Relativistic K Electron Wave Functions by the Variational Principle

The variational principle is applied to obtain the Dirac wave functions of the K electrons of heavy atoms, using the method of variable parameters. In formulation, three parameters are used. The Coulomb and spin-spin interactions of the two K electrons are taken into consideration as well as the effect of the rest of the atom. A numerical example for mercury, Z=80, is given. Its K absorption edge is calculated and relativistic wave functions obtained, using one variable parameter. The results justify the use of screened hydrogenic wave functions although the screening constant (~0.5) is somewhat higher than that given by Slater's rules. Calculations using two variable parameters are also given and the total energy is found to have a saddle point and not a true minimum. This is briefly discussed in the light of the hydrogen atom.