Partial-wave dispersion relations for the coupled $\alpha +n$ and $t+d$ channels of the $Z=2\mathrm{}$ five-nucleon system have been solved by the matrix $\frac{N}{D}$ technique. Driving terms have been constructed from one- and two-cluster exchange graphs with parameters of vertex functions taken from studies of $A\le 4$ subsystems. Accurate solutions to the coupled $N$ and $D$ equations have been obtained by a Pagels approximation based on [$N,N-1\mathrm{}$] Padé approximants. Coulomb forces in charged-fragment channels were incorporated via the repeated $\frac{N}{D}$ scheme of Kinoshita and Kugler. No proper treatment has been given of the anomalous threshold of the $t+d\to \alpha +n$ proton-exchange graph. Calculated $\alpha +n$ scattering phase shifts lack uniqueness, due to strong sensitivity to the inaccurately known vertex parameters used as input, but display the basic features of repulsion in the $s$ wave, occurrence of resonances in the $p$ waves, and existence of the small ${3/2}^{+}$, $d$-wave resonance just above the $t+d$ threshold. Failure of the calculation to produce the width of the $p$-wave resonances is attributed to the improper treatment of the anomalous threshold. Differential cross sections for $t+d\to \alpha +n$ show reasonable agreement with experiment in both the forward and backward directions but lack details of the observed structure at medium angles. The latter again occurs for the calculated $t+d$ elastic scattering cross sections which moreover are unsatisfactory at forward angles. A comparison with other coupled-channel calculations of light systems is attmpted.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}\mathrm{}(n,n)\mathrm{}{}_{}{}^4{}_{}{}^{}\mathrm{He}$, $E=0\mathrm{}-40$ MeV; calculated $S_{\frac{1}{2}}$ through $D_{\frac{3}{2}}$ phase shifts; ${}_{}{}^3{}_{}{}^{}\mathrm{H}\mathrm{}(d,n)\mathrm{}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{H}\mathrm{}(d,d)\mathrm{}$, $E=6\mathrm{} \mathrm{and} 14.2$ MeV; calculated $\sigma \left(\theta \right)$. Dispersion-relation method.

• Received 11 February 1974

DOI:https://doi.org/10.1103/PhysRevC.10.1253