Three-dimensional nuclear dynamics in the quantized ATDHF approach

The quantized adiabatic time-dependent Hartree-Fock theory is numerically applied to the low energy large amplitude collective dynamics of heavy ion systems ranging from α + α to ¹⁶O + ¹⁶O. The problem is reduced to three successive steps. First, for the lowest mode the optimal, i.e., maximally decoupled, collective path {φ_q} is evaluated by solving a coupled set of nonlinear differential equations for the single-particle wave functions _q^(a)(r) of φ_q, depending on the collective coordinate q and three spatial coordinates. A density-dependent interaction with a direct finite range Yukawa-term is employed and three-dimensional coordinate- and momentum-grid techniques are used, including fast Fourier methods. In a second step the quantized collective Hamiltonian H_c(q, d/dq) is extracted from {φ_q} by means of generator coordinate techniques involving, besides q, a conjugate variable p. Starting from {φ} this procedure includes the numerical evaluation of the classical potential, (q), of the intertia parameter, (q), of the quantum corrections with regard to rotation, translation and collective q-motion, (q), and of the centrifugal potential. The third step consists of actually calculating the subbarrier fusion cross section by means of WKB methods applied to the collective Hamiltonian H_c(q, d/dq). The theoretical numbers are compared with results from Hartree-Fock calculations with quadrupole constraint, and with experimental data. The microscopic aspects of the dynamics, the relation to other theories, and the practical and conceptual problems arising from the quantized ATDHF theory are discussed in detail.