Finite nucleus uniform distribution

Many model potentials (pnuc f) have been used [131] but two have become most important in electronic structure calculations. These are the homogeneous and the Gaussian charge distributions. The homogeneously or uniformly charged sphere is a simple model for the finite size of the nucleus. It is piecewise defined, because the positive charge distribution is confined in a sphere of radius R. The total nuclear charge -f-Ze is uniformly distributed over the nuclear volume 4 rR /3,... 

The use of Gaussian spinors in relativistic electronic structure calculations the effect of the boundary of the finite nucleus of uniform proton charge distribution. Chem. Phys., 225 (1997) 239-246. 

The electron—nucleus potential is not quite trivial. For larger atoms the radial functions that are large at the nucleus are affected by the finite charge distribution of the nucleus. It is sufficient to use the potential for a uniform charge distribution of radius R... 

By considering also relativistic effects, in addition to s electrons relativistic pi/2 electrons will also turn out to have finite density at the place of the nucleus. Then, for a uniformly charged spherical nucleus of radius R, single-electron approximation gives the following radial density distribution Pe r) ... 

---