The implications of representing the $S_{\frac{1}{2}}\alpha -\mathrm{N}$ interaction by an attractive potential with an excluded bound state, rather than by a repulsive potential, are explored with three-body models of the ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ ground states. After an introduction to the underlying theory, comparisons are made between the predictions of the two models for ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ $\beta$ decay, the shell structure of ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, and the $\alpha$-deuteron properties of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$. A major conclusion is that the appropriate choice for the $S_{\frac{1}{2}}\alpha -\mathrm{N}$ interaction should be extractable from electron coincidence experiments of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(\mathrm{e},{\mathrm{e}}^{\prime }\mathrm{d}){}_{}{}^4{}_{}{}^{}\mathrm{He}$ or ${}_{}{}^6{}_{}{}^{}\mathrm{Li}(\mathrm{e},{\mathrm{e}}^{\prime }\alpha ){}_{}{}^2{}_{}{}^{}\mathrm{H}$ type.

• Received 9 February 1984

DOI:https://doi.org/10.1103/PhysRevC.29.2319