High accuracy Dirac-finite-element (FEM) calculations for H ₂ ⁺ and Th ₂ ^{179 +}

Abstract:

A two-dimensional, fully numerical approach to the four-component first-order Dirac-differential-equation utilizing the Finite-Element-Method (FEM) is employed for H ₂ ⁺ and Th ₂ ^{179 +}. Using elliptic-hyperbolic coordinates and further one-dimensional singular transformations, scaling transformations and extrapolation techniques (geometrical over iteration steps and logarithmic over grid points) we achieve for the molecules H ₂ ⁺ and Th ₂ ^{179 +} relative accuracies better than 10^-12 for 1(1/2) g energies.