The diagonalization of the effective Hamiltonian H^eff yields  the model-space parts of the target relativistic wavefunctions (|m>, |n>, ...). Provided that efficient `diagrammatic' algorithms are employed, no explicit approximation for the remainder (outer-space) parts of the wavefunctions is obtained. A convenient way to incorporate the contributions from these parts to transition property values consists in a perturbative calculation of transition density matrices.

The first-order approximation for the m - n transition spin-free density matrix ^mnR compatible with the use of the present approximation for H^eff is given by

where

J and J' are model-space determinant indices and the determinants |K> are out of the model space,
s,r are the spatial orbital indices,
E_sr denotes the spin-free one-electron r -> s excitation operator,
the definition of energy denominators  D(I,K) is the same as used for H^eff .

The  m -> n  transition value of an one-electron property (A_nm) is readily obtained as

where A is the property matrix in the chosen spatial orbital basis.

References