Multiphoton ionization of hydrogen in ultrastrong laser fields

The three previous calculations of this process yield differing results for the transition rate. We show the relations between them and difficulties with each of them. One difficulty is that the finite spatial extent of the laser field has been omitted. It is also found that a laser field, which is sufficiently intense to be labeled ultrastrong, makes the electron move relativistically so that it becomes necessary to use Volkov states to describe the electron in the laser field. The transition rate is obtained, with the use of a C${\mathrm{O}}_2$ laser as an example, and it is found that the transition rate rises as the laser intensity rises. This is a consequence of the use of relativistic kinematics and is not true nonrelativistically.