The dipole sum rule with an approximate Hamiltonian

Abstract

The familiar ƒ; sum rule for the electric dipole interaction of a complex charge-current system with the electromagnetic field is known to be simply applicable even when exchange forces and other non-classical dynamical effects are present. Evaluation of the ƒ; sum for absorption from the ground state can be made knowing only the Hamiltonian and the ground state wave function. For complex systems the exact wave function is rarely known. Two methods of estimating the ƒ; sum are then attractive whenever an independent particle model is empirically favored: (i) use of the best IPM wave functions and the true Hamiltonian, or (ii) use of the same wave functions but the equivalent one-body potential found to give best energy levels for the IPM. In the first calculation, dynamical correlations are neglected; in the second, a spurious contribution to the sum arises from the velocity dependent form typical of an equivalent one-body potential. We compute the ƒ; sum by both methods in a nuclear example. The results show the differences of principle which arise, though the numerical agreement is rather close. Physical arguments are given for the origin of this close agreement, which can be expected only in particular cases. No criterion for the reliability of such IPM sum rule calculations is known.