Perturbative and complete model space linked diagrammatic expansions for the canonical effective operator

摘要

Effective Hamiltonians and effective operators produce, respectively, exact energies and matrix elements of a timehyphen;independent operatorAfor a finite number of eigenstates of a timehyphen;independent HamiltonianH. We obtain degenerate and quasidegenerate perturbative expressions for the particularly useful canonical effective operatorAcirc;Cthrough second order in perturbation theory. The correspondingAcirc;Cdiagrammatic expressions are derived for the case whereAcirc;Cacts in a complete finite space. Our first order results have been used previously forabinitiocomputations of dipole and transition dipole moments in diatomic hydrides and for testing the assumptions in semiempirical methods for dipole properties. A brief discussion is also provided on the computational labors required by first and second orderAcirc;Cmanyhyphen;body calculations, the derivation ofAcirc;Cdiagrams whenAcirc;Cacts in an incomplete finite space, and on the derivation of diagrammatic rules forAcirc;Cin arbitrary perturbation order.