Determination of the Total Angular Momentum of Residual Nuclear States from Deuteron Stripping Angular Distributions

A model based on diffraction techniques yields general formulas for large-angle differential cross sections in deuteron stripping (and other rearrangement) reactions in which the entrance- and exit-channel particles are strongly absorbed. It is found that for a spin-zero target, the character of the large-angle distributions depends critically on the angular-momentum transfer $L$ (or parity of the residual state) in an unusual way. For $L$ even, cross sections exhibit oscillations that have twice the period of the usual forward-angle stripping oscillations, while for $L$ odd, there is almost no oscillatory structure. Furthermore, the even-$L$ oscillations for $L=4n$ are out of phase with those for $L=4n+2\mathrm{}$, $n=0, 1, \cdots$. A unique determination of the total spin $J=L\pm \frac{1}{2}$ of the residual nuclear state in deuteron stripping is possible when entrance- and exit-channel spin-orbit scattering, proportional to $\sigma ·1$, is introduced into the diffraction model. The spin-orbit amplitude is characterized by distributions of opposite parity from the spin-independent amplitude. For the case of $L$ odd, the spin-independent amplitude is a relatively smooth function of angle, characteristic of odd-parity distributions, while the spin-dependent amplitude exhibits the even-parity ($L\pm 1$) large-angle diffraction oscillations. The analysis for $L=1\mathrm{}$ shows that the $J=L+\frac{1}{2}=\frac{3}{2}$ state is characterized by an $L=0\mathrm{}$ angular distribution for the spin-dependent amplitude, while the $J=\frac{1}{2}$ state shows oscillations typical of $L=2\mathrm{}$. Consequently, a unique phase rule is obtained for identification of the total spin $J$ of the residual state since the large-angle oscillations for $J=\frac{3}{2}$ are out of phase with those for $J=\frac{1}{2}$. A comparison of the predictions of the model with recent experiments is also presented.