Target polarization effects in nuclear reactions

Abstract

Abstract Considerations of direct reactions, based on a distorted-wave formalism, show that the effects of polarized targets represented by the tensor, ϱkκ(a), correlated to the polarization of the residual nucleus, represented by ϱkκ(b) when the target is unpolarized, provided that the transferred total angular momentum j is unique. Two related processes are considered: (1) A beam of unpolarized particles is incident on an unpolarized target and the angular dependence of the reaction-product yield associated with each tensor ϱkκ (a) is measured. (2) With no polarization in the entrance channel, the angular dependence of the polarization of the residual nucleus is measured by identifying the coefficient of the Ykκ(ϑγ, φγ) in the triple angular correlation involving the incident beam, the reaction product and the de-excitation gamma radiation. It is found that these angular dependences are identical; furthermore the relative magnitudes of the partial cross sections in (1) and (2), for a given reaction-product angle, lead to a determination of j. Polarization tensors ϱkκ(a) of rank k > 2jmax should not affect the angular distributions. No detailed assumptions are made concerning the nature of the projectile or reaction product, nor the spin-dependence of either the interaction or the channel distortions, except that such distortions be independent of the spins of the target and residual nuclei. Upper bounds may also be given, provided that j is unique, to both the magnitudes of the asymmetry in the angular distributions associated with a given polarization tensor and the magnitudes of the polarization of the residual nucleus. For a given rank of polarization these upper bounds are functions merely of a, b, and j. In several cases, because of the accidental vanishing of Racah coefficients. selection rules may be given for polarization effects of a particular rank. The polarization correlation applies to a variety of direct processes, including knock-on phenomena. Experiments are proposed which help to disentangle direct-stripping amplitudes from those normally referred as involving heavy-particle stripping where the polarization correlation is not simple unless additional assumptions are made concerning the spin dependence of optical-model potentials. It is demonstrated that provided j is unique, a series of measurements with polarized projectiles incident on polarized targets is sufficient to overdetermine the reaction amplitudes. Several processes are considered which involve spinless projectiles and reaction products and targets of integral spin. These need not be direct processes. So long as the target is appropriately polarized, observation of the reaction product, parallel or anti-parallel to the original motion, leads to a determination of the parity of the residual nucleus, and to the identification of non-zero spin states.