Ionization rates ofH2+in an intense laser field by numerical integration of the time-dependent Schrödinger equation

A numerical method of integration of the time-dependent Schrödinger equation is presented for the hydrogen atom and for the ${\mathrm{H}}_2^{+}$ molecule. Cylindrical coordinates are used and the wave function is expressed as a Bessel-Fourier series. This expansion allows one to eliminate singularities present in the Hamiltonian and to use a unitary split operator to evaluate numerically multiphoton transitions. Laser-induced ionization rates for ${\mathrm{H}}_2^{+}$ are calculated and compared with rates for the hydrogen atom. A strong dependence of the ${\mathrm{H}}_2^{+}$ ionization rates on the initial vibrational excitation is found.