent,and its remarkable feature is that it can cause a limited number of bound states,in which the physical processes such as electron collision and photoionization have been studied by a large number of scholars.In this paper,Hulthén potential,screened Coulomb potential and exponential cosine screened Coulomb potential are studied,which are used to describe different plasma environments according to the strength of screening effect.At the same time,quantum confined systems have attracted much attention due to their important role in high pressure physics,liquid physics,astrophysics and other fields.It is a good description of the interaction between confined isolated systems and their surroundings,such as confined systems in quantum heterostructures,core-shell structures,zeolite,fullerenes and so on.In the impenetrable spherical potential,electrons are confined in a finite region,the dispersion of the wave function decreases,and the corresponding energy decreases.In this work,free or confined hydrogen-like ions under plasma screening potentials are discussed based on the above two models.In fact,whether free or confined system under the plasma screening potentials,it is mostly impossible to obtain analytical solutions.The only exception is the s state of hydrogen atom under the Hulthén potential,which is also the particularity of the Hulthén potential.In addition,all other results need to be obtained by numerical calculation.Therefore,there is a natural requirement for the accuracy of numerical results.Only by obtaining the energy eigenvalue and eigenfunction with high precision can we study the atomic structure and dynamics more accurately.In this paper,the generalized pseudospectral method is used,which is a global configuration method,regardless of the size of the confined radius,screening strength can maintain high precision.It has been proved to produce fairly reliable results in a variety of important systems including quantum confined systems,especially in the calculation of single electron atoms.On this basis,multipole polarizability and hyperpolarizability are studied in this work.Multipole polarizability is a key parameter to determine the electronic structure of atoms and molecules.Dipole polarizability can be used to estimate many macroscopic properties such as refractive index and dielectric constant.Hyperpolarizability plays a significant role in non-linear optics and is closely related to two-photon transition energy.The multipole polarizability can be easily obtained by calculating the transition energy and oscillator strength using the sum-over-states method.The second-and fourthorder correction coefficients are dipole polarizability and hyperpolarizability.The research content of this paper can be divided into three directions.Firstly,the multipole polarizability of the s state(1s-5s)of free hydrogen atom under the Hulthén potential is calculated,and the decrease of the polarizability of the non-ground states at the weak screening is explained theoretically.At present,the exact value of multipole polarizability under Hulthén potential is not given.There are comparative results of dipole polarizability,but most of them are not accurate,so the detailed numerical results are given here.Secondly,the multipole polarizability of the ground state of the confined hydrogen atom under three plasma screening potentials is calculated and the crossover phenomenon of the multipole polarizabilty with the change of the confined radius is discussed.There are discrepancies between the existing results of dipole polarizability of confined hydrogen atom under plasma screening potential,and there are few studies on extreme conditions.Therefore,we hope to provide high precision results as the benchmark values for reference.At the same time,we develop the Z?-scaling law to establish the quantitative relationship between the single electron systems with different nuclear charge number and reduced mass.Under this framework,the dipole polarizability of confined positronium in plasma screening potential is studied,and its effective approximation model is discussed.Finally,the hyperpolarizability of hydrogen atom s state(1s-5s)under screened Coulomb potential and exponential cosine screened Coulomb potential is calculated.The problem of negative hyperpolarizability except ground state is discussed and the zero screening parameter is defined.The existence fluctuation of hyperpolarizability of 3s-5s state is studied,and the applicable range of perturbation theory is estimated.In the case of plasma screening potential,the calculation of static hyperpolarizability of hydrogen atom is less,so it is necessary to give high-precision results.