The collection path |(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 |(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 |(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-Fock minimum with random phase approximation eigenmodes. The resulting equations for the path are compared with the outcome of related theories, particularly of semiclassical nature. It is remarkable that both sorts of approaches, on one hand the generator coordinate method with correlated states and on the other the quantized adiabatic time dependent Hartree-Fock theory, are virtually identical in the results, although they are of different conceptual origin and use different techniques. It is shown that the use of a correlated path does not cause numerical complications. NUCLEAR STRUCTURE Collective path derived by GCM, inclusion of RPA correlations, relation to adiabatic TDHF. © 1979 The American Physical Society.
