Research On Nuclear Mass Effects In Helium-like Systems

In the past several decades,the high precision spectroscopy of helium atoms developed rapidly,and important progress has been made in both experimental measurements and theoretical calculations.The comparison of high-precision experimental values and theoretical values provides an effective way for high-precision test of basic physical theories(such as QED),determination of fundamental physical constants(such as fine structure constant ?),and determination of nuclear charge distribution radii and magnetic moment distribution radii.Theoretically,in order to obtain the high-precision transition frequency of helium atom,the correlation effect of electrons,the relativistic effect,quantum electrodynamics effect(QED),the finite mass effect of the nucleus and even the finite charge distribution radius of the nucleus must be calculated to desired accuracies.For lighter atomic systems,the impact of the finite mass of the nucleus on the energy levels is at the order of ?/M?10-4,which is a considerable contribution to the precision spectroscopy,so it must be accurately calculated.The main goal of this thesis is to strictly calculate the influence of the finite mass of the atomic nucleus on the non-relativistic energy levels of the helium atom and helium-like ions(Z=3?10)in Hylleraas coordinates,including the first-,second-and third-order mass polarization coefficients.This article mainly contains the following contents:(1)The basis theoretical methods and calculation techniques for solving the Schrodinger equation of the three-body system in Hylleraas coordinates are introduced and discussed,including the three-body Hylleraas-type variational basis function,the derivation of non-relativistic Hamiltonian(normal mass shift and specific mass shift),power method,Cholesky decomposition,etc.(2)Under the assumption of infinite nuclear mass,the Hylleraas-type variational function are constructed,the Rayleigh-Ritz variational method are used to solve the non-relativistic Schrodinger equation of helium atom and helium-like ions(Li+?Be2+?…?Ne8+),and the high-precision non-relativistic eigen energies and eigen wave functions of the 1 s 2 1S?1s2s1S?1s2p1P?1s2s3S and 1 s2p 3 P states are obtained.(3)Using the Rayleigh-Schrodinger perturbation method to calculate the first,second and third order mass polarization coefficients of the 1 s 2 1S?ls2s1S?1 s2p1P?1s2s3S and 1 s2p 3 P states of helium atom and helium-like ions(Li+?Be2+…?Ne8+),that is,the ?/M order,(?/M)2 order and(?/M)3 order of the energy level of the finite mass effect of the nucleus corrected and studied the variation of these mass polarization coefficients with the nuclear charge number Z.In the current literature,the mass polarization coefficients of helium atoms and helium-like ions have only been calculated to first-order and second-order,and there is no results of third-order mass polarization coefficients.This paper systematically studies the mass polarization coefficients of helium atom and helium-like ions 1 s 2 1S?1s2s1S?1s2p1P?1s2s3S and 1 s2p3P states up to the third order,The Dalgarno-Lewis method is used to avoid the infinite summation problem in the second-order perturbation calculation,and the accuracy of the mass polarization coefficient is greatly improved;the first-order perturbation wave functions obtained by us lay the foundation for the calculation of finite nuclear effect of the relativistic and QED corrections in the future.