Partial-wave dispersion relations for the nonrelativistic five-nucleon system

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.