Partial-Wave Analysis for Certain Simple Systems with Application to the ReactionO16(d,α1)N*14

Abstract

The angular distributions of spin-zero even-parity particles emerging from a compound nucleus formed by a $1^{+}$ and $0^{+}$ pair are displayed in a simple form which facilitates parametrizing the differential cross section in terms of partial waves. The method is applied to the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(d,{\alpha }_1){}_{}{}^{14}{}_{}{}^{}N_{}^{*}{}_{}{}^{}$ data of Jobst et al. to display the resonant partial waves corresponding to ${}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ states. Intrinsically ambiguous solutions of number $2^{lmax}$ are found empirically. The problem of selecting the correct solution is discussed. Data with polarized deuterons are of no help since the analyzing powers are energy-independent (cf. Jacobsohn and Ryndin, who first noted that the reaction is an absolute detector of deuteron alignment).