Theory of Polarized Particles and Gamma Rays in Nuclear Reactions

The complete specification of the spin states of a particle of spin $i$ resulting from a nuclear reaction requires a knowledge of all irreducible spin tensor moments ${{T}_{\ensuremath{\kappa}}}^{q}(|\ensuremath{\kappa}|\ensuremath{\le}q\ensuremath{\le}2i)$. A general calculation is made of the spin tensor moments arising from a nuclear reaction initiated by an arbitrarily polarized initial beam. All sums over magnetic quantum numbers are performed by the use of the $S$ matrix and Racah formalisms. The results are expressed in terms of the $G$ function which is related to the Fano $X$ function. All selection rules follow from the properties of the $G$ function. In particular, a generalization of the Eisner-Sachs selection rules are given. The problem of the detection of polarized particles is considered.The $S$-matrix formalism is extended to include the possibility of gamma-rays in nuclear reactions. Analogous formulas to those of Blatt and Biedenharn are given for the angular distribution of gamma-rays. A simple recipe yields a general result for the polarization and angular distribution of radiation from aligned nuclei. Finally, the theory is extended to include the possibility of an arbitrarily polarized target nucleus as well.