Nuclear charge distribution effect on high-accuracy calculations of the ground state energies of hydrogen-like systems

Notre Dame (ND) and Dual-Kinetic-Balance (DKB) basis sets based on B-spline functions are used respectively to solve Dirac equation of hydrogen-like ions in the Gaussian Charge Distribution Model. The ground state energies are compared with those in the Point Charge Distribution Model and their corresponding experimental values. It is found that the nuclear charge distribution effect plays an important role, and the relative correction is gradually notable as Z increases. When Z is 100, the correction approaches 10^-3. In the near nuclear region, the wavefunctions in the two models are also presented. With the increase of Z, the difference of the wavefunctions is more obvious. Differing from the most of work which apply the B-splines to long-range calculations, in our work, the B-spline functions are successfully extended to study the short-range interaction between electron and nucleus. (authors)