Relativistic effects on the ${\mathrm{H}}^{-}$ resonances converging to the $\mathrm{H}\mathrm{}(n=2\mathrm{})\mathrm{}$ threshold

The series of H${}^{-}$ resonances of ${}^1{P}^o$ symmetry predicted to converge exponentially to all thresholds has been investigated below the H$\mathrm{}(n=2\mathrm{})\mathrm{}$ threshold. It is shown that the series will be terminated already after the third resonance when the relativistic and radiative splitting of the H$\mathrm{}(n=2\mathrm{})\mathrm{}$ states is considered. Resonance parameters of this third resonance have been calculated with highly correlated wave functions. The resonance is predicted to be situated $19\mu$eV below H${(2p}_{1/2})$ with a width of $0.06\mu$eV. Accurate resonance parameters are also given for the first two resonances and the photoabsorption cross section is calculated for the threshold region.