Shell model states in the continuum

We suggest a method for calculating scattering phase shifts and energies and widths of resonances which utilizes only eigenenergies obtained in variational calculations with oscillator basis and their dependence on oscillator basis spacing $\ensuremath{\hbar}\mathrm{\ensuremath{\Omega}}$. We make use of simple expressions for the $S$ matrix at eigenstates of a finite (truncated) Hamiltonian matrix in the oscillator basis obtained in the HORSE ($J$-matrix) formalism of quantum scattering theory. The validity of the suggested approach is verified in calculations with model Woods-Saxon potentials and applied to calculations of $n\ensuremath{\alpha}$ resonances and nonresonant scattering using the no-core shell model.