Time-dependent hartree-fock theory with Skyrme's interaction

The time-dependent Hartree-Fock theory (TDHF) and its adiabatic approximation (ATDHF) are formulated in coordinate space using effective density-dependent interactions of Skyrme type. For this purpose it is necessary to derive the energy density of a Slater determinant without assuming the single-particle states to be invariant under time-reversal. The corresponding Hartree-Fock Hamiltonian is obtained by varying the total energy with respect to the single-particle density matrix. With the Skyrme interaction TDHF theory leads to an equation of continuity for the single-particle density. The ATDHF equation is transformed into a finite set of inhomogeneous differential equations. Hydrodynamic-like expressions for the collective kinetic energy are established in case the single-particle wave functions have certain generalised scaling properties. TDHF and ATDHF are applied to the description of isoscalar monopole vibrations in ¹⁶O and ⁴⁰Ca.