A consistent microscopic theory of collective motion in the framework of an ATDHF approach

Based on merely two assumptions, namely the existence of a collective Hamiltonian and that the collective motion evolves along Slater determinants, we first derive a set of adiabatic time-dependent Hartree-Fock equations (ATDHF) which determine the collective path, the mass and the potential, second give a unique procedure for quantizing the resulting classical collective Hamiltonian, and third explain how to use the collective wavefunctions, which are eigenstates of the quantized Hamiltonian.

Time-dependent ground-state correlations in heavy ion scattering

Using a time-dependent generator-coordinate method, we derive a theory for time-dependent collective ground-state correlations which account for some quantum fluctuations about a TDHF trajectory. This theory is particularly suited for evaluating spreading widths of collective one-body operators. As an application we study head-on collision of heavy ions in a one-dimensional model. As one of the prominent results we find a substantial enhancement of the spreading width of the internal excitation energy due to the correlations.

Quantized ATDHF: theory and realistic applications to heavy ion fusion

The quantized ATDHF theory is reviewed and discussed in the context of the generator coordinate method. This allows for a derivation which does not require an a posteriori quantization process. The ATDHF equations are then solved numerically on a coordinate and momentum grid in fully three dimensional geometry. The theory is applied to various heavy ion systems, where potentials, mass parameters and quantum corrections are evaluated and compared to conventional results from constrained Hartree-Fock. Subbarrier fusion cross sections are calculated and compared with experiment.

Collective mass parameters and linear response techniques in three-dimensional grids

We discuss four prescriptions for evaluating a collective mass parameter suitable for translations, rotations and large amplitude collective motions. These are the adiabatic time dependent Hartree-Fock theory (ATDHF) and the generator coordinate method (GCM), both with and without curvature corrections. As practical example we consider the16O+16O collision using a recently developed density dependent interaction with direct Yukawa and Coulomb terms. We present a fast iteration scheme for solving the linear response equation in a three-dimensional coordinate or momentum space grid. As test cases we consider the rotational and translational inertia parameters for various distances between the…

Mean field methods in large amplitude nuclear collective motion

The time dependent Hartree-Fock method (TDHF) is reviewed and its success and failure are discussed. It is demonstrated that TDHF is a semiclassical theory which is basically able to describe the time evolution of one-body operators, the energy loss in inclusive deep inelastic collisions, and fusion reactions above the Coulomb barrier. For genuine quantum mechanical processes as e.g. spontaneous fission, subbarrier fusion, phase shifts and the description of bound vibrations, the quantized adiabatic time dependent Hartree-Fock theory (quantized ATDHF) is suggested and reviewed. Realistic three-dimensional calculations for heavy ion systems of A1+A2<32 are presented. Applications to various …

A time dependent RPA-theory for heavy ion reactions

The time dependent Hartree Fock theory (TDHF) is generalized by incorporating 2p-2h correlations into the TDHF Slater determinant in order to improve the description of two-body observables. To this end a time dependent RPA theory (TDRPA) is formulated using the quasi boson approximation. The approach turns out to be readily applicable requiring only minor changes in the present time TDHF codes. The theory is exemplified by considering the spreading width of the fragment particle number in a nucleus-nucleus collision. The TDRPA states are furthermore used to formulate a scattering theory for heavy ion collisions which incorporates the quantum corrections of orderh2 by means of a gaussian pa…

Collective subspaces for large amplitude motion and the generator coordinate method

The collection path $|\ensuremath{\varphi}(q)〉$ to be used in a microscopic description of large amplitude collective motion is determined by means of the generator coordinate method. By varying the total energy with respect to $|\ensuremath{\varphi}(q)〉$ and performing an adiabatic expansion a hierarchy of equations is obtained which determines uniquely a hierarchy of collective paths with increasing complexity. To zeroth order the $|\ensuremath{\varphi}(q)〉$ are Slater determinants, to first order they include 2p-2h correlations. In both cases simple noninterative prescriptions for an explicit construction of the path are derived. For a correlated path their solutions agree at the Hartree…

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 $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ 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.

Time Dependent Hartree-Fock and Beyond