Negative-energy states properties

Similar to nonrelativistic Hartree-Fock theory, the Dirac-Roothaan Eqs. (10.61) are solved iteratively until self-consistency is reached. However, because of the properties of the one-electron Dirac Hamiltonian entering the Fock operator, molecular spinors representing unphysical negative-energy states (recall section 5.5) show up in this procedure. As many of these negative-continuum... 

More appropriate than perturbation approaches for improving on the energy are variational approaches (under the specific caveats discussed in chapter 8 with respect to the negative-energy states), because the total electronic energies obtained are much better controlled, an essential property since the exact reference is not known for any interesting many-electron molecule. In particular, we shall address the second-generation MCSCF methods mentioned in chapter 8. For reference to molecular Cl and CC theory, please consult sections 8.5.2 and 8.9, respectively. 

Second-order properties are often evaluated using coupled-perturbed Hartree-Fock (CPHF) theory. The CPHF wave function is essentially the first-order perturbed wave function, which, as we saw above, must include the negative-energy states. Thus, in the relativistic case, the CPHF method must include both the positive- and negative-energy states. 

The relativistic mean meson field (R.MF) theory formulated by Teller and others [8, 9, 10] and by Walecka [11] is quite successful in both infinite nuclear matter and finite nuclei[12, 13, 14]. In the RMF model, only positive-energy baryonic states are considered to study the properties of ordinary nuclei. This is the so-called no-sea-approximation . However, an interesting feature of the RMF theory is the existence of bound negative-energy baryonic states. This happens because the interaction with the vector field generated by the baryon-... 

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