Spin and Parity Analysis at All Production Angles

Bohr's symmetry method is applied to an unstable spin-j state X, which is produced in a reaction A+B→C+X and then decays according to X→D+E. Particles A, B, C, D are assumed to be spinless, and E is either a spinless particle or a gamma ray. Parity is conserved in production, but not necessarily in decay. The angular distribution of E, in the rest system of X, is I(θ)=1/2Σa_LP_L(cosθ), where L<~2j and the polar angle θ is measured from the normal to the production plane. The coefficients a_L depend upon the production angle δ and upon the dynamics of the production. It is proved here that the sign of the maximum-complexity coefficient a_2j depends only upon the parity of X, and that the magnitude of a_2j is not zero but lies between bounds which depend upon j and the parity alone. The implied test for j and the parity has the following advantages: (1) The spin j is equal to half the largest L in I(θ). Addition of a small amount of a higher P_L, which always improves the fit, is forbidden by the lower bound of a_2j. (2) The bounds of a_2j are independent of δ. Any (perhaps biased) average over δ may be performed before expanding I(θ) in the P_L. (3) All the data are condensed into a single test quantity a_2j, whose statistical error is reliably known.