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 been used 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 Schrödinger 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.