Resonant electron scattering and dielectronic recombination in two-center atomic systems

Electron scattering and dielectronic recombination with an ion in the presence of a neighboring atom is studied. The incident electron is assumed to be captured by the ion, leading to resonant excitation of the atom which afterwards may stabilize either by electron reemission or radiative decay. We show that the participation of the atom can strongly affect, both quantitatively and qualitatively, the corresponding processes of electron scattering and recombination. Various ion-atom systems and electronic transitions are considered. In particular we show that electron scattering under backward angles may be strongly enhanced, provided the incident energy lies very close to the resonance. Besides, we derive the scaling behavior of two-center dielectronic recombination with the principal quantum numbers of the participating atomic states. The resonant enhancement in this process is shown to be so strong that it can compete with ordinary single-center recombination even after integrating over a rather broad distribution of incident electron energies.

Figure 1

Schemes of two-center resonant scattering (2CRS) and two-center dielectronic recombination (2CDR). An incident electron is first captured at center $A$, leading to resonant excitation at center $B$. Subsequently, this metastable state may either decay backwards (via ICD) in the case of 2CRS or radiatively stabilize by photoemission in the case of 2CDR.

Figure 2

Differential cross sections for Rutherford scattering from a proton and for 2CRS from a ${\mathrm{H}}^{+}$-He system. In the latter case, the incident electron is captured to the $1s$ ground state of hydrogen, with simultaneous excitation of the helium atom to the $1s2p$ state. The atoms are separated by $R=5\text{Å}$ along the $z$ axis. The incident electron energy is resonant with ${\varepsilon }_p=7.6$ eV. The dashed blue line shows the (incoherent) 2CRS cross section according to Eq. (9). For comparison, the dotted black line illustrates the cross section for Rutherford scattering from an isolated proton at the same electron energy [see Eq. (10)]. The solid red line shows the full cross section where the respective amplitudes have been added coherently [see Eq. (17)].

Figure 3

Same as Fig. 2, but in the 2CRS process the electron is captured to the $2s$ state in the hydrogen atom forming center $A$, while another hydrogen atom—representing center $B$—is simultaneously excited to the $2p_0$ state. The energy of the incident electron is in exact resonance with ${\varepsilon }_p=6.8$ eV. Top: $R=10\text{Å}$, bottom: $R=15\text{Å}$.

Figure 4

Dependence of 2CRS on the incident electron energy, expressed through the detuning $\mathrm{\Delta }={\varepsilon }_p+{\epsilon }_0-{\varepsilon }_0-{\epsilon }_1$, for backward scattering angle ($\vartheta =\pi$). The two-center system is the same as in Fig. 3, with interatomic distances of $R=8\text{Å}$ (dashed red line) and $R=10\text{Å}$ (solid red line), respectively. The dotted black line shows the nonresonant background of Rutherford scattering from an isolated proton.

Figure 5

Dependence of the 2CDR cross section on the principal quantum number $n_A$. An incident electron recombines with a proton to form a hydrogen atom in the presence of a neighboring ${\mathrm{He}}^{+}$ ion. The electron is captured to the $n_{A}s$ state of hydrogen, with simultaneous excitation of the ${\mathrm{He}}^{+}$ ion to the $2p_0$ state. The atoms are separated by $R=10\text{Å}$ along the $z$ axis. The black circles refer to the case of exact resonance, where for each value of $n_A$ the incident energy is chosen to give $\mathrm{\Delta }=0$ [see Eq. (34)]. Instead, the red diamonds show the corresponding results for a nonzero detuning of $\mathrm{\Delta }=6.6\times {10}^{-6}$ eV. For comparison, the crosses show the cross section for radiative recombination of the electron with an isolated proton [see Eq. (36)].

Figure 6

Dependence of the 2CDR cross section on the principal quantum number $n_B$. As in Fig. 5, an incident electron recombines with a proton to form a hydrogen atom in the presence of a neighboring ${\mathrm{He}}^{+}$ ion. The electron is captured to the $1s$ ground state of hydrogen, with simultaneous excitation of the ${\mathrm{He}}^{+}$ ion to the $n_B{p}_0$ state. The atoms are separated by $R=10\text{Å}$ along the $z$ axis. While the black circles refer to the case of exact resonance, where for each value of $n_B$ the incident energy is chosen to give $\mathrm{\Delta }=0$, the red filled (open) diamonds show the corresponding results for nonzero detuning of $\mathrm{\Delta }=6.6\times {10}^{-8}$ eV ($\mathrm{\Delta }=6.6\times {10}^{-6}$ eV) [see Eq. (34)].

Figure 7

Dependence of 2CDR on the principal quantum number $n_A$ for two different atomic systems. In both cases, an incident electron recombines with a proton at center $A$, forming a hydrogen atom in the $n_{A}s$ state. The filled circles refer to a neutral helium atom as center $B$ which is excited to the $1s2p$ state, whereas the open circles show our results for a neighboring hydrogen atom which is excited to the $2p_0$ state. The atoms are separated by $R=10\text{Å}$ along the $z$ axis and the incident electron energies are always chosen to be in exact resonance.