Dynamical alignment of H$_{2}^+$ in an intense ultrashort laser pulse

We will present a study of ionization and dissociation of H$_{2}^+$ in an intense ultrashort laser pulse. Our results include all degrees of freedom $-$ classical for the nuclei and quantum mechanical for the electron. Similar previous calculations$^{1,2}$ have obtained the electronic wave function using a basis expansion. We, however, are solving the time-dependent Schr\"{o}dinger equation on a three dimensional grid in the lab frame. One of our goal is to study dynamical alignment of H$_{2}^+$ and its fragments. We consider a distribution of initial nuclear positions and momenta so that our results are suitable for direct comparison with experiment. \\ $^1$M. Ullmann, T. Kunert, F. Grossmann, R. Schmidt, Phys. Rev. A {\bf 67}, 013413 (2003). \\ $^2$E. Deumens, A. Diz, R. Longo, and Y. \"{O}hrn, Rev. Mod. Phys. {\bf 66}, 917 (1994)