Resonance and interference phenomena in the photoionisation of a hydrogen atom in a uniform electric field. I. Resonances below and above the potential barrier

The photoionisation cross section for a hydrogen atom placed in a uniform electric field is calculated using separation of the variables in parabolic coordinates and the semiclassical approximation with account for the tunnelling and reflection above the top of the potential barrier. The corrections to the semiclassical approximation are established accounting for the peculiarities of the effective potential barrier form. The approximate separation of the centrifugal terms contribution in the phase barrier form. The approximate separation of the centrifugal terms contribution in the phase integrals allows the latter to be expressed via hypergeometric functions. The structure in the energy dependence of the cross section is associated with its complex poles. The motion of the poles under variation of the photon energy is investigated. The equations defining the resonance positions and widths are obtained and analysed for energies below and above the potential barrier. The boundary between these two regions is described. The analytical expressions for the parameters of resonances lying above the barrier are obtained for the first time. In the vicinity of the resonance the cross section can be well parameterised by Fano's formula. The approximate expressions for the profile index are deduced. The analytical results are compared with numerical calculation data. The recent experiments on the photoionisation of rubidium and sodium atoms are discussed.