Correction for truncation in coupled-channels optical potentials

Coupled-channel calculations using uniform optical parameters are compared for rotational and harmonic vibrator sequences of states, truncating all states of the sequence above a certain nuclear energy level. It is found that the inelastic cross section for the highest included state is somewhat larger than a coupled-channel calculation which includes the next state of the sequence. This effect is due to the absence of the absorption taking place through the truncated state. Except at very low bombarding energies, the cross sections for lower states in the sequence are virtually unaffected by the truncation. Approximate formulas are presented and tested for correcting the optical potential of the highest included state. Good agreement is obtained with coupled-channel calculations that include these higher states explicitly. Application is made to the problem of obtaining inelastic deformation parameters β with distorted-wave Born approximation and with different coupling schemes