Drell-Hearn-Gerasimov Sum Rule: Examples and Counterexamples

Abstract

We investigate by means of examples whether the Drell-Hearn-Gerasimov sum rule can hold simultaneously for a lightly bound state and for its constituents. Subject to certain assumptions, whose applicability is discussed, we find in particular that if the rule holds for the nucleons, then it holds for the deuteron but fails for ${\mathrm{He}}^3$ and ${\mathrm{H}}^3$. If neutron and proton masses were appreciably unequal, then the rule would fail for the deuteron as well.