Expected energy deposit

5.2 Expected energy deposit

The predicted differential observable recoil spectrum, assuming a standard virial Maxwellian velocity distribution, is of the form

where $f$ is the quenching factor which reflects the relative efficiency with which the nuclear recoil energy is recorded in the signal channel compared to a $γ$ -ray of the same energy. $E0$ is the characteristic energy for the virialized WIMP population, $F$ is the form factor referred to previously, and $r$ is a kinematic factor dependent on the relative masses of the WIMP and target nuclei. Somewhat more complex formulae result when modified velocity distributions are used (e.g. incorporating a Galactic cut-off), or the rate is convolved through the instrument response. A falling recoil spectrum with a maximum recoil energy $∼$ 100 keV is expected. For larger target nuclei, such as iodine, the form factor further suppresses the recoil spectrum above 50 keV.

Inelastic WIMP scattering (producing excited nuclear states) can also occur. $γ$ -rays emitted from nuclear relaxation can be self-absorbed in the detector producing characteristic spectral lines. Experiments of this sort have been performed [15 , 52 , 17 ]; the cross-sections are much lower than the elastic ones and the technique will not be discussed further.