The Classical Dynamic Behaviors Of H₂～+ In Intense Laser Fields With The Structure-Preserving Method

The studies of interaction of intense laser pulses (The intensity is more than 10¹⁴W/cm²) with atoms and molecules have been an active area during the past two decades. With the development of femtosecond lasers, the femto-chemistry becomes possible where chemical reaction dynamics can be probed at the atomic scale. The Hydrogen molecular ion H₂⁺ was always chosen for theoretical and experimental study because it is the simplest molecular system, which consists of one electron and two protons. During the recent years, some numerical calculations about population effects in harmonic generation by H₂⁺ are considered. Because the perturbation theory is not appropriate for the intense laser field, people usually attempt to study this problem by solving numerically the 3-dimensional time-dependent Schr?dinger equation (TDSE). A clear structure in the kinetic energy spectra and three separate Coulomb explosion velocity groups corresponding to critical distances of about 8, 11 and 15a.u. of H₂⁺ and D2+ system were observed in experiment; laser-induced dissociation and ionization of H₂⁺ were studied using coincidence 3D momentum imaging.While quantum methods can provide exact solutions to the multi-photon dynamics, the classical theories can also be used to study the same problems and the corresponding results are in good agreement with quantum calculations, such as the strong-field ionization, the stabilization of a molecule in super-intense laser fields, etc. Recently, classical simulations of the dissociation, ionization and Coulomb explosion of H₂⁺ employing a 1D model have also been studied.The classical dynamics of Hydrogen molecular ion H₂⁺ in an intense field have been studied by the classical theory and the symplectic method. In this paper, 3D model of H₂⁺ is used, with the bare Coulomb potential replaced by a screened potential to avoid the singularities at close electron–proton encounters. The initial conditions are chosen at random in the field-free case, and then 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. As expected, the ionization and Coulomb explosion probabilities increase and the dissociation probability decreases with the increasing intensity. The peak of the ionization process occurs sooner for higher laser intensity. Once ionized, the Coulomb energy between the nuclei will be released quickly through the Coulomb explosion. This leads to the rapid increase of internuclear separation. So the dissociative ionization channel follows ionization directly. We could also observe that the dissociation probability is much larger than ionization probability in weak laser field; this phenomenon could also be seen in the quantum calculations using the exact 1+3D model.In the 3D model the dissociation probability is smaller in the intense laser field as the electron departs in different directions. In addition, we also calculate the average distance from electron to the mass-center for various relative phases and the change of the average internuclear separation (R(t)|—) with the time, which illustrate that the stronger laser pulse would enhance the ratio of high-energy parts of the kinetic energy spectrum of the nuclei. Besides, we also calculate the probabilities of ionization, dissociation and Coulomb explosion of the HD+ system in the one-color and two-color laser field,and get the following conclusion: 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 HD²⁺ is heavier than H₂⁺, so the electron could be ionized easier and the two nucleuses can't be separated from each other so quickly. Moreover, the natural life of HD²⁺ is longer than the one of the H₂²⁺. In conclusion, although the classical trajectory method can't describe some quantum effects, it is in agreement with quantum-mechanical calculations in many cases and may be extended to larger molecular system.