3 tal results [3], show that the decreasing of the intensity of the laser pulse causes a decrease in the signal of the high- energy band with respect to the low-energy band (Fig. 2). To derive the details of the KER structure, we represent a time-dependent construction of this signal in Fig. 3. As can be seen in this figure, at first the high-energy band appears between $_{∼}$4.8 to $_{∼}$8.1 cycles of the laser pulse (note that the meaning of t = 0 in our simulation, as shows in Fig. 1, is 2.5 cycles earlier than of the peak of the laser pulse). After this duration, it seems that the path- way of the ionization with high-energy fragment is closed and another pathway of the ionization with low-energy fragment is opened. Therefore, this figure proposes that there are two distinct pathways for the ionization with different energies and time domains. adopted a general non-linear coordinate transformation for both electronic and nuclear coordinates. For the spa- tial discretization, we have constructed a finite difference scheme with a non-uniform (adaptive) grid for z and ρ electronic coordinates which are finest near the nuclei and coarsest at the border regions of the simulation box. A finite difference scheme with an adaptive grid is used also for R coordinates that is finest for small R and become a coarse grid for large R . Using a fine grid for electronic coordinate ( z and ρ ) near the nuclei and for small val- ues of internuclear distance coordinate ( R ) improves the treatment of the electron dynamics near the nuclei (the Coulomb singularities) and bound states of the nuclear dynamics, while the use of a coarse grid near the borders improves the speed of calculations. The grid points for z , ρ , and R coordinates in our simulation are 560, 155, and 240 respectively. The finest grid sizes values in this adaptive grid schemes are 0.13, 0.2, and 0.025 respec- tively for z , ρ , and R coordinates. The grids extend up to z max = 54, ρ max = 25, and R max = 16. The simulation setup is shown schematically in Fig. 1. The laser pulse in this simulation suddenly turns on at time τ$_{on}$ . We are assuming τ$_{on}$ is the time on which a H + 2 (D + 2 ) is suddenly created according a Frank- Condon transition from the neutral H$_{2}$ (D$_{2}$) to H + 2 (D + 2 ) σ$_{g}$ state (Fig. 1). In an intense laser field, some parts of D + 2 wavepackage become unbound and outgo- ing through different channels. A part of this unbound wavepacket becomes outgoing as D + + D through dis- sociation channel (DC) and another part becomes out- going through dissociation-ionization channel (DIC) as D + + D + (Fig. 1). The nuclear components in the dissociation-ionization channel possess both dissociation and Coulomb explosion energies [9]. Figure 4 represents the space-time population of the ground state (1 sσ$_{g}$ ), first exited state (2 pσ$_{u}$ ), other non- ionization states (ONIS), and total non-ionization states (TNIS). The difference between the population of TNIS and the population of 1 sσ$_{g}$ + 2 pσ$_{u}$ equals to the space- time population of the ONIS. This Figure shows explic- itly the charge resonance among 1 sσ$_{g}$ , 2 pσ$_{u}$ , and ONIS. The resonance between 1 sσ$_{g}$ and 2 pσ$_{u}$ is very strong and a weaker coupling of these two states with the ONIS are visible in the ONIS’s figure. These figures show explicitly the space-time dissociation-ionization pathways of D + 2 . Note that, the reduction of the population of the TNIS in the dissociation pathways is due to the ionization. Fig- ure 4 shows that the population of 2 pσ$_{u}$ becomes consid- erable over $_{∼}$2-5 internuclear distances and $_{∼}$3-8 cycles and for ONIS over $_{∼}$3-7 internuclear distances and $_{∼}$5-11 cycles. D + 2 in the dissociative pathways is considerably ionized and will has little population before it dissociates, as has shown in the next figures. To see the details of the dissociation ionization path- ways, it is important to derive separately the space- dependent population and time-dependent population of different states. Fig. 5 represents the time-dependent population of the ground state (1 sσ$_{g}$ , GS), first exited state (2 pσ$_{u}$ , ES), the ground and first exited states to- gether (GES), other non-ionized states (ONIS), total non-ionized states (TNIS) or norm, and finally the time- dependent population of the ionized states (IS). As can be seen in this figure, the population of the ONIS in- creases considerably from about 4 cycles. The charge res- onance between different states is observable. A strong charge resonance between Gs and Es appears after 2 cy- cles results in the population of 2 pσ$_{u}$ becoming more than that of 1 sσ$_{g}$ state occasionally. In this figure a weaker charge resonance is also observed between the GES and ONIS. Figure 2 shows the simulation KER spectra and com- pares with the experimental result. In this figure, the dotted red line is related to the experimental result [3] for the 480 nm linearly polarized laser pulse with I=4 . 0 × 10 14 W cm − 2 intensity and $_{∼}$100 fs pulse duration. The black solid, grey solid, and blue dot-dash lines show simula- tion results that are respectively related to 4 . 0 × 10 $^{14}$, 3 . 5 × 10 $^{14}$, and 3 . 0 × 10 14 W cm − 2 intensities and a 480 nm wavelength. The simulation results show ex- plicitly two bands, a high-energy and a lo-energy band which also have appeared in the experimental results [3]. Some inconsistencies can be seen in Fig. 2 between the experimental and simulation KER spectra related to I=4 . 0 × 10 14 W cm − 2 intensity. These inconsistencies are due to some experimental uncertainties in the shape and duration of the laser pulse and the unavoidable simplifica- tions and approximations applied in the simulation setup. However, Fig. 2 shows many similarities and correspon- dence between experimental and simulation results. The simulation results, in correspondence to the experimen- Figure 6 shows the internuclear populations of the ion- ization of D + 2 related to the 4 . 0 × 10 14 W cm − 2 intensity in Fig. 2. The internuclear populations of the ioniza- tion of D + 2 in Fig. 6 have been derived by the virtual detector method [15, 18]. Indeed, this figure represents the R-dependent ionization rate, with an arbitrary unit, of D + 2 beyond BOA [9]. The BOA approach has often III. RESULTS AND DISCUSSION