High-precision Calculation Of Low-energy Electron-helium Elastic Scattering With The Confined Variational Method

Quantum few-body physics has always been an important branch of quantum mechanics.The key to studying the quantum few-body system is to solve the Schrodinger equation.It is difficult to solve the Schrodinger equation in a nonrelativistic Coulomb few-body system,which has more than two particles.It's a good way to use numerical solutions to study quantum few-body physics.In this thesis,one of the important nu-merical methods is to expand the wave function with the explicitly correlated Gaussian functions.We focus on studying the scattering process between particles.This thesis introduces the form and application of explicitly correlated Gaussian functions,variational principle,an optimization method for explicitly correlated Gaussian functions.The theoretical calculation focuses on the scattering of an electron by helium atom based on the confined variational method(CVM)and the explicitly correlated Gaussian(ECG)functions.For e-He scattering in low energy,the S-and P-wave phase shifts calculated by Nesbet in 1979 have been accepted as a benchmark until now.Compared with the previous CVM calculations of this same system,we extended our work on e-He scattering to higher partial waves under higher scattering energies.We performed a detailed investigation on the finite nuclear mass of the S-wave phase shifts and the influence of long-range polarization on the scattering length.The results agree with the recent measurements by Shigemura for the total cross-section in the critical low-energy region.There is no doubt that our work contributes to further understanding of the e-He scattering process.Our results build a new benchmark for future theories and experiments.