The asymptotically exact equations

The first equations for macroscopic densities n (f) come from a set (7.1.1) provided (m + m ) — 1. Consider, for instance, an equation for the density 

Making transformations here we used equation (7.1.3) and the fact that 91 1 as well as p p depend on r = f - f/l only. (It permits to change the integration variable in equation (7.1.4).) 

Note that after making limiting transition ao 00 the equation for gi i is steady-state. Equation (7.1.5) contains integrals of functions p2,i and gi 2-A study of the equations defining these functions leads to relations with functions like gm,i and gi m Let us consider for definiteness equation for 52,1 

In equation (7.1.6) the first and the last term in the r.h.s. turns out to zero as (70 — oo. The integral terms contain functions 52,2 in which there exist several defects A in the recombination sphere around B which, in their turn, have partners to recombine at r tq. In the limit of instant annihilation such functions have another order of magnitude in cTq.  

A set (7.1.7) could be solved simply with respect to functions gm,i- To shortem these equations let us introduce more compact expressions fi = fi n-r( ), 5m-i,o( r m 0 = Pm, Q- Finally, we arrive 

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