Physical asymptoticity in nonlinear many-body reaction theories from nuclear mean-field approximations

Abstract

The qualitative property of physical asymptoticity for a reaction theory is defined and the conditions under which it is guaranteed are determined. For the linear Schrödinger time evolution, physical asymptoticity is automatic; for its nonlinear approximants, conditions upon both the S-matrix coefficients and the asymptotic channel solutions must be met. The time-dependent S-matrix Hartree-Fock (TDSHF) description is physically asymptotic by construction. However, neither the initial-value time-dependent Hartree-Fock (TDHF) nor the function integral stationary phase (FISP) mean-field descriptions as discussed heretofore are physically asymptotic. But a physically asymptotic Hartree-Fock functional integral stationary phase description (AHFSP) is constructed by utilizing the freedom to impose translational invariance upon the FISP channel states. Its comparison with the (physically distinct) TDSHF description is therefore of special interest.