Accurate Calculation Of Atomic Structure Based On Generalized Pseudospectral Method

In recent years,there are many studies on the calculations of atomic properties in different external environments.They are involved in Laser atom interaction,nuclear and atomic physics,and astrophysics.The study of simple systems can provide theoretical basis for complex system's investigation.Hydrogen atom,as the simplest one-electron atomic system,is often chosen primarily as the research object.Accurate calculation results of various physical quantities for simple systems in the external field can directly reflect the changes of atomic states under the action of external field.The accuracy of atomic structure calculations depends on the accuracy of wave functions.The generalized pseudospectral method is a collocation method based on global functions.The basic idea of GPS method is to discretize coordinates,and then transform the integration into summation.Its powerfulness and robustness has been well established in solving the radial Schr?dinger equation with high accuracy.However,in our recent work,it is found that the previous calculations of some radial expectation values of confined systems based on GPS method show significant discrepancies with other theoretical methods.In this work,the extrapolation method is used to solve the problem that GPS can not get the system wave function of the origin.Due to the wave function of s-wave state for hydrogen atom at the origin is non-zero,an extrapolation method must be combined with the GPS method to calculate various radial expectation values.The GPS method combined with extrapolation can fully reproduce all radial quantities obtained by other theoretical methods,yet with more flexibility,efficiency,and accuracy.Then the present GPS-extrapolation method is applied to calculate the relativistic fine structure corrections for swave state of the hydrogen atom,including the relativistic correction of the kinetic energy,the spin-orbit coupling term and the Darwinian term.It is also applied to the calculation of hyperfine splitting for s-wave state of the hydrogen atom.For the calculation of fine structure and hyperfine structure,the combination of GPS and extrapolation method can not only get the result consistent well with the theoretical predictions of the confined hydrogen atom in the low-lying state,but also establish benchmark results for high-lying excited states.It is also verified that the perturbation treatment of the fine and hyperfine interactions is validated in a wide range of confinement radius.The electric multipole polarizabilities of one-electron atom embedded in weakly-coupled Debye plasmas are calculated based on GPS method in the non-relativistic framework.The static dipole,quadrupole,octopole,hexadecapole polarizabilities and Z-scaled polarizabilities for hydrogen atom in both ground and excited states at a variety of Debye screening parameters are calculated in high precision based on the sum-over-states method.The calculation of polarizability shows that the contribution of bound states to the polarizability decreases as increasing the plasma screening strength,whereas the contribution from continuum states is enhanced.At very small screening parameters where the plasma environment starts to take effect,it is found that the 26)-pole polarizability for s-wave states with principle quantum number 9)?7)+ 1 has an abrupt change from its non-screening value to infinity.The phenomenon is attributed to the sudden non-degeneracy of different angular momentum states in the n shell.With continuously increasing the screening strength,the polarizability decreases to certain value and,eventually,it approaches infinity at the critical screening parameter.For those states with 9)? 7),the 26)-pole polarizabilities show the regular changes from the nonscreening value to infinity.The comparison of present results with theoretical calculations available in the literature shows that our work has established the most accurate prediction of multipole oscillator strengths and polarizabilities for one-electron atoms in Debye plasmas up to now.