High-precision Calculation Of Energy Levels And Polarizability Of Helium Atomic Systems

The precise calculation of the few-body atoms and molecules are important in both theoretical and experimental researches.In the various methods this thesis adopt the Rayleigh-Ritz variational method and construct the generalized eigenvalue equation to study the property of Helium.In the variational approach,researchers always use different basis sets to deal with particular situations in their calculations.Hylleraas basis set has a good performance in the study of Helium as it can reflect the correlation of two electrons.With the measuring accuracy increasing,in the numerical calculation we should go on considering more relativistic and QED effects to meet the needs of study.In the processes of calculating the above-mentioned effects we always have to consider the whole energy spectrum of helium including continual states,which makes the problem more complex.In order to ensure the correctness of our results,we should use different basis sets to verify with each other.In this thesis we constructed another effective and conventional basis set,called Hylleraas-B-splines basis set,through coupling Hylleraas basis set with B-spline basis set which is also widely used in the calculation field.Different with Hylleraas basis,Hylleraas-B-spline basis adopt B-splines functions rather Taylor polynomial to support our searching space.B-spline functions are near completeness,high locality and L2 integrable in one finite region.As B-spline functions have those features,our basis possesses the capacity for simulating continual states.On the other hand,because of considering the correlation of two electrons,using this basis to calculate the lower energy levels of Helium-like atoms is also suitable.This thesis exhibit the procedure of constructing Hylleraas basis through calculating the energy levels and polarizabilitise of helium.On this basics,some properties of helium have been discussed.