Density-Matrix Analysis for Spin Determination

The general properties of the density matrix of an unstable particle produced in a two-body collision are analyzed with a view toward deriving useful tests for the spin of the particle. Spin tests are obtained for production on polarized and on unpolarized targets, and special situations which do not allow for a complete determination of the density matrix are examined. Production of the unstable particle from a spinless boson incident on a spin-\textonehalf{} fermion is discussed in particular, and a special decomposition of the density matrix for that case appears to be quite useful for formulating tests of spin. Inequalities that must be satisfied from the elements of the density matrix are expressed in terms of directly measurable quantities and shown to provide general sets of spin tests.