A scheme for the extraction of WIMP-nucleon scattering cross sections from total event rates

We propose a scheme that allows to analytically determine the three elementary cross sections and connect the solutions to the relative sign between the proton and the neutron spin scattering amplitudes once the measurements of total event rate from three appropriate targets become available. In this way it is thus possible to extract the maximum information on the supersymmetric parameter space obtainable from direct detection experiments, in the case that the dark matter particle is the lightest neutralino. Our scheme is based on suitably normalized forms of the isospin momentum dependent structure functions entering in the spin-dependent elastic neutralino-nucleus cross section. We compare these functions with the commonly used ones and discuss their advantages: in particular, these allow in the spin-dependent cross section to factorize the particle physics degrees of freedom from the momentum transfer dependent nuclear structure functions as it happens in the spin-independent cross section with the nuclear form factor.The authors acknowledge support from the Spanish MICINN projects Consolider-Ingenio 2010 Programme, MultiDark Grant No. CSD2009-00064 and FPA2009-10773, and from Junta de Andalucia under Grant No. P07FQM02962