Reality conditions for classical motions along collective paths

The equations of motion along a large amplitude collective path $\left|q\mathrm{}\right(t),p\mathrm{}(t)\mathrm{}〉$ are shown to require, in general, complex parameters $q$ and $p$. It is shown, however, that real values are sufficient if $|q,p〉$ is constructed by Hartree-Fock with coordinate and momentum constraint. In addition, the motion along the particular paths suggested by the adiabatic time-dependent Hartree-Fock theory and by the local harmonic approach is proved to be stable against small imaginary displacements.

NUCLEAR STRUCTURE Classical motion, collective path, constrained Hartree-Fock, adiabatic time-dependent Hartree-Fock, local harmonic approach, large amplitude collective motion, complex generator coordinates.