REVIEW OF MATHEMATICS, NUMERICAL FACTORS, AND CORRECTIONS FOR DARK-MATTER EXPERIMENTS BASED ON ELASTIC NUCLEAR RECOIL

We present a systematic derivation and discussion of the practical for mulae needed to design and interpret direct searches for nuclear recoi l events caused by hypothetical weakly interacting dark matter particl es. Modifications to the differential energy spectrum arise from the E arth's motion, recoil detection efficiency, instrumental resolution an d threshold, multiple target elements, spin-dependent and coherent fac tors, and nuclear form factor. We discuss the normalization and presen tation of results to allow comparison between different target element s and with theoretical predictions. Equations relating to future direc tional detectors are also included.