Photodissociation of the ${\text{HeH}}^{+}$ ion into excited fragments $\left(n=2,3\right)$ by time-dependent methods

The total and partial photodissociation cross sections of the molecular ion ${\text{HeH}}^{+}$ are computed by time-dependent methods for fragmentation into the excited shells $n=1,2,3$ up to a photon energy of 40 eV. ${{}^1\Sigma }^{+}$ and ${}^1\Pi$ states are considered for parallel and perpendicular transitions for different initial rotational or vibrational excitations. Nonadiabatic radial and rotational couplings are taken into account. The results from coupled-channel equations are compared with the Born-Oppenheimer approximation. A time-dependent calculation with a femtosecond laser pulse is carried out to simulate a recent crossed beam photodissociation imaging experiment with vacuum ultraviolet free-electron laser [H. B. Pedersen et al., Phys. Rev. Lett. 98, 223202 (2007)]. The dominance of photodissociation perpendicular to the photon polarization is confirmed.

Figure 1

(Color online) Adiabatic and diabatic potential energy curves of the ${{}^1\Sigma }^{+}$ (full lines) and ${}^1\Pi$ (dashed lines) of the ${\text{HeH}}^{+}$ molecular ion. The adiabatic curves are computed at the state average CASSCF level. The diabatic curves are obtained from the transformation matrix $\mathbf{D}\left(R\right)$ solution of the equation ${\partial }_R\mathbf{D}\left(R\right)=-\mathbf{F}\left(R\right)\mathbf{D}\left(\mathbf{R}\right)$ where $\mathbf{F}\left(R\right)$ is the approximate “$2\times 2$” nonadiabatic radial coupling matrix.

Figure 2

(Color online) Total photodissociation cross section ${\sigma }_{0v^{″}{J}^{″}\to {\Lambda }^{\prime }}\left(E\right)$ [Eq. (1)] for the transition ${}^1\Sigma \to {}^1\Sigma$ for the parallel orientation of the molecular axis with respect to the field for the case $J^{″}=0\to J^{\prime }=1$ (full line), $J^{″}=1\to J^{\prime }=0,2$ (dotted line with open circles), $J^{″}=10\to J^{\prime }=9,11$ (dashes) for $v=0$ and $J^{″}=0\to J^{\prime }=1$ for $v=1$ (dots).

Figure 3

(Color online) Photodissociation cross section averaged over an isotropic orientation with respect to the laser field, bold line: $J^{″}=0\to J^{\prime }=1$ for $v=0$ with in dotted line the contribution of the parallel orientation (${}^1\Sigma \to {}^1\Sigma$ transitions) and in dashed line, the contribution of the perpendicular orientations (${}^1\Sigma \to {}^1\Pi$ transitions); open circles: $J^{″}=10\to J^{\prime }=9,11$ for $v=0$ ; diamonds: $J^{″}=0\to J^{\prime }=1$ for $v=1$.

Figure 4

(Color online) Comparison of the total photodissociation cross section for a isotropic orientation of the molecular axis with respect to the field for the case $v=0$, $J^{″}=1\to J^{\prime }=0,2$ with previous works.

Figure 5

(Color online) Partial cross sections section computed from Eq. (3) for a parallel orientation for transitions $J^{″}=0\to J^{\prime }=1$ from the vibrational state $v=0$. The sum of the partial cross sections is compared with that obtained by Eq. (4) and with the total cross section calculated by Eq. (2). Panel a: sections larger than ${10}^{-18}{\text{cm}}^2$. Panel b: sections larger than $5\times {10}^{-19}{\text{cm}}^2$.

Figure 6

(Color online) Partial cross sections larger than $5\times {10}^{-19}{\text{cm}}^2$ computed from Eq. (3) in the Born-Oppenheimer approximation for a parallel orientation for transitions $J^{″}=0\to J^{\prime }=1$ from the vibrational state $v=0$. The sum of the partial cross sections BO (full line) is compared with that the results obtained in the nonadiabatic case (triangles).

Figure 7

(Color online) Partial cross sections larger than ${10}^{-18}{\text{cm}}^2$ computed from Eq. (3) for a perpendicular orientation for transitions $J^{″}=0\to J^{\prime }=1$ from the vibrational state $v=0$. Panel a: Born-Oppenheimer approximation; panel b: nonadiabatic case.

Figure 8

(Color online) Average partial cross section for the fragmentation into ${\text{H}}^{+}$ and neutral He computed from Eq. (3) for an isotropic orientation for transitions $J^{″}=0\to J^{\prime }=1$ from the vibrational state $v=0$. Panel a: Born-Oppenheimer approximation; panel b: nonadiabatic case.

Figure 9

(Color online) Population in the excited electronic states during the photodissociation of the ground $v=0$, $J=0$ state by a pulse of 30 fs and a maximum intensity of $8.775\times {10}^{11}\text{W}{\text{cm}}^{-2}$. Panel (a) parallel orientation (Only fragments having an asymptotic probability larger than $3\times {10}^{-4}$ are shown); panel (b) perpendicular orientation.

Figure 10

(Color online) Kinetic energy release for the fragment $\text{He}\left(1snl\right)$ during the photodissociation of the ground $v=0$, $J=0$ state by a pulse of 30 fs. The distribution is averaged over an isotropic orientation.

Figure 11

(Color online) Angular distribution of the $\text{He}\left(1snl\right)$ fragment for a kinetic energy release in the range 13.5–14 eV during the photodissociation of the ground $v=0$, $J=0$ state by a pulse of 30 fs. The intensity $I_0$ is taken from the contribution of the parallel and perpendicular orientation in Fig. 10.