Consequences of the Nuclear Charge Distribution

We have already seen above that the choice of a point-like atomic nucleus limits the Dirac theory to atoms with a nuclear charge number Z c, i.e., Zmax 137. A nonsingular electron-nucleus potential energy operator allows us to overcome this limit if an atomic nucleus of finite size is used. In relativistic electronic structure calculations on atoms — and thus also for calculations on molecules — it turned out that the effect of different finite-nucleus models on the total energy is comparable but distinct from the energy of a point-like nucleus (compare also section 9.8.4). 

We approach the effect of finite nuclear charge models from a formal perspective and introduce a general electron-nucleus potential energy Vnuc, which may be expanded in terms of a Taylor series around the origin. 

We obtain from the Dirac equation for the hydrogen atom for the coefficients of the term 

The result of the different origin behavior of the radial functions transfers to the many-electron case and creates substantial drawbacks for numerical methods applied to solve the radial equation. Numerical solution methods 

Spinors in Externai Scalar Potentials of Varying Depth 

---