The threshold behaviour of the multiphoton ionisation cross section is examined analytically for the ground-state hydrogen atom. The cross sections become independent of the electron momentum. Generalisation of the results is indicated.
Two-photon ionisation of atomic hydrogen in the ground state with linearly and circularly polarised light is considered. In the region above the one-photon ionisation threshold expressions for the two-photon ionisation transition matrix elements are obtained using the non-relativistic dipole approximation. The two-photon ionisation rate is calculated above and below the one-photon ionisation threshold. Above threshold the total cross section for two-photon ionisation has no resonances and diminishes more rapidly than the photoionisation cross section as the wavelength decreases.
Two-photon ionisation of atomic hydrogen is considered in the non-relativistic dipole approximation at the photoelectric threshold and above it. In this region are obtained convergent analytical expressions for the radial transitions matrix elements, necessary for the calculation of ionisation rates. Partial and total cross sections per unit intensity are calculated for two-photon ionisation of atomic hydrogen in excited states with 2<or=n<or=9 by linearly and circularly polarised light at the photoelectric threshold and above it. At the photoelectric threshold calculations are also carried out for the two-photon ionisation of atomic hydrogen in the ground state.
The general expression for the amplitude of the probability of ionisation by a multiphoton absorption process is derived. Its non-relativistic limit is taken and the bipolar approximation is used for calculating the ionisation cross-section of hydrogen-like atoms. This latter involves the summation over intermediate virtual states by means of: a) a recursion relationship concerning angular functions, b) a particular technique which when applied to radial functions makes it possible to solve a system of inhomogeneous first-order differential equations. (authors) [French] On etablit l'expression generale de l'amplitude de probabilite d'ionisation par un processus d'absorption multiphotonique. On en prend la limite non-relativiste et l'on utilise l'approximation dipolaire avant de calculer la section efficace d'ionisation d'atomes hydrogenoides. Cette derniere fait intervenir des sommations sur des etats virtuels intermediaires effectuees a l'aide: a) d'une relation de recurrence qui concerne les fonctions angulaires, b) d'une technique particuliere qui, appliquee aux fonctions radiales, conduit a resoudre un systeme d'equations differentielles inhomogenes du premier ordre. (auteur)