Higher order averages of primary recoil distributions
Higher order averages of primary recoil distributions
One problem of interest in radiation damage theory is the slowing down of an energetic primary knockon in its own lattice. The primary starts at the origin, slows down and comes to rest at a final vector distance r= (x$_{s})$. In this paper we study averages over the distribution w(r) of the final...
Saved in:
Personal Name(s):  Leibfried, G. (Corresponding author) 

Contributing Institute: 
Publikationen vor 2000; PRE2000; Retrocat 
Imprint: 
Jülich
Kernforschungsanlage Jülich, Verlag
1963

Physical Description: 
p. 118 
Document Type: 
Report Book 
Research Program: 
ohne Topic 
Series Title: 
Berichte der Kernforschungsanlage Jülich
119 
Link: 
OpenAccess OpenAccess 
Publikationsportal JuSER 
One problem of interest in radiation damage theory is the slowing down of an energetic primary knockon in its own lattice. The primary starts at the origin, slows down and comes to rest at a final vector distance r= (x$_{s})$. In this paper we study averages over the distribution w(r) of the final positions. The slowing down is described here by a series of subsequent and independent twobody collisions. The scattering centers are supposed tobe at random ratherthan arrangedin alattice. The reasons for the choice of this randorn rnodel have been discussed in Ref.$^{1}$. The collisions thernselves are described by a total scattering cross section a,the corresponding rnean free path $\lambda=1/n\sigma$ (n being the density of lattice atorns) and the distribution G of energies and directions after one collision *. These quantities are energy dependent **. Analytical expressions for linear ($\overline{X_{s})}$ and quadratic ($\overline{X_{s}X_{t})}$ averages have been given in two previous papers$^{1, 3}$. The method of derivation was rather tedious and a little clumsy. The purpose of this paper is to give a rnore elegant rnethod which also is easily extended to higher order averages $\overline{(X_{s}X_{t}X_{u}, X_{s}X_{t}X_{u}X_{v}}$ and so on). These higher order averages irnprove the knowledge of the distribution, which, of course, would be the rnost desirable quantity to calculate. Since the basic physical ideas and the importance of this problem in radiation damage have been discussed already several tirnes, we will not repeat this here, but rather will treat the rnathernatical aspects. 