  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 $\hbar\Omega$. 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 $n\alpha$ resonances and
non-resonant scattering using the no-core shell model.
