Subexcitation electrons path length

In the problem of retardation of subexcitation electrons, the two important characteristics are the thermalization time and the thermalization path length. In condensed media the key role is played by thermalization path length, which determines how far can an electron travel away from its parent ion when it is thermalized. The thermalization path length determines the probability of formation of a free ion. 

The thermalization path length of subexcitation electrons has been the object of many discussions from the time the first track models appeared up to this day. The reason is that for quite a long time there were no direct methods of measuring the path lengths of slow electrons, while the corresponding theoretical analysis is very difficult owing to the need to take into account all the processes relevant to retardation of subexcitation electrons. 

Samuel and Magee250 were apparently the first to estimate the path length /th and time rth of thermalization of slow electrons. For this purpose they used the classical model of random walks of an electron in a Coulomb field of the parent ion. They assumed that the electron travels the same distance / between each two subsequent collisions and that in each of them it loses the same portion of energy A E. Under such assumptions, for electrons with energy 15 eV and for AE between 0.025 and 0.05 eV, they have obtained Tth 2.83 x 10 14 s and /th = 1.2-1.8 nm. At such short /th a subexcitation electron cannot escape the attraction of the parent ion and in about 10 13 s must be captured by the ion, which results in formation of a neutral molecule in a highly excited state, which later may experience dissociation. However, the experimental data on the yield of free ions indicated that a certain part of electrons nevertheless gets away from the ion far enough to escape recombination. 

The subsequent theoretical calculations of the rate of energy loss and of the path lengths of subexcitation electrons were based on formula (5.22). Since the velocity of subexcitation electrons is much smaller than the speed of light, from (5.22) we get the following expression... 

So, as one can see, this method of determining the thermalization path length is not straightforward and involves many assumptions and suppositions. First, the value of r0 depends on the specific choice of the function F r) (see, e.g., Ref. 269) and is too uncertain to enable us to determine the processes that are responsible for retardation of subexcitation electrons in a medium (see the discussion in Ref. 271). However, by comparing the values of r0 for different substances we are able to determine some of the factors that affect the path length of slow electrons. Since the value of r0 depends on the density p of the liquid, it is reasonable to compare the products prQ rather than the values of r0 themselves. 

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