New sum rule for the nuclear magnetic polarizability

I extend the well-known photonuclear sum rule that relates the strength of the photoexcitation of the giant dipole resonance in a nucleus to the number of elementary scatterers-nucleons to the case of virtual photons. The new sum rule relates the size of the magnetic polarizability of a nucleus to the slope of the transverse virtual photoabsorption cross section integrated over the energy in the nuclear range. I check this sum rule for the deuteron where necessary data is available, discuss possible applications and connection with other sum rules postulated in the literature.