Hamiltonian Chang-Pelissier-Durand

If we wish to incorporate some level of relativistic effects into the zeroth-order Hamiltonian, we cannot start from Pauli perturbation theory or direct perturbation theory. But can we find an alternative expansion that contains relativistic corrections and is valid for all r that is, can we derive a regular expansion that is convergent for all reasonable values of the parameters The expansion we consider in this chapter has roots in the work by Chang, Pelissier, and Durand (1986) and HeuUy et al. (1986), which was developed further by van Lenthe et al. (1993, 1994). These last authors coined the term regular approximation because of the properties of the expansion. 

In the development of the Pauli Hamiltonian in section 17.1, truncation of the power series expansion of the inverse operator after the first term yielded the nonrelativistic Hamiltonian. In (18.1), the zeroth-order term is the Hamiltonian first developed by Chang, Pelissier, and Durand (1986), often referred to as the CPD Hamiltonian. The name given by van Lenthe et al. is the zeroth-order regular approximation, ZORA, which we will adopt here. The zeroth-order Hamiltonian is... 

Chang, C., Pelissier, M. and Durand, P. (1986) Regular Two-Component Pauli-Like Effective Hamiltonians in... 

Chang, Ch., Pelissier, M., and Durand, Ph. (1986). Regular two-component Pauli-like effective Hamiltonians in Dirac theory. Phys. Scr., 34, 394-404. 

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