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 $\mathrm{\hslash }\mathrm{\Omega }$. 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.