## D. Collisions of type (21) n or (21) $^{n}$(2) 

We know that at the beginning of a capture process, 2 and 3 have zero relative velocity and at the end, 1 and 2 have zero relative velocity. If we examine a given process under time reversal, we see that, initially, 1 and 2 have zero relative velocity and, finally, 2 and 3 have zero velocity. If the particle labels “1” and “3” are exchanged, one has a new capture process. If this time reversal and label exchange is done to the process (32) $^{n}$, what results is (21) n and when it is done to (2)(32) $^{n}$, what results is (21) $^{n}$(2) . This means that if (32) n or (2)(32) n is allowed for a point ( a, b ) = ( a$_{0}$, b$_{0}$ ) , then (21) n or (21) $^{n}$(2) , resp., is allowed for the point ( a, b ) = ( b$_{0}$, a$_{0}$ ) . Therefore the allowed regions for these processes may be generated by reflecting the previously determined regions about the line b = a. 

