SS-HORSE extension of the no-core shell model: Application to resonances in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>He</mml:mi><mml:mprescripts /><mml:none /><mml:mn>7</mml:mn></mml:mmultiscripts></mml:math>

Theoretical ab initio studies of resonances in the unbound ${\rm^{7}He}$ nucleus are presented. We perform no-core shell model calculations with $NN$ interactions Daejeon16 and JISP16 and utilize the SS-HORSE method to calculate the $S$ matrix for two-body channels $n{-}{\rm^{6}He}$ and $n{-}{\rm^{6}He^{*}}$ with ${\rm^{6}He}$ respectively in the ground and excited $2^{+}$ states as well as for the four-body democratic decay channel ${{\rm^{4}He}+n+n+n}$. The resonant energies and widths areobtained by numerical location of the $S$-matrix poles. We describe all experimentally known ${\rm^{7}He}$ resonances and suggest an interpretation of an observed wide resonance of unknown spin-parity.