B-spline Basis Set Method To Calculate The Helium Atom Lamb Shift

Precision calculation and spectroscopy measurement of few-electron atoms,such as hydrogen and helium,is of important significance in examining atomic structure theory,determining fundamental physical constants and extracting basic properties of nuclei.The high accuracy energy level calculation need to take relativistic effect,Lamb shift arising from quantum electrodynamics(QED)effect,and nuclear structure effect into account.The calculation of Lamb shift has been one of the fundamental and frontier research project.The calculation of the Bethe-logarithm(BL)appeared in leading QED correction with desired accuracy is very challenging and limit the precision of theoretical prediction.To obtained BL with high accuracy,it is necessary to uniformly deal with low-energy bound states and high-energy continuum states(energy span of nearly 20 orders of magnitude),which is a challenging problem in the field of computing atomic physics.Traditional exponential-type and Gaussian-type basis-set methods suffer from linear dependence and numerical instability.Thus,it is a meaningful project to develop new basis-set method with stable numerical calculation and high computational efficiency.The main content in this thesis is to develop B-spline basis-set method to solve Hydrogen and helium atoms,and then calculated Bethe-logarithm using pseudo-state approach.Combined with the results in literature,we then give our theoretical prediction of Lamb shift for helium low-lying states.The concrete contents include:(1)Using the B-spline basis-set method to calculate the Bethe-logarithm of hydrogen atom under the length,velocity and acceleration gauge,and assessing the applicability and reliability.(2)On the basis of(1),B-spline configuration interaction method(CI)is developed,and the Bethe-logarithm of S,P and D states of helium atom is calculated by using pseudo-state approach.Our calculation shows that most of BL values have 6-7 accurate figures.By comparing the accuracy of energy spectrum and Bethe-logarithm,it is proved that the traditional configuration interaction method can realize the high precision calculation of Bethe logarithm.(3)The lamb shift of partial P and D states of helium atoms is given and compared with that of experiment.The difference between theory and experiment is less than one thousandth.The results of this thesis are of methodological significance for the calculation of the atomic precision spectrum.B-spline basis-set method is used widespread in computing atomic and molecular physics for past three decades.The achievement in this thesis represents a new application of the B-spline basis-set method.