Radiative association processes to specific rovibrational levels in low-energy ${\mathrm{Na}}^{+}+{}^{87}\mathrm{Rb}$ collisions

The radiative association processes for ${\mathrm{Na}}^{+}$ colliding with ${}^{87}\mathrm{Rb}\left(5s\right)$ atoms have been investigated by using the quantum-mechanical method. The total and partial cross sections that associate to the specific rovibrational states are calculated rigorously in the energy range of ${10}^{-13}-1.2\times {10}^{-2}\mathrm{eV}$. The association cross sections display rich resonance structures. The ratios of rotationally resolved cross sections to total association cross sections and the ratios of vibrationally resolved cross sections to rotationally resolved cross sections are calculated and presented. For energies less than ${10}^{-9}\mathrm{eV}$, association to $X{}^2{\Sigma }^{+}$ ($J=1$) dominates over all other association states. As the energy increases, each resonance of the total cross sections is associated with the given angular component of specific bound states. In the energy range of ${10}^{-13}-1.2\times {10}^{-3}\mathrm{eV}$, the vibrational states $v=27$ and $v=28$ are the most probable final states. The probability for the formation of molecular ion ${\mathrm{NaRb}}^{+}$ in the rovibrational states is discussed. The existence of Cooper minima in the radiative association cross sections is found and illustrated.

Figure 1

Adiabatic potentials of ${\mathrm{NaRb}}^{+}$ as a function of internuclear distance. The $X{}^2{\Sigma }^{+}$ and $A{}^2{\Sigma }^{+}$ states correspond to $\mathrm{Na}\left(3s\right)+{\mathrm{Rb}}^{+}$ and ${\mathrm{Na}}^{+}+\mathrm{Rb}\left(5s\right)$ channels in the asymptotic regions, respectively.

Figure 2

Dipole matrix element for ${\mathrm{NaRb}}^{+}$ between $X{}^2{\Sigma }^{+}$ and $A{}^2{\Sigma }^{+}$ states.

Figure 3

Total and partial radiative association cross sections to final rotational state $J$ and vibrational states $v=25$, 27, 50, 80, and 100. (a) $J=1$; (b) $J=0$.

Figure 4

The dipole matrix $M_{J^{\prime },J}$ as vibrational quantum number of ν = 0–112 for collision energy at $E={10}^{-13}\mathrm{eV}$. (a) $J^{\prime }=0$, $J=1$; (b) $J^{\prime }=2$, $J=1$; (c) $J^{\prime }=1$, $J=0$.

Figure 5

The partial radiative association cross section to final rotational state $J=1$ as a function of vibrational quantum number ν = 0–112 at $E={10}^{-13}\mathrm{eV}$.

Figure 6

Total and partial radiative association cross sections to final rotational state $J$ and vibrational states $v=20$, 25, 27, 50, 80, and 100. (a) $J=10$; (b) $J=15$.

Figure 7

Total and angular-resolved radiative association to $v=27$ cross sections. (a) ${10}^{-8}<E<{10}^{-6}\mathrm{eV}$; (b) ${10}^{-6}<E<{10}^{-5}\mathrm{eV}$.

Figure 8

Total and angular-resolved radiative association to $v=28$ cross sections. (a) ${10}^{-5}<E<5\times {10}^{-5}\mathrm{eV}$; (b) $5\times {10}^{-5}<E<1.5\times {10}^{-4}\mathrm{eV}$; (c) $1.5\times {10}^{-4}<E<5\times {10}^{-4}\mathrm{eV}$; (d) $5\times {10}^{-4}<E<1.2\times {10}^{-3}\mathrm{eV}$.