Channeling in direct dark matter detection I: channeling fraction in NaI (Tl) crystals

TL;DR

The paper develops analytic, continuum-model estimates of channeling fractions for recoiling lattice nuclei in NaI(Tl) crystals, highlighting the strong temperature dependence and the difference from channeling of incident ions. Using Lindhard-type axial and planar potentials, the authors derive energy-dependent critical distances and angles, incorporate Debye thermal vibrations, and compute per-channel and total recoiling-channeling probabilities via angular averaging and channel-by-channel recursion. They show that recoiling lattice nuclei exhibit smaller channeling fractions than incident ions, with maxima around a few hundred keV and substantial suppression from dechanneling by Tl impurities; these results yield conservative upper bounds and stress the need for Monte Carlo simulations to obtain precise, quantitative predictions. The study informs interpretation of direct dark matter searches (e.g., DAMA) and supports future work on daily modulation and channeling in NaI(Tl) and other crystals by providing a transparent analytic framework and clear temperature-dependent behavior. The analytic approach, while approximate, connects crystallography, thermal vibrations, and WIMP-induced recoils to quantify how channeling can alter the observed scintillation signal and thus the inferred WIMP properties.

Abstract

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) 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.

Figures (1)

• Figure 1: One eights of the NaI crystal unit cell with the red and blue spheres representing Na and I ions respectively. The solid, dashed and dot-dashed lines show the $<$100$>$, $<$110$>$, and $<$111$>$ axes respectively. The {100}, {110} and {111} planes are perpendicular to the respective axes with equal indices.