Production of Polarized Particles in Nuclear Reactions

A general calculation of the polarization resulting from nuclear reactions is made by means of the S matrix and Racah formalisms. All sums over magnetic quantum numbers are performed; and the resulting polarization is expressed as a series in associated Legendre polynomials, each coefficient being manifestly real. All selection rules follow immediately from the requirements for the nonvanishing of the Racah and X coefficients. The only restriction required is to a two-body break-up.Higher spin tensor moments are required for the complete specification of the state of polarization of a beam of particles of spin greater than {}. A general expression is given for arbitrary spin moments resulting from a nuclear reaction. The result is expressed as a series in the spherical harmonics with all coefficients being manifestly real. The previous results of Blatt and Biedenharn for the angular distribution follow as a special case of the result. A generalization of the Eisner-Sachs rules for the complexity of angular distributions is also given.