Quantized ATDHF and angular momentum projection: three-dimensional applications to heavy ion scattering

The quantized adiabatic time-dependent Hartree--Fock (qATDHF) theory is extended to the calculation of observables in nuclear phenomena using general many-body techniques including angular momentum projection. All calculations are performed using three-dimensional coordinate and momentum-grid techniques. The Bonche--Koonin--Negele interaction as well as several Skyrme-type forces has beenused in the simple Hartree--Fock (HF) calculations of 12C and 20Ne nuclei. Further, the maximally decoupled collective path is evaluated within qATDHF, and the angular momentum projected kernels are inserted into the GCM formalism. As a test case, this formalism is applied to the phase shifts of elastic α--α scattering because they can be compared to experimental values. The same techniques are applied to the α--16O system and the results are compared with those obtained by solving the collective Schroedinger equation in a Gaussian Overlap Approximation, as in a previous publication. The GCM, extended to complex energies, is used to extract the widths of the resonance levels of the 01+, 04+, 0- bands in α--16O scattering. A model calculation, in which the structure of the nuclei is kept fixed to their HF ground state, is performed for the same α--16O system. We get quite different results with this ''sudden'' approximation than with the adiabatic calculation. The present calculations show that it is indeed possible to connect general and symmetry conserving many-body techniques to the qATDHF theory and to obtain in this way a purely microscopic framework which can be handled numerically, thus allowing evaluation of observables which are accessible to experiments. copyright 1987 Academic Press, Inc