Quantum and semiclassical studies on photodetachment cross sections of H^- in a harmonic potential

The photodetachment cross section of H^- in a linear harmonic oscillator potential is investigated. This system provides a rare example that can be studied analytically by both quantum and semiclassical methods with some approximations. The formulas of the cross section for different laser polarization directions are explicitly derived by both the traditional quantum approach and closed-orbit theory. In the traditional quantum approach, we calculate the cross sections in coordinate representation and momentum representation, and get the same formulas. We compare the quantum formulas with closed-orbit theory formulas, and find that when the detachment electron energy is larger than 3/2ħω, where ω is the frequency of the oscillator potential, the quantum results are shown to be in good agreement with the semiclassical results.