Level Shifts of Shell-Model States in the Continuum

A unified theory of nuclear reactions has been given in which shell-model states are rigorously incorporated as states of the compound nucleus. Shell-model states above the particle emission threshold are given a clear interpretation; the calculation of resonance energies and level widths from them is clearly defined. The level shifts resulting from the interactions of these states with the continuum are discussed, and shown to have been mostly included in the usual shell-model calculations. Limits on a residual shift due to damping are derived and evaluated for the giant resonance levels in ${\mathrm{O}}^{16}$.