  Consider a complex energy $z$ for a $N$-particle Hamiltonian $H$ and let
$\chi$ be any wave packet accounting for any channel flux. The time independent
mean field (TIMF) approximation of the inhomogeneous, linear equation
$(z-H)|\Psi>=|\chi>$ consists in replacing $\Psi$ by a product or Slater
determinant $\phi$ of single particle states $\phi_i.$ This results, under the
Schwinger variational principle, into self consistent TIMF equations
$(\eta_i-h_i)|\phi_i>=|\chi_i>$ in single particle space. The method is a
generalization of the Hartree-Fock (HF) replacement of the $N$-body homogeneous
linear equation $(E-H)|\Psi>=0$ by single particle HF diagonalizations
$(e_i-h_i)|\phi_i>=0.$ We show how, despite strong nonlinearities in this mean
field method, threshold singularities of the {\it inhomogeneous} TIMF equations
are linked to solutions of the {\it homogeneous} HF equations.
