High Precision Calculations And Applications Of Electrostatic Multipole Polarizabilities For Hydrogen-like Ions

The calculation of precise spectroscopy for simple atomic systems-hydrogen atomand hydrogen-like ions is always an important basic research period, which has impor-tant applications in quantum mechanics, quantum electrodynamics and quantum feldtheory. Polarizability is a basis physical quantity of atoms and molecules, which deter-mines the atomic and molecular responses properties to an external electric or magneticfeld. The polarizability with high accuracy can be applied to optical frequency standards,for example, one of the optical clock system errors is Stark shift that relies on the atomicpolarizability. The calculations of hydrogen-like ions polarizabilities with high accuracyprovides test of basic physical theories and can be used to determine uncertainties offundamental physical constants, such as Rydberg constant and the ratio of proton andelectron, and then can be used to test basic physical with a higher level.In this dissertation, electrostatic multipole polarizabilities for hydrogen-like ions arecalculated based on B-splines, which have many good mathematical properties, such as,linear independence, completeness and B-spline knots continuing adjustment. The maincontent of this dissertation is as follows:The multipole expansion of the polarization interaction between a charged particleand an electrically neutral object has long been known to be asymptotic in nature, i.e.,the multipole expansion diverges at any fnite distance from the atom. However, themultipole expansion of the polariztion potential of a confned hydrogen atom is shown tobe absolutely convergent at a distance outside the atoms confnement radius, R0. Themultipole expansion of the dispersion potential between two confned hydrogen atoms isalso shown to be absolutely convergent provided the two atoms satisfy R>2R0, where Ris the inter-nuclear separation. These results were established analytical using oscillatorstrength sum rules and verifed numerically using a B-spline description of the hydrogenground state and its excitation spectrum. The above conclusions support Brooks earlieranalysis.The static multipole polarizabilities α (up to four) for hydrogen-like ions in theground-state (1S1/2) are obtained with high accuracy from Dirac equation using the B-spline basis sets. The efect of negative-energy states to the polarizabilities and sumrules are discussed. The analytical expressions for the multipole polarizabilities as αZfnction, where α being the fne structure constant and Z being the nuclear charge, arealso proposed.The present dipole polarizabilities coincide well with Goldman’ results. And, the validation of Kaneko’ expansions for multipole polarizabilities is tested to themagnitude of O(α2Z2).