A numerical study of resonance contributions to nuclear sum rules

The modified form of the nuclear sum rule which was proposed by Berggren is applied to a simple solvable problem and it is demonstrated, within the confines of that problem, that the continuum contribution to the sum rule is often dominated by the contribution from a few resonances, just as Berggren had anticipated. It is further shown that the bound, virtual and resonant states of the Hamiltonian considered form a complete set of states in terms of which the internal region of space can be expanded.