Time evolution of coherent ground-state correlations and the TDHF approach

We present a formalism and some of its applications aimed at describing RPA-like correlations on top of a time-dependent mean field. These correlations correspond to the zero-point oscillations of collective modes orthogonal to the TDHF trajectory. They are not the result of some instantaneous local RPA equations but they evolve freely from some given initial conditions. A generalized time-dependent generator coordinate (TDGCM) variational formulation leads to explicit equations of motion for both f( q, t) and | φ_q( t> in | ψ( t)> = ∝d qf( q, t)| φ_q( t)>, the correlated time-dependent wave functions. The q-distorted Slater determinants | φ_q( t)>, obey well known TDHF equations of motion while f( q, t) obey a time-dependent generator coordinate integral equation. This last one is further simplified by the assumption of gaussian overlaps for the correlations, so that one can then solve for the time dependence of the correlations by evaluating a few TDHF trajectories differing by small amounts in the collective variables q considered. This TDGCM method is applied in a one-dimensional TDHF scheme. Momentum, energy and breathing fluctuations are studied, as well as their mutual interaction. We find that the fluctuations can be enlarged by an order of magnitude over the values predicted by pure TDHF.