Xenon Isotope Filtering at the Kinematic Edge of Inelastic Dark Matter

RESUMO

Motivated by high-energy xenon recoil searches, we study isotope-dependent endothermic dark-matter scattering near the upper speed boundary of a truncated Galactic halo. Small differences among xenon nuclear masses shift the minimum incident speed and can be strongly amplified when the required velocity approaches the end of the halo distribution. We formulate the isotope-resolved coherent-contact rate and separate this kinematic filtering from high-momentum nuclear suppression. For $m_\chi=1.1~\TeV$, $\delta=365~\keV$, and $E_R=248~\keV$, the kinematic-only benchmark gives $f_{136}^{\rm kin}\simeq0.289$, while after Helm weighting the largest contribution is $f_{132}\simeq0.346$ and the $^{136}$Xe fraction falls to $\simeq0.094$. For idealized pure-isotope targets at fixed detector mass, microscopic coupling, and halo, the integrated $225$--$271~\keV$ responses relative to natural xenon are approximately $0.404$, $1.235$, and $1.693$ for $^{129}$Xe, $^{132}$Xe, and $^{136}$Xe, respectively. A single effective-xenon nucleus also fails to reproduce the full isotope sum accurately near the edge, changing the benchmark window rate by about $8\%$ and producing larger spectral distortions. These quantitative results depend on the high-speed halo and on the assumed nuclear response; the isotope-dependent kinematic support does not. The calculation is a theory-level diagnostic rather than an LZ likelihood fit or event-by-event isotope identification.