Fully <i>ab-initio</i> all-electron calculation of dark matter-electron scattering in crystals with evaluation of systematic uncertainties

Abstract

We calculate target-material responses for dark matter–electron scattering at the all-electron level using atom-centered Gaussian basis sets. The all-electron effects enhance the material response at high momentum transfers from dark matter to electrons, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>q</a:mi><a:mo>≳</a:mo><a:mi mathvariant="script">O</a:mi><a:mo stretchy="false">(</a:mo><a:mrow><a:mn>10</a:mn><a:mi>α</a:mi><a:msub><a:mrow><a:mi>m</a:mi></a:mrow><a:mrow><a:mi>e</a:mi></a:mrow></a:msub></a:mrow><a:mo stretchy="false">)</a:mo></a:mrow></a:math>, compared to calculations using conventional plane wave methods, including those used in ; this enhances the expected event rates at energy transfers <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>E</f:mi><f:mo>≳</f:mo><f:mn>10</f:mn><f:mtext> </f:mtext><f:mtext> </f:mtext><f:mi>eV</f:mi></f:math>, especially when scattering through heavy mediators. We carefully test a range of systematic uncertainties in the theory calculation, including those arising from the choice of basis set, exchange-correlation functional, number of unit cells in the Bloch sum, <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi mathvariant="bold">k</h:mi></h:math>-mesh, and neglect of scatters with very high momentum transfers. We provide state-of-the-art crystal form factors, focusing on silicon and germanium. Our code and results are made publicly available as a new tool, called (“”). Published by the American Physical Society 2024