Ion Channeling in Direct Dark Matter Detection

The channeling of the ion recoiling after a collision with a WIMP changes the ionization signal in direct detection experiments, producing a larger signal than otherwise expected. We give estimates of the fraction of channeled recoiling ions in NaI (Tl), Si, Ge, CsI, and solid Xe, Ar and Ne crystals using analytic models produced since the 1960's and 70's to describe channeling and blocking effects. We find that the channeling fraction of recoiling lattice nuclei is smaller than that of ions that are injected into the crystal and that it is strongly temperature dependent. Channeling is a directional effect which depends on the velocity distribution of WIMPs in the dark halo of our Galaxy and could lead to a daily modulation of the signal. We compute upper bounds to the expected amplitude of daily modulation due to channeling using our estimates of the channeling fractions. After developing the general formalism, we examine the possibility of finding a daily modulation due to channeling in the data already collected by the DAMA experiment. We find that even the largest daily modulation amplitudes would not be observable for WIMPs in the standard halo in the 13 years of data taken by the DAMA collaboration. For these to be observable the DAMA total rate should be 1/40 of what it is or the total DAMA exposure should be 40 times larger. The daily modulation due to channeling will be difficult to measure in future experiments