Quantum calculations for photodetachment cross sections of H in an equilateral triangle cavity

In this paper, the photodetachment cross section of negative hydrogen ion inside a tube cavity with an equilateral triangle cross section is investigated by the traditional quantum approach. Then the analytic formulas each as a function of photon energy having been derived, some interesting oscillations in the photodetachment cross section are shown from the numerical illustrations. The formulas indicate that the oscillations are related to the positions of the ion and the photon polarization. The polarization of photons being perpendicular to the normal direction of the triangle, the cross sections apparently display large amplitude sawtooth-shaped oscillations, while being parallel to the normal direction of the triangle, oscillations are still present and observable from the quantum calculations, although the amplitudes of the oscillations are rather small. The subtle effect is also observed in the quantum theory for photodetachment in an electric field. The formulas also reveal threshold behaviors in the photodetachment cross sections. The threshold is expressed as E-th = 8 pi(2) / 9 iota(2) (m(2) broken vertical bar n(2) - mn), where l is the length of the triangle side, n and m are for all integers with m >= 2 n. When the polarization of photons is perpendicular to the normal direction of the triangle and the energy of the detached electron is above each threshold, the threshold behavior is. Delta sigma alpha (E - E-th) (-1/2). When the polarization of photons is parallel to the normal direction of the triangle and the energy of the detached electron is above each threshold, the threshold behavior is Delta sigma alpha(E - E-th) (1/2). Furtherly, if the negative hydrogen ion is placed near one corner of the equilateral triangle, the quantum results show agreement with those from the closed-orbit theory when the negative hydrogen ion is in a wedge with an opening angle of 60 degrees. If that occurs, the five sinusoidal oscillations, each of which will correspond to one closed orbit, can be extracted from the photodetachment cross sections. These five closed orbits are definitely the orbits when the negative hydrogen ion is in a wedge with an opening angle of 60 degrees.