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A new quantum dynamical model has been developed to describe the dissociativeionization of deuterium molecular ions by intense laser pulses ($\tau=10$ fs,$\lambda=200$ nm and $I=3\times10^{13}$ W/cm$^{2}$). We calculated theionization probability densities by solving the time-dependent Schr\"odingerequation numerically. Throughout the simulation the nuclear vibration wasconsidered as a dynamic variable with fixed molecular axis orientation.Benchmark calculations were performed for the ionization of$\mathrm{HeH}^{++}$, for which accurate numerical results are available in theliterature, in order to check the performance of this new restricted model.

Towards the full quantum dynamical description of photon induced processes in $\mathrm{D}_{2}^{+}$