Classical Dynamics Of 2-Dimensional Hydrogen Molecular Ion (H₂～+) In Intense Laser Field

Hydrogen molecular ion H₂⁺ under an ultrashort laser pulse is currently a very active area of the theoretical and experimental research. A H 2 molecule in the 1sσg electronic state and a given vibrational state will absorb photons in making a transition to the final dissociating 2pσ_u state (repulsion state or anti-bonding state). Because the perturbation theory is not appropriate for the intense laser field, people usually attempt to study this problem by solving numerically time-dependent Schr odinger equation (TDSE) to study the atom-laser and molecule-laser interaction is one of the popular and the reasonable methods in present theoretical research.During the recent years, some numerical calculations about population effects in harmonic generation by H₂⁺ are considered. In principle, the dynamic evolution of the atoms and molecules under an intense electromagnetic field should be described with quantum theory. With the development of femto-second lasers, the femto-chemistry becomes possible , The classical theory is used to study the dynamic behaviors of the molecules and atoms in the ultrashort intense laser pulse, and it has demonstrated that classical explanations of some new phenomena in the intense field of atom and molecule physics, such as the stabilization of a molecule in a superintense high-frequency laser field, the high harmonic generation of an atom and the enhanced ionization of an atom in the strong laser field , and so on.In this paper, two-dimension model of H₂⁺ is adopted. Classical trajectory method is used to study classical dynamics of two-dimensional Hydrogen molecular ion H₂⁺ in intense laser field. The Hamiltonian canonical equations of H₂⁺system in the intense laser field are solved numerically by means of the symplectic method under these initial conditions. We discuss the probabilities of ionization, dissociation and Coulomb explosion of the H₂⁺ system in the one-color and two-color laser field. The peak of the ionization process occurs sooner for higher laser intensity. The ionization leads to the rapid increase of internuclear separation. So the dissociation ionization channel follows ionization directly.We also discuss the probabilities of ionization, dissociation and Coulomb explosion of the HD⁺ system in the ultrashort laser field, and compared to the classical dynamics of H₂⁺, we find that they present similar classical dynamics quantitatively. However, the ionization channel of HD⁺ opened earlier than that of H₂⁺, But the dissociation and Coulomb explosion channels opened later at the same condition. We suppose that it is because the nucleus of HD + is heavier than that of H₂⁺, two nucleus can't be separated from each other so quickly.In conclusion, we have approached classically the dynamic evolution of 2D hydrogen molecular ion under intense laser pulse. The results show that it is similar with the dynamic evolution of 1D hydrogen molecular ion. We think that the model predictions for the onset of channels as a function of pulse intensity shall be helpful in understanding the dynamic characteristics of a 2D molecule ion under intense pulse.