Adiabatic Time-Dependent Hartree-Fock Calculations of the Optimal Path, the Potential, and the Mass Parameter for Large-Amplitude Collective Motion

The adiabatic time-dependent Hartree-Fock theory is reformulated in order to yield a simple differential equation for the collective path with accompanying simple expressions for the collective mass and the potential. With use of three-dimensional coordinate- and momentum-space techniques and density-dependent interactions, the new adiabatic time-dependent Hartree-Fock formalism is applied to $\alpha -\alpha$ scattering and correspondingly to the fission mode of ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$. In the overlapping region the resulting collective mass deviates strongly from the reduced mass.