Time dependent variation perturbation calculation of two-photon transition probability and hyperfine shift in hydrogen atom under plasma environment

Abstract

A new theoretical approach has been adopted to calculate the non-relativistic parity conserved two-photon transition probability (TPTP) from ground to excited S and D states along with the hyperfine splitting (HFS) of ground and excited S states of H atom within principal quantum number n ≤4 under classical and quantum plasma environment represented by screened potential model. The methodology involves direct calculation of TPTP via an intermediate virtual state obtained from time dependent variation perturbation formalism. The standard formula with sum over states representing the TPTP has been replaced by its variational equivalent obtained from currently established procedure for two-photon excitation via fourth order time dependent variation perturbation theory. Unlike previous methodologies the current formalism yields a compact representation of the physical nature of the intermediate virtual state having well defined profile. The HFS has been evaluated under first order perturbation theory. The plasma embedded ground state energy is obtained from standard diagonalization procedure. Finite Slater type basis sets have been used for the ground and all the excited states. The variational coefficients for the excited states are determined from optimization of an appropriate time averaged variational functional. Results for free H atom agree well with existing estimates for all the states. The results for the plasma embedded states follow smooth and interesting pattern.