Hamiltonian atomic, complex scaling

The complex coordinate rotation (CCR) or complex scaling method (5,6,10,19) is directly based on the ABCS theory (1-3), therefore Reinhardt (5) also called it the direct approach. A complex rotated Hamiltonian, H 0), is obtained from the electron Hamiltonian of the atom, H, by replacing the radial coordinates r by re, where 0 is a real parameter. The eigenproblem of this non-Hermitian operator is solved variationally in a basis of square-integrable functions. The matrix representation of H ) is obtained by simple scaling of matrices T and V representing the kinetic and Coulomb potential part of the unrotated Hamiltonian H,... 

Abstract Variational methods can determine a wide range of atomic properties for bound states of simple as well as complex atomic systems. Even for relatively light atoms, relativistic effects may be important. In this chapter we review systematic, large-scale variational procedures that include relativistic effects through either the Breit-Pauli Hamiltonian or the Dirac-Coulomb-Breit Hamiltonian but where correlation is the main source of uncertainty. Correlation is included in a series of calculations of increasing size for which results can be monitored and accuracy estimated. Examples are presented and further developments mentioned. 

---