Electron Thermalization in Liquefied Rare Gases

Liquefied rare gases(LRGs) are very important both from the fundamental point of view and in application to ionization chambers. In these media, epithermal electrons are characterized by a very large mean free path for momentum transfer -10-15 nm, whereas the mean free path for energy loss by elastic collision is only -0.5 nm. This is caused by coherence in momentum transfer scattering exhibited by a small value of the structure factor at low momentum transfers 

The mean energy loss in an elastic collision may be taken as 5(m/M) [(e) — (3/2)fegT] where (e) is the mean electron energy, nt/M is the ratio of electron mass to that of the rare gas atom, and S is a numerical parameter. The collision rate may be approximated by A0 1 (2(e)/m)m. The equation for the rate of energy loss may now be given as follows  

Ignoring the effect of the initial energy, since that is much greater than kBT, the solution of the above equation gives the thermalization time tih as 

Taking Ay = 15 nm, . = 5 eV, and other values as before, the b value for LAr is evaluated as 1400 nm, which is much larger than 133 nm, obtained by fitting the free-ion yield to the Onsager formula (vide supra). Similar calculations for LKr and LXe give b values of the gaussian thermalization distribution 

FIGURE 8.6 Evolution of the electron diffusion coefficient in LAr starting with an initial velocity 4.8 times the thermal velocity. Reproduced from Mozumder (1982). 

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