The cross-over from tunnelling to multiphoton ionization of atoms

We present a theory illuminating the cross-over from strong-field tunnelling ionization to weak-field multiphoton ionization in the interaction of a classical laser field with a hydrogen atom. A simple formula is derived in which the ionization amplitude appears as a product of two separate amplitudes. The first describes the initial polarization of the atom by virtual multiphoton absorption and the second the subsequent tunnelling out of the polarized atom. Tunnelling directly from the ground state and multiphoton absorption without tunnelling appear naturally as the limits of the theory.