Atomic resonances above the total ionization energy

A rigorous result obtained using the theory associated with dilatation analytic potentials is that by performing a complex coordinate rotation, $r_j\to r_j{e}^{i\theta }$, on a Hamiltonian whose potential involves only pairwise Coulombic interactions, one can show that when $\theta =\frac{\pi }{2}$, no complex eigenvalues (resonances) appear whose energies have a real part greater than the total ionization energy of the atomic system. This appears to conflict with the experimental results of Walton, Peart, and Dolder, who find resonance behavior above the total ionization energy of the ${\mathrm{H}}^{--}$ system and also the theoretical stabilization results of Taylor and Thomas for the same system. A possible resolution of this apparent conflict is discussed and a calculation to check its validity is proposed.