This work explores the vibrational state-selective photoassociation (PA) in the ground state of the HX (X = F, Cl, I) molecule by solving the time-dependent Schrödinger equation. For the three systems, the vibrational level of [Formula: see text] is set to be the target state and the PA probability of the target state is calculated and compared by considering different initial collision momentums. It is found that the PA probabilities are in accordance with Franck–Condon overlap integral for the HI and HCl systems, but it is not the case for the HF system. Moreover, for the HF system, it is shown that the PA probability of the target state is largest and the multiphoton transition is more likely to occur.

The atom-atom-ion three-body recombination (TBR) of mixed He and X (X = H or D) systems is investigated by solving the Schrödinger equation using the adiabatic hyperspherical representation method. It is shown that the dominant products after a TBR in the ultracold limit (E ≤ 0.1 mK × k) are different for the two systems. For the HeHeH system, the rate of TBR into the HeH ion is nearly two orders of magnitude larger than that of TBR into the neutral He molecule. In contrast, the yield of He is a little higher than that of HeD for the HeHeD system. Furthermore, since the adiabatic potentials become more attractive and the nonadiabatic couplings become much stronger by substituting D for H in the HeHeH system, the total TBR rate for the HeHeD system is nearly two orders of magnitude larger than that for the HeHeH system.

The dissociation of the molecular ion HD + in moderate-intensity laser pulses is studied using the time-dependent quantum wave packet method. Simulation of the time of flight (TOF) neutral atom spectra produced from dissociation of the v = 10 vibrational state at a laser intensity of 10 12 W/cm 2 and from v = 0 at the intensity of 5 × 10 12 W/cm 2 are calculated. Good agreement is found with previous experimental results [Phys. Rev.