Quantum calculations for photodetachment cross sections of H^- in an inhomogeneous electric field

We calculate the photodetachment cross sections of H^- in a gradient electric field based on traditional quantum approach. The system provides a rare example that the formulas for the cross sections can be explicitly derived by both the quantum approach and closed-orbit theory. The quantum results are compared with those of the closed-orbit theory. The correct phase values in the closed-orbit theory are essential and necessary to produce accurate cross sections. Our quantum results remove some previous ambiguities in assigning the phase values in the closed-orbit theory (G. C. Yang and M. L. Du 2007 Phys. Rev. A 75 029904E).