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Calculating dark matter scattering and absorption rates with the energy loss functions (ELF)

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DarkELF

DarkELF is a python package capable of calculating interaction rates of light dark matter in dielectric materials, including screening effects. The full response of the material is parametrized in the terms of the energy loss function (ELF) of material, which DarkELF converts into differential scattering rates for both direct dark matter electron scattering and through the Migdal effect. In addition, DarkELF can calculate the rate to produce phonons from sub-MeV dark matter scattering via the dark photon mediator and most multiphonon processes. It also computes the absorption rate for dark matter comprised of dark photons. The package currently includes precomputed ELFs for Al,Al2O3, GaAs, GaN, Ge, Si, SiO2, and ZnS, and allows the user to easily add their own ELF extractions for arbitrary materials.

See arXiv 2104.12786 for a description of the implementation

Authors

Brian Campbell-Deem, Simon Knapen, Jonathan Kozaczuk, Tongyan Lin, Connor Stratman, and Ethan Villarama

Physics

ELF

Currently DarkELF contains ELF look-up tables obtained with the GPAW density functional theory code for Si and Ge, as well as data-driven Mermin model for the remaining materials. The Lindhard ELF is also included. DarkELF also comes with a number of measured ELFs in the optical limit for energy depositions below the electronic band gap, which is relevant for phonon processes. Additional materials and ELF computations may be added at a later date. When using a particular ELF computation, please refer to the relevant experimental papers and/or GPAW package. These references can be found in arXiv 2104.12786.

DM electron scattering

DarkELF can calculates DM-electron scattering rates in dielectric materials by making use of ELF of the material, as described in arXiv 2101.08275. This approach automatically includes screening effects.

DM - nucleon scattering through the Migdal effect

DarkELF can compute the rate for ionizations through the Migdal effect, as derived in arXiv 2011.09496. Currently we provide calculations in the soft limit, assuming the free ion or impulse approximation. For a number of materials we also include the tabulated form factors for the atomic Migdal effect, as computed by Ibe et. al. (arXiv 1707.07258).

DM - phonon scattering

DM - phonon scattering through a light dark photon mediator (arXiv 1712.06598, 1807.10291) can also be computed in terms of the ELF. DarkELF can also calculate the rate for multiphonon production in dark matter scattering, including daily modulation effects (arXiv 2205.02250 for the isotropic approximation, 2411.03433 for anisotropic crystals and daily modulation).

DM - Absorption

If the DM is itself a light dark photon, it can be absorbed on phonons (arXiv 1712.06598, 1807.10291) or electrons (arXiv 1608.02123, 1608.01994), the rate of which can be extracted directly from the ELF.

Requirements and Usage

DarkELF requires python 3.6 or higher, equipped with the numpy, scipy, pyyaml and pandas packages. The multiphonon module uses the vegas monte carlo package, which can be found here https://pypi.org/project/vegas/ The tutorial notebooks require a jupyter installation, but this is in general not needed for DarkELF itself.

The examples folder contains a tutorial jupyter notebook for each of the processes outlined above. Appendix A of the DarkELF paper contains additional explanations of the various functions and settings that are available to the user.

Citation guide

If you use DarkELF, please refer to the corresponding paper arXiv 2104.12786. For the specific processes, please refer to the papers outlined in the sections above.

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Calculating dark matter scattering and absorption rates with the energy loss functions (ELF)

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