Multiphoton dissociation or ionization: Partial widths and branching ratios for time-periodic Hamiltonians

Multiphoton dissociation or ionization partial widths Γₙ and branching ratios for time-periodic Hamiltonians H(r,t)=H₀(r)+{λ}V(r,t) are obtained from the asymptotic analysis of the complex scaled metastable Floquet states and for V(r,t)=H₁(r)cos({ω}t) also from the leading term in the Born-series expansion of the T matrix (LTB). It is shown here that within the framework of the LTB approximation the branching ratios are given by σₙ₊₁/σₙ =({λ}{π}/2)²{}〈φ_E+ωn⁽⁰⁾{}H^₁(x){}{φ} _E+ω(n+1)⁽⁰⁾², where {φ⁽⁰⁾} are the continuum eigenfunctions of the field-free Hamiltonian H₀. Therefore for strong enough laser intensity the ratio σₙ₊₁/σₙ may become larger than 1 and multiphoton dissociation or ionization processes will be more efficient than the single-photon process. When the partial widths Γₙ (defined to be a factor of the residue of the S matrix at a pole) are small, then Γₙ₊₁/Γₙ{}σₙ₊₁/σₙ.