A new method for theoretical calculation of atomic hyperfine structure

Abstract

Schrödinger equation is a nonrelativistic wave equation, which does not have Lorentz invariance. Therefore, this equation has a large theoretical error in the precise calculation of hydrogen-like system. So the commonly used method is Dirac-Hartree-Fock approximation in the calculation of atomic system. However, we have found a new eigen equation, whose eigenvalue of the hydrogen-like system approximates the calculation of quantum electrodynamics. Hence, we propose a new calculation scheme for the atomic hyperfine structure based on the eigen equation and the basic principle of Hartree-Fock variational method, and come to our conclusion through the correlation calculation of excited single states of hydrogen atom, U 91+ ion, helium atom and lithium atom as well as the comparison with NIST, that is, our method is a better improved model of the stationary Schrödinger equation. Meanwhile, we list the correlation algorithms of energy functional, two-electron coupling integral and radial generalized integral in the appendix.