Magnetic dipole energy-weighted sum rules with a delta interaction

The spectral distribution method is applied to linear energy-weighted sum rules (LEWSR) for magnetic dipole transitions using a two-body, spin-dependent delta interaction. The authors learn that in evaluating the ground-state expectation value of the sum-rule double commutator operator, it is crucial to have accurate ground-state wavefunctions. For example, in ²⁸Si with a delta interaction, the expectation value would vanish if the ground state was taken to be the closed j shell d⁶₅2 nu /d⁶ ₅2 pi / (as shown by Traini). However, with the properly correlated ground-state wavefunction one obtains a substantial contribution to LEWSR. These correlations are automatically taken care of int the spectral distribution method.