Finite-element gauge function optimization for accurate current density calculations

The optimum gauge function is determined for an H₂⁺ ion in an ultra strong magnetic field by using the Kennedy-Kobe theory [ P. K. Kennedy and D. H. Kobe Phys. Rev. A 30 51 (1984)] combined with the finite element method. The divergence-free current density obtained by this method vanishes at the positions of protons. From this observation, we put the question as to whether there exists the nuclear cusp condition of current density or not, which is analogous to Kato’s cusp condition of electron density. We will show a few cases where the current density vanishes exactly at the maximum of electron density.