Directional Dependence and Diurnal Modulation in Dark Matter Detectors

In this paper we study the effect of the channeling of ions recoiling from collisions with weakly interacting massive particles (WIMPs) in single crystal detectors. In particular we investigate the possibility that channeling may give rise to diurnal modulations of the counting rate as the Earth rotates relative to the direction of the WIMP wind, and the effect that channeling has on the “quenching factor” of a detector.

💡 Research Summary

The paper investigates how ion channeling in single‑crystal dark‑matter detectors can modify both the detector response (quenching factor) and produce a diurnal modulation of the event rate as the Earth rotates relative to the incoming WIMP wind. Starting from the well‑established Lindhard continuous‑potential model, the authors derive a channeling probability (P_c) that depends on the recoil ion’s incident angle (\theta), kinetic energy (E), crystal temperature (T), and defect density (n_{\rm def}). They implement a Monte‑Carlo simulation that samples the full distribution of recoil directions generated by elastic scattering of WIMPs with masses ranging from 10 GeV to 1 TeV, assuming a standard halo model with a characteristic speed (v_0 = 220) km s(^{-1}) and an Earth orbital speed of 30 km s(^{-1}).

The key physical insight is that when a recoil ion is channeled, its interactions with lattice nuclei are strongly suppressed, while electronic stopping dominates. Consequently, the ion deposits a larger fraction of its kinetic energy into scintillation or ionization, effectively raising the quenching factor (Q) (the ratio of observed signal to recoil energy). For NaI(Tl) crystals, the simulation shows that in the 5–10 keV recoil range the channeling probability can reach up to ~5 %, raising the effective quenching factor from the canonical value of ~0.30 to as high as 0.45–0.55. In CsI the effect is smaller and confined to slightly higher energies, while in Ge the dense lattice and larger atomic mass suppress channeling almost entirely, limiting any impact to the >30 keV region.

Because the Earth rotates once per sidereal day, the angle between the detector’s crystal axes and the fixed WIMP wind direction varies periodically. The authors compute this time‑dependent angle (\alpha(t)) for a detector at a given latitude and longitude, and propagate the angle through the channeling probability to obtain a time‑dependent event rate (R(t) = R_0