Factorization as an approximate property of the scattering of composite systems

Abstract
It is shown that total cross sections for the scattering of two composite systems will factorize to an extremely good approximation provided that the two systems do not differ markedly from each other either in number of constituents or size. Two separate cases are examined in detail: the optical case, in which the constituents are much smaller than the system, and the overlap case, in which the constituents are larger than the radius in which the constituent centers are confined. The smooth transition between these two regions is examined when the numbers of constituents are two and three.