The $d+N$ systems are studied in a three-body model, using phenomenological $N-N$ interactions. The scattering matrices are calculated by using the Kohn-Hulthén variational method. Then, they are analytically continued to complex energies and their singularities are localized. We find a virtual state at $E=-1.66$ MeV in ${}^3\mathrm{H}$ and a pair of states at $E=(-0.42\pm i0.52)$ MeV in ${}^3\mathrm{He}$ relative to the $d+N$ thresholds, respectively. In addition, we discuss some general aspects and problems of virtual states which may be useful also in the study of other systems, like ${}^{10}\mathrm{Li}.$

• Received 26 August 1998

DOI:https://doi.org/10.1103/PhysRevC.59.1207