Application of the momentum translation method to multiphoton ionization of hydrogen by intense electromagnetic fields

Abstract

A nonperturbative theory, the momentum translation method, is applied to multiphoton ionization of hydrogen by an intense electromagnetic field. Using an approximation depending on a large number of photons absorbed, analytical results are presented for transitions from a 1S state to Coulomb states in the continuum. Results not only show the characteristic perturbation theory dependence of the intensity raised to the Nth power for an Nth order process, but give an explicit expression for the transition as a function of the number of photons absorbed, and the final electron angular momentum and energy. This type of functional dependence is very obscure in perturbation theory by its very nature. In particular, transitions to states with angular momenta 2, 4, and 6 dominate the l=0 transition in the absorption of 12 photons with energy of 1.17 eV, while l=3, 5, 7 transitions dominate the l=1 transition when 13 photons are absorbed. Also for particular values of the field intensity and final angular momentum the transition matrix is larger for a larger number of photons absorbed.