We study the basic integral equation in Lindhard’s theory describing the energy given to atomic motion by nuclear recoils in a pure material when the atomic binding energy is taken into account. The numerical solution, which depends only on the slope of the velocity-proportional electronic stopping power and the binding energy, leads to an estimation of the ionization efficiency which is in good agreement with the available experimental measurements for Si and Ge. In this model, the quenching factor for nuclear recoils features a cutoff at an energy equal to twice the assumed binding energy. We argue that the model is a reasonable approximation for Ge even for energies close to the cutoff, while for Si is valid up to recoil energies greater than $\sim 500\mathrm{eV}$.

• Received 22 January 2020
• Revised 6 April 2020
• Accepted 9 April 2020

DOI:https://doi.org/10.1103/PhysRevD.101.102001

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Published by the American Physical Society