Neutralino inelastic scattering with subsequent detection of nuclear γ rays

We consider the potential benefits of searching for supersymmetric dark matter through its inelastic excitation, via the “scalar current,” of low-lying collective nuclear states in a detector. If such states live long enough so that the γ radiation from their decay can be separated from the signal due to nuclear recoil, then background can be dramatically reduced. We show how the kinematics of neutralino-nucleus scattering is modified when the nucleus is excited and derive expressions for the form factors associated with exciting collective states. We apply these results to two specific cases: (1) the Iπ=5/2+ state at 13 keV in 73Ge, and (2) the rotational and hence very collective state Iπ=3/2+ at 8 keV in 169Tm (even though observing the transition down from that state will be difficult). In both cases we compare the form factors for inelastic scattering with those for elastic scattering. The inelastic cross section is considerably smaller than its elastic counterpart, though perhaps not always prohibitively so