Anomalous Decline of Molecular Ion Mobility in Cooled Helium Gas

We present a first successful theoretical account of the ion mobilities of ${\mathrm{N}}_2^{+}$ and ${\mathrm{O}}_2^{+}$ in helium gas at 4.3 K. Measured mobilities of various molecular ions at low effective temperatures reportedly tend to values smaller than their polarization limits, with the exception of ${\mathrm{N}}_2^{+}$ [J. Sanderson et al., J. Phys. B 26, L465 (1993); J. Sanderson et al.J. Phys. B27, L433 (1994)]. The present theoretical results obtained by the classical trajectory calculations agree with the experimental ones very well, and make it definitive that the anomalous decline of molecular ion mobility is caused by a Feshbach-like resonance due to the anisotropic interaction potential between a molecular ion and a helium atom. The mechanism thus revealed is supported by quantitative quantum mechanical calculations. The process appears very similar to that of laser cooling.

Figure 1

Calculated interaction potentials for the ${\mathrm{N}}_2^{+}\mathrm{\text{−}}\mathrm{He}$ (upper panel) and ${\mathrm{O}}_2^{+}\mathrm{\text{−}}\mathrm{He}$ (lower panel) systems as a function of $R$ for fixed values of $\theta =0°$ (solid line), 45° (dotted line), and 90° (dashed line).

Figure 2

Reduced mobilities $K_0$ of ${\mathrm{N}}_2^{+}$ and ${\mathrm{O}}_2^{+}$ in helium gas at 4.3 K. Lines are the results by the CT calculations for ${\mathrm{N}}_2^{+}$ (solid line) and ${\mathrm{O}}_2^{+}$ (dashed line). Open squares and circles are the experimental values for ${\mathrm{N}}_2^{+}$ in Ref. 2 and for ${\mathrm{O}}_2^{+}$ in Refs. 3, 19, respectively. Exact $K_{\mathrm{pol}}$ values are $16.35{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ for ${\mathrm{N}}_2^{+}$ and $16.22{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ for ${\mathrm{O}}_2^{+}$.

Figure 3

Time-dependent populations for the rotational states $j=0$, 2, and 4 of the ${\mathrm{O}}_2^{+}$ ion in the collision with helium at $T_{\mathrm{eff}}=11.6\mathrm{K}$. The initial angular momentum of helium is $l=10$.

Figure 4

Total maximum excitation rates from $j=0$ to $j^{\prime }=2$ and 4 for the ${\mathrm{O}}_2^{+}\mathrm{\text{−}}\mathrm{He}$ (squares) and ${\mathrm{N}}_2^{+}\mathrm{\text{−}}\mathrm{He}$ (circles) systems as a function of the collision energy $T_{\mathrm{eff}}$.