Free-Ion Yield in Liquefied Rare Gases

FIGURE 9.3 A low-LET track in a liquefied rare gas (LRG). Even at a minimum LET, the electron thermalization length ( 103 nm) greatly exceeds the inter-positive-ion separation of R2+ ( 102 nm). Thus, the geometry approximates cylindrical symmetry rather than a collection of isolated ionizations. Reproduced from Mozumder (1995a), with the permission of Elsevier . 

Vd = pE is the drift velocity. The recombination and escape probabilities are now given by PR = NR /n+° L0 and Pkc = 1 - Pr. Since Vd = i, but T /r1 these probabilities are independent of mobility. However, the initial separation r0 is expected to depend (increase) with electron mobility, thus making the escape probability indirectly dependent on the mobility. These effects are quite similar to those in the Onsager theory 

Detailed comparison of calculated and experimental results for the variation of the escape probability with the external field in Lar, LKr, and LXe has been made by Mozumder (1995a, b, 1996) using the data on LET, W value, mobility, and so forth. Experiments are with MeV electrons or beta-emitters having minimum LET in these liquids. The external field generally does not have any preferred direction relative to the track axis. Mozumder (1995a) argues that in such 

Values of rh in LAr, LKr, and LXe at their respective temperatures are 1568, 3600, and 4600 nm. Wide variation of thermalization length around the rms value is of course expected. However, the escape probability has been found to be insensitive to rg in these cases around their rms values. Therefore, averaging Pesc over the distribution of thermalization length has been deemed unnecessary when r() is taken equal to rth. 

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Figure 6 Fast electron-induced free ion yields in liquefied rare gases. (Redrawn from the data of Doke, T., Portgal Phys., 12, 9,1981.)...

In liquefied rare gases (LRG) the ejected electron has a long thermalization distance, because the subexcitation electrons can only be thermalized by elastic collisions, a very inefficient process predicated by the small mass ratio of the electron to that of the rare gas atom. Thus, even at a minimum of LET (for a -1-MeV electron), the thermalization distance exceeds the interionization distance on the track, determined by the LET and the W value, by an order of magnitude or more (Mozumder, 1995). Therefore, isolated spurs are never seen in LRG, and even at the minimum LET the track model is better described with a cylindrical symmetry. This matter is of great consequence to the theoretical understanding of free-ion yields in LRG (see Sect. 9.6). 

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