A detailed analysis of the extension of the Barshay-Temmer theorem to reaction product pairs that are members of the same SU(4) multiplet (Wigner supermultiplet) is presented. Nonzero values of the total orbital angular momentum within fragments in the presence of residual spin orbit splitting is shown to destroy symmetry of the reaction products around 90° except in a sum rule sense. Departures from reaction symmetry are related to the SU(4) breaking parameter in the effective nucleon-nucleon potential and it is shown that the asymmetry should decrease with increasing $A$. A comparison of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}(p, {}_{}{}^2{}_{}{}^{}\mathrm{H})2p$ and ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$(${}_{}{}^3{}_{}{}^{}\mathrm{H}$, ${}_{}{}^6{}_{}{}^{}\mathrm{He}$)${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ angular distributions illustrates this point. Finally, a prediction is made for the ratio of analyzing powers for the ${}_{}{}^6{}_{}{}^{}\mathrm{He}$+${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{He}$+${}_{}{}^6{}_{}{}^{}\mathrm{Li}$*(3.56) final states.

NUCLEAR REACTIONS Antisymmetric scattering theory. Symmetry around 90° of $\sigma \left(\theta \right)$ for $a(b, c)c^{\prime }$ reactions derived for SU(4) invariant potentials. Angular symmetry breakdown related to size of SU(4) breaking potential through DWBA. Discussion of ${}_{}{}^3{}_{}{}^{}\mathrm{He}(p, d)2p$, ${}_{}{}^9{}_{}{}^{}\mathrm{Be}(t, {}_{}{}^6{}_{}{}^{}\mathrm{He}){}_{}{}^6{}_{}{}^{}\mathrm{Li}\left({}_{}{}^6{}_{}{}^{}\mathrm{Li}_{}^{*}{}_{}{}^{}\right)$, and ${}_{}{}^9{}_{}{}^{}\mathrm{Be}(\overrightarrow{\mathrm{t}}, {}_{}{}^6{}_{}{}^{}\mathrm{He}){}_{}{}^6{}_{}{}^{}\mathrm{Li}\left({}_{}{}^6{}_{}{}^{}\mathrm{Li}_{}^{*}{}_{}{}^{}\right)$ reactions.

• Received 19 November 1982

DOI:https://doi.org/10.1103/PhysRevC.27.1375