kinetic theory - How much do we know about the characteristic time for electron-ion recombination for a dense plasma?

As mentioned, how much do we know about the characteristic time for electron-ion recombination for a dense (noble gas) plasma (i.e. density of electrons at $\approx 10^{21} \textrm{cm}^{-3}$) at $10000 \textrm{K}$ (i.e. at around $\approx 1\textrm{eV}$)?

The dominant mechanism for electron-ion recombination at this temperature and density for a thermalised plasma seems to be three-body recombination (or dielectronic recombination). The mentioned process is the backward process as represented in the equation, $ X + e^- \rightarrow X^{+1} + e^- + e^- $, where $X$ denotes the participating atom. The cross section of its inverse process, electron impact ionization, has been measured experimentally (probably at a low density of $X$), and the rate of this inverse process can be obtained from the cross section (i.e. $\approx $, where $<\cdots>$ denotes a thermal average over the energy of the impacting electron, $v$ the thermal velocity of the impacting electron and $\sigma$ the cross section). It seems that the rate of three-body recombination can be obtained from the principle of detailed balance.

The problem is that the density effect of $X$ has been ignored. It seems that we are extrapolating the cross sections at low densities of $X$ to obtain the cross sections at high densities of $X$. Of course the obtained cross sections for Xenon for example, are about (PRA, 65, 042713, doi:10.1103/PhysRevA.65.042713) $10^{-16} \textrm{cm}^2$, which suggests a length $\approx 10^{-10} \textrm{m}$. The average separation between the atoms seems to be greater than this value at $21\times 10^{21} \textrm{cm}^{-3}$, and so the density effect may be unimportant. Yet the argument is ad-hoc.

Is there any reason to believe that the electron-ion recombination time (or rate) will be significantly different from the one obtained using the above procedure? ("significantly" means the correct time will be several orders larger/smaller than the calculated time). Thanks.