New Lower Bound on Fermion Binding Energies

We derive a new lower bound for the ground state energy $E^{\rm F}(N,S)$ of N fermions with total spin S in terms of binding energies $E^{\rm F}(N-1,S \pm 1/2)$ of (N-1) fermions. Numerical examples are provided for some simple short-range or confining potentials.