The energy density formalism of Brueckner is extended to the complex domain with the use of a complex two-body effective interaction, so as to generate simultaneously the real and imaginary part of the ion-ion interaction potential. A simple effective interaction consisting of a density dependent delta function repulsion and a Gaussian attraction is chosen for the real part of the complex effective interaction, whereas the imaginary component is derived by using the forward scattering amplitude approximation. In using this approximation, emphasis has been given to use the complex two-body matrix $\mathcal{T}$, where the propagator has the nuclear many-body Hamiltonian rather than the free two-body matrix $t$. For the average nucleon-nucleon cross section $〈\sigma 〉$, required in constructing the complex effective interaction, a modified version of the relation suggested by Bohr and Mottelson is used which compares quite well with that of Clemental and Villi. The real part of the ion-ion interaction potential calculated in this model has already been reported in an earlier work and the present work deals with the calculation of the imaginary part of the potential for five pairs of spherical nuclei. The region of the potential beyond the surface is parametrized into a Woods-Saxon shape. The calculated imaginary potential for the system ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$-${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ is compared with the phenomenological one of Becchetti et al. and the agreement between the two sets of potentials is found to be quite good in the region beyond the strong absorption radius.

NUCLEAR REACTIONS Complex two-body effective interaction, forward scattering amplitude approximation, imaginary part of ion-ion interaction potential.

• Received 16 August 1979

DOI:https://doi.org/10.1103/PhysRevC.21.1883