Solutions of the Spin-Free Modified Dirac Equation

In the next section, we will examine some properties of the solutions of the spin-free modified Dirac equation, and we then proceed to a closer inspection of the one-electron operators in the modified formalism before treating the two-electron terms. 

Solutions of the Spin-Free Modified Dirac Equation 

Two critical questions about the removal of the spin dependence from the Dirac equation are, What effect does this have on the eigenvalue spectrum and How is the wave function modified These questions may be answered by a similar process to that used for the atomic Dirac equation in chapter 7. The second question has as an auxiliary question, How does the wave function behave in the nonrelativistic limit  

The eigenvalue spectrum of (15.14) may be deduced from the behavior of the equations in the region far from the nuclei, where V 0 and consequently all terms involving V are negligible. The spin-free modified Dirac equation in this region may be written (in Hartree atomic units) 

Substituting for from the first of these equations into the second gives the 

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