A projection operator approach is presented for the determination of energies and widths of shape resonances in low-energy heavy-ion scattering. The method produces essentially the same results as standard $S$-matrix techniques in much less time, and works best for narrow virtual and quasibound resonances that could easily be missed by a scan. Examples for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ are given.

NUCLEAR REACTIONS Shape resonances in low-energy heavy-ion collisions; calculated $E_{\mathrm{RES}}$ and $\Gamma$. Projection operators; no scanning. Comparison with $S$-matrix methods.

• Received 27 December 1979

DOI:https://doi.org/10.1103/PhysRevC.21.2675