Multiphoton Excitation of an Ozone Molecule in Laser Fields

The multiphoton excitation of O3 molecules in laser fields is discussed using the second quantization and unitary transformations. It is successful to derive the total Hamiltonian (including the stretch-vibration Hamiltonian of an ozone molecule, the laser fields Hamiltonian and the interaction Hamiltonian between O3 and laser fields), the transition probabilities from the ground state to excited states and the expressions for the average number of photons absorbed by molecules from laser fields. The calculated stretch-vibration energy spectrum of O3 molecules is in good agreement with that of experiments. There are two peaks of single-photon transition at 1042.5 and 1103.0 cm-1, respectively. The three peaks of the two-photon transition are at 1027.5, 1055.5 and 1101.0 cm-1 respectively. The peaks at 1014.5, 1028.0, 1043.0 and 1100.5 cm-1 are four peaks of the three-photon transition. The amplitudes of the three-photon transition probability are about 6 orders of magnitude less than those of the two-photon transition which are about 14 orders of magnitude less than those of the single-photon transition. The laser field intensity is taken as 5×10-2 W/cm2, which is different from 109 W/cm2 in the former researches. This theoretical model can be used to discuss the multiphoton excitation for all of the molecules with a C2v symmetry, but inadequate to calculate the n-photon (n≥4) transition. In the computational process, it is found that the transition probability changes with the intensity of the laser field, which needs further research in the future.