Theoretical Calculations On Energy Structure Of Few-Body Atomic System

Recently,energy structure of few-body atomic system has been one of the focus of atomic physics.In this paper,basing on variational method,the energy level structure of excited states for Kr³³⁺ ions and metastable states of anti-proton helium are studied theoretically with different forms of wave function.As for highly charged ions Kr³³⁺,the wave functions of 1s2np,1s2nd and 1s2nf?2?n?9?states are set up with basis functions of square integrable Slater type,and the non-relativistic energies are calculated.In order to improve the accuracy of calculation,we considered some corrections for Kr³³⁺ system including the first order relativistic correction,the quantum electrodynamics?QED?correction and the higher-order relativistic correction.Then the ionization energy,excitation energy,transition energy,wavelength and fine structure are calculated.For metastable states of anti-proton helium,the wavefunctions are constructed with molecular expansion and variation method.The basis functions including the electronic association coordinates are similar to the generalized Hylleraasby basis sets,and the variational wave function are determined using the quasi random exponential method.In this work,we calculated the non-relativistic energies of the anti-proton helium,the results made good foundation for further calculations on relative energies.In this work,the energy levels of excited states for Kr³³⁺ ions obtained agree well with the experimental values.For example,the absolute error of the non-relativistic energy with the core correction and valence electron effect for 1s22p state is 0.00009668,the relative error is 6.81×10-8,the absolute differences between the theoretical values and the experimental values range from 0.202‰ to 0.745‰.The non-relativistic energies of anti-proton helium with N=39?42,l=0?4 obtained with the molecular expansion and variational method are in good agreements with the values of Korobov,the accuracy achieve 13?14 effective numbers.The calculation results acquired make us have a better understanding of energy structures of few-body atomic system.The theoretical research carried out in this work not only test the theoretical model and the accuracy of the theoretical method but also meet the requirements of the high accuracy theoretical calculations.