What happens to two-electron resonances when their energy approaches the break-up threshold?

Using semiclassical S-matrix theory in a simulated electron-hydrogen scattering experiment and converged quantum calculations for the widths of high-lying resonances in $\rm H^-$ we show that resonance formation (or the lifetime of resonances) below the fragmentation threshold E=0 and ionization above threshold have the same energy dependence $|E|^{1. 127}$ for $|E|\to 0$. Hence, series of resonances which have been characterized by approximate quantum numbers will disappear towards threshold