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Recent experimental evidences have prompted us to study the dynamics of laser-assisted rotational excitation of a diatomic molecule due to an ion impact. The collision time between the ion and the molecule is very small (few atomic units) and the laser pulses considered are of picosecond range. We study the evolution of the rotational probabilities by varying the various laser parameters (pulse shape, field strength, pulse width, frequency) and collision parameters (impact parameter b, collisional velocity v). It is found that the probabilities of the rotational states depend strongly on the laser pulse parameters and the collision parameters. The study is more emphasised by studying ⟨J^{2}⟩ (a parameter defining the extent of the rotational excitation) and ⟨J_{z}⟩ for the system under concern. For higher value of b, the maximum value obtained by ⟨J^{2}⟩ increases and vice versa. Also, the molecule enters the transient mode for large b and v.
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