Dirac equation eigenvalue spectrum

In perturbation theory, one often considers the essential spectrum. It consists of the continuous spectrum together with the accumulation points of the eigenvalues. Whenever the potential vanishes at infinity, the essential spectrum of the Dirac equation is the set... 

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)... 

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