# Does high energy limit of ionization process recover elastic scattering?

in my previous intuitive understanding, when some particle scatters with a bound state electron and leads to a continuous final state with recoil energy much larger than the initial binding energy, the process should be similar to elastic scattering, since the momentum transfer $$q$$ is large and one can take the initial state as plane-wave.

However, in some literature on dark matter direct detection based on ionization, the calculation seems not to recover the elastic scattering limit. In these cases, one needs to calculate the ionization form factor

$$\sim\langle f |e^{i \vec{q} \cdot \vec{x}}| i \rangle$$

with $$i$$ denoting initial bound electron with discrete energy level, $$f$$ denoting final state continuum and $$e^{i \vec{q} \cdot \vec{x}}$$ being the momentum transfer. When the initial state is plane-wave, this leads to momentum conservation $$\delta (\vec{p}_i + \vec{q} - \vec{p}_f)$$. For bound states like the electrons around the XENON, the atomic factor is related to the spatial overlapping between $$\langle f|$$ and $$e^{i \vec{q} \cdot \vec{x}}| i \rangle$$ , which seems to decrease with the recoil energy. This is very surprising to us at first. And then we found the figure 7 of https://arxiv.org/abs/1904.07127, which claims that when the recoil energy is 2 keV, the form factor is dominated by $$n=3$$ shell, instead of $$n=4$$ or $$n=5$$ with more binding electrons. This seems to also hint that the high energy limit of ionization deviates from the elastic scattering.

This is really something confusing to me. Is there are some more intuitive understanding to explain why the high energy limit of ionization deviates from the elastic scattering or some previous calculations/paper?