The Thomas-Reiche-Kuhn Sum Rule in the No-Core Shell Model

Sum rules of transition strengths can provide insight into atomic and nuclear structure. The Thomas-Reiche-Kuhn (TRK) sum rule is one such example of an energy-weighted sum rule for electric-dipole transitions. The TRK sum rule is known to have an exact analytical expression for purely local potentials and therefore any deviations indicate a momentum dependence on interactions used in the model. We apply the TRK sum rule to nuclear wavefunctions computed using the ab initio no-core shell model. We find that our calculations of the TRK sum rule are relatively insensitive to the model space truncation and are very similar between ground and excited states. Finally, we compare the TRK sum rules of nuclear spectra using different interactions including more 'soft', evolved interactions. These interactions are known to have more non-locality and as expected, we see a greater violation of the TRK sum rule.