Charge exchange operators sum rules and proton-neutron T=0 and T=1 pairing interactions

We study sum rules for charge exchange operators of the Gamow-Teller and Fermi type and explore what can be learned from them about proton-neutron pairing in T=0 and T=1 channels. We consider both energy weighted (EWSR) and non-energy weighted (NEWSR) sum rules. We use a schematic Hamiltonian to stress the distinctive roles of T=1 and T=0 pair interactions and correlations in the sum rules. Numerical results for 44Ti are presented for both schematic and realistic interactions.