Collision frame of reference

The integrals over the collision cross section S+ can be computed analytically by defining a linear transformation i(vi2) from the laboratory frame of reference into the collision frame of reference (Fox Vedula, 2010). The linear transformation does not depend on xn (only on V12) and thus it can be taken outside of the integrals. We can define a transformation... 

The transformation matrix from the laboratory frame (x) into the collision frame of reference (x ) depends only on the relative velocity vector V12 = vi - V2. By convention, V12 is aligned with the x axis. Thus, the orthonormal transformation matrix defined such that x = Lx can be written as... 

We would now like to evaluate explicitly the integrals in the collision terms appearing in Eq. (6.23). We will do this separately for each term involving the collision angles, and then reconstruct the final result at the end. The term V iACv) can be written in the collision frame of reference using xu = L xj2... 

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