Ionization of Atoms by Slow Heavy Particles, Including Dark Matter

Atoms and molecules can become ionized during the scattering of a slow, heavy particle off a bound electron. Such an interaction involving leptophilic weakly interacting massive particles (WIMPs) is a promising possible explanation for the anomalous $9\sigma$ annual modulation in the DAMA dark matter direct detection experiment [R. Bernabei et al., Eur. Phys. J. C 73, 2648 (2013)]. We demonstrate the applicability of the Born approximation for such an interaction by showing its equivalence to the semiclassical adiabatic treatment of atomic ionization by slow-moving WIMPs. Conventional wisdom has it that the ionization probability for such a process should be exponentially small. We show, however, that due to nonanalytic, cusplike behavior of Coulomb functions close to the nucleus this suppression is removed, leading to an effective atomic structure enhancement. We also show that electron relativistic effects actually give the dominant contribution to such a process, enhancing the differential cross section by up to 1000 times.

Figure 1

The ratio $R$ of the atomic structure factor ${|⟨ϵs_{1/2}|e^{-i\mathit{q}·\mathit{r}}|3s_{1/2}⟩|}^2$ for the ionization of $3s_{1/2}$ electrons in iodine ($I_{3s_{1/2}}=1.1\mathrm{keV}$, $ϵ=2\mathrm{keV}$) calculated with relativistic (hydrogenlike Dirac) wave functions to that obtained with nonrelativistic wave functions, using the true nuclear charge $Z=53$. (The momentum conversion is $1\mathrm{MeV}/c\approx 268\mathrm{a}\mathrm{.}\mathrm{u}\mathrm{.}$)