Two-spinor fully relativistic finite-element (FEM) solution of the two-center Coulomb problem

Abstract

A highly accurate 2-spinor fully relativistic solution of the two-center Coulomb problem utilizes the finite-element method (FEM). Like in previous work on the 4-spinor Dirac equation we use elliptic–hyperbolic coordinates, global factors, further one-dimensional singular coordinate transformations and extrapolation techniques. In the same grid 2-spinor energies for H 2 + are up to four orders more accurate than 4-spinor values, for the super-heavy Th 2 179+ up to one order and one generally finds, high convergence orders similar to a non-relativistic approach. The 2-spinor values converge from above, exhibit remarkable properties and the calculations are considerably faster and more stable.