## 3 Results and Discussion
### The Dissociative Ionization of Molecule \(\rm{CF_{2}Br_{2}}\) in 800 nm Laser Fields  
According to the Keldysh theory [5], we calculated the critical intensity of 9.0 \(\times\) 10\({}^{13}\) W/cm\({}^{2}\) in the 800 nm laser field, where the MPI is favored over the TI in the range from 5.0 \(\times\) 10\({}^{13}\) to 9.0 \(\times\) 10\({}^{13}\) W/cm\({}^{2}\) in our experimental conditions. The preceding section has explained that DI is the dominant process for molecules under femtosecond laser pulses. Hence in our experimental conditions (70 fs FWHM), the multiphoton ionization occurs first, then the dis  
Figure 2: The sliced images, corresponding velocity distributions and peak values (eV) of the fragment ions (**a**) \(\rm{CF_{2}}^{+}\)(50), (**b**)Br\({}^{+}\) (80), (**c**)\(\rm{CF_{2}Br^{+}}\) (130) and (**d**)\(\rm{Br_{2}}^{+}\) (160) in 800 and 400 nm laser fields. The open scatters (\(\Circinus\)) and (\(\square\)) are the experimental data in 800 nm(red) and 400 nm (blue) laser fields, the green dash lines (——) represent the envelope of each fitting Gaussian function and the red and blue solid lines (——) are the final fitting curves of the velocity distribution. sociation process follows, namely multiphoton dissociative ionization (MPDI) [25,26]. Next, the estimated reaction channels and related the appearance energy (E\({}_{\text{AP}}\)) are listed as Table 1, where E\({}_{\text{AP}}\) denotes the required energy to switch on the channel [27]. The expression is shown in the following Equation (2), where E\({}_{\text{EP}}\) and E\({}_{\text{R}}\) represent the sum of energy of the reaction products and reactants, respectively. In the above channels, the i, j and k represent the photon number absorbed by the molecules, hv is the one photon energy (1.55 eV@800 nm). Once the E\({}_{\text{AP}}\) were calculated, the number of photons absorbed has been determined. Hence, the number of photons i, j and k are 8, 11 and 11, respectively. On the other hand, the ion yields as a function of the laser intensity in the MPDI process meets the following Equation (3):  
\[\text{E}_{\text{AP}}=\sum\text{E}_{\text{P}}-\sum\text{E}_{\text{R}} \tag{2}\]  
\[\text{W}_{\text{n}}\propto\sigma\text{I}^{\text{n}} \tag{3}\]  
where \(\sigma\) is the photoionization cross-section, I denotes the laser intensity and n represents the number of photon involved in the ionization process. In order to assess the consistency for the estimated reaction channels, the relationship between the ion yields and laser intensity was measured. In Figure 3, the slope of the curves obtained by fitting and shown in logarithmic coordinate matches the calculated photon number, which suggests that the estimated reaction pathways occur in a MPDI regime. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Channel** & **Reaction Path** & **\textasciitilde** **E\({}_{\text{AP}}\)(eV)** \\ \hline (1) & CF\({}_{2}\)Br\({}_{2}+\)ihv \(\rightarrow\) CF\({}_{2}\)Br\({}_{2}^{+}+\) e\({}^{-}\rightarrow\) CF\({}_{2}\)Br\({}^{+}+\) Br \(+\) e\({}^{-}\), & 11.19 \\ (2) & CF\({}_{2}\)Br\({}_{2}+\)ihv \(\rightarrow\) CF\({}_{2}\)Br\({}_{2}^{+}+\) e\({}^{-}\rightarrow\) Br\({}^{+}+\) CF\({}_{2}\)Br \(+\) e\({}^{-}\), & 15.85 \\ (3) & CF\({}_{2}\)Br\({}_{2}+\)khv \(\rightarrow\) CF\({}_{2}\)Br\({}_{2}^{+}+\) e\({}^{-}\rightarrow\) CF\({}_{2}\)\({}^{+}+2\)Br \(+\) e\({}^{-}\), & 15.61 \\ \hline \hline \end{tabular} \({}^{\star}\)Calculated in G4 theory.  
\end{table} 
Table 1: The estimated reaction channels and the related energy. Figure 3: The schematic diagram of the ion yields as a function of the laser intensity in logarithmic coordinates, the red dashed line represents the critical intensity for multi-photon ionization (MPI) and tunnel ionization (TI). After molecules absorb enough photons and overcome the ionization potential barrier, the residual amount of energy resulting from the difference between the photons energy and the energy required to activate the reaction channel is transferred to internal degrees of freedom and translational energy of the fragments.