The positions and widths of nuclear resonance states of the nuclei ${}^8\mathrm{Be},$ ${}^5\mathrm{He},$ and ${}^5\mathrm{Li}$ have been calculated in the microscopic cluster model using a real square integrable basis. The imposition of Gamow or scattering asymptotic boundary conditions onto the wave function is avoided. The approach is based on the notion of the continuum level density. This density is smoothed by the Strutinsky averaging procedure and it is calculated by making use of the eigenvalues of the full and the free Hamiltonian matrices. The continuum level density is connected to the S matrix and has a Breit-Wigner peak around the resonance energy. This approach is compared with the complex scaling method and with the exact calculation of the scattering phase shift.

• Received 8 June 1999

DOI:https://doi.org/10.1103/PhysRevC.60.064315