Projection operator method for resonances in repulsive core potentials.

Abstract

A projection operator method is presented for the extraction of resonance energies, shifts, and widths of bound states embedded in the continuum for potentials that have a repulsive core. The procedure is applicable for heavy ion as well as nucleon-nucleus collisions. The original potential is modified beyond the radius where the repulsive core merges into the attractive part of the potential by a harmonic oscillator potential whose shape is determined primarily by the harmonic oscillator frequency. The method requires that the size of the modified well be fixed for only one particular l value. It is then automatically determined for a range of other l values. The extracted bound states can be used reliably in ensuing diagonalization procedures and in treating continuum-continuum coupling. The method is readily applicable to the determination of widths in those situations where the normal phase shift procedure cannot be employed. As a test case the procedure is applied to $^{12}$C${+\mathrm{}}^{12}$C for l=0 to 8 and yields resonance energies and widths in very good agreement with a phase shift analysis.