Comparison of the Migdal transition probabilities in electron-atom inelastic cross sections

TL;DR

This work assesses the reliability of Migdal transition probabilities for dark matter–nucleus scattering by directly comparing them to total single-electron inelastic cross sections in isolated Ar and Xe. Using a center-of-mass formalism and a Born-level Coulomb interaction, the cross section is connected to Migdal transition factors derived from FAC calculations, revealing sizable discrepancies: ~30% for Argon and ~80% for Xenon around 1 keV. The dominance of outer-shell excitations (Ar: 3p; Xe: 5p, with 4d contributing at higher fractions) explains much of the difference and highlights sensitivities to shell structure and correlation effects. The study also contrasts these results with Bethe-type and Salvat cross sections, noting underestimation in the keV regime and emphasizing avenues for improvement, including multi-channel and liquid-atom effects for realistic detector contexts.

Abstract

The Migdal transition probabilities for dark matter scattering are compared to the total single-electron inelastic cross sections of electron-atom scattering for isolated Ar and Xe. The comparison is done by expressing the electron-atom scattering cross section by connecting the Migdal probability. The resultant differences are around $30 \ \%$ for Ar and $80 \ \%$ for Xe in $\sim$ 1 keV of incoming electron energy. The transition is dominated from the $3p$ shell electrons for Ar. For Xe, $5p$ states dominate the contribution, but, $4d$ states give $\sim 40\ \%$ contribution at 1 keV.

Figures (2)

• Figure 1: The total excitation and ionization cross section of electron-atom scattering $\sigma(E_{{\rm kin},I})$ as the function of kinetic energy for incoming electron in laboratory frame $E_{{\rm kin},I}$. The calculation results using the transition probabilities of Ref. Ibe:2017yqa are shown by the solid lines and the comparison values are shown by the dashed lines. The red lines show the single excitation case and blue lines show the single ionization case. (top:) For Ar case. The database value for comparison is taken from Phelps Phelps:2024. (bottom:) For Xe case. The database value for comparison is taken from Morgan Morgan:2024. The ionization data is limited up to 1 keV.
• Figure 2: The comparison of total inelastic cross section $\sigma(E_{{\rm kin},I})$. The calculation results using Ref. Ibe:2017yqa are shown by the solid lines and the comparison values are shown by the dashed and dotted lines. (top:) For Ar case. The dotted lines are from the theoretical calculation in Ref. inokuti1975total with the Hartree-Fock calculation. The database value is taken from Phelps Phelps:2024. (bottom:) For Xe case. The dotted lines are from the theoretical calculation in Ref. salvat2022inelastic and not convergent at low energy region because of its formula. The database value is taken from Morgan Morgan:2024.