Search for excited states in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow/><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow/><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:math>

The $d+N$ systems are studied in a three-body model, using phenomenological $N\ensuremath{-}N$ interactions. The scattering matrices are calculated by using the Kohn-Hulth\'en variational method. Then, they are analytically continued to complex energies and their singularities are localized. We find a virtual state at $E=\ensuremath{-}1.66$ MeV in ${}^{3}\mathrm{H}$ and a pair of states at $E=(\ensuremath{-}0.42\ifmmode\pm\else\textpm\fi{}i0.52)$ 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 ${}^{10}\mathrm{Li}.$

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