Rotational relaxation of fluoromethane molecules in low-temperature collisions with buffer-gas helium

We propose a method to study the rotational relaxation of polar molecules [here taking fluoromethane $\left({\mathrm{CH}}_3\mathrm{F}\right)$ as an example] in collisions with 3.5 K buffer-gas helium (He) atoms by using an electrostatic guiding technique. The dependence of the guiding signal of ${\mathrm{CH}}_3\mathrm{F}$ on the injected He flux and the dependence of the guiding efficiency of ${\mathrm{CH}}_3\mathrm{F}$ on its rotational temperature are investigated both theoretically and experimentally. By comparing the experimental and simulated results, we find that the translational and rotational temperatures of the buffer-gas cooled ${\mathrm{CH}}_3\mathrm{F}$ molecules can reach to about 5.48 and 0.60 K, respectively, and the ratio between the translational and average rotational collisional cross sections of ${\mathrm{CH}}_3\mathrm{F}-\mathrm{He}$ is $\gamma ={\sigma }_t/{\sigma }_r=36.49\pm 6.15$. In addition, the slowing, cooling, and boosting effects of the molecular beam with different injected He fluxes are also observed and their forming conditions are investigated in some detail. Our study shows that our proposed method can not only be used to measure the translational and rotational temperatures of the buffer-gas cooled molecules, but also to measure the ratio of the translational collisional cross section to the average rotational collisional cross section, and even to measure the average rotational collisional cross section when the translational collisional cross section is measured by fitting the lifetime of molecule signal to get a numerical solution from the diffusion equation of buffer-gas He atoms in the cell.

Figure 1

Schematic diagram of buffer-gas cooling experimental setup. The helium is injected into the cell through the buffer-gas fill line which is thermally connected to the 33 and the 3.5 K stage, respectively. The heated molecular line is connected to a special inlet assembly, which has a bad thermal connection to the buffer-gas cell through a polyimide tube. This allows for the heating of the molecular fill line up to 215 K without affecting the temperature of the buffer-gas cell much. Outside of the buffer-gas cell, the helium atoms and molecules are pumped away by activated charcoal. After extracted from the buffer-gas cell, the molecular beam is first collimated by two collimators, then guided by two segments of quadrupole electric fields to the detection area and detected by QMS. The inset illustration in the upper right corner shows the electric field distribution of cross sectional area for $\pm$ 4 kV high voltage applied on the electrodes.

Figure 2

(a) TOF signals of guided cold ${\mathrm{CH}}_3\mathrm{F}$ beams; high voltages applied on the quadrupole guide are $\pm 4$ kV, respectively. The inset illustration in the upper right corner shows the TOF rising slope after switching on the high voltage, which is applied on the first segment of the quadrupole guide. (b) Velocity distribution of guided cold ${\mathrm{CH}}_3\mathrm{F}$ beams obtained by differentiation. The forward velocity of the maximum probability density is at 103 m/s and the FWHM of the velocity distribution is 73 m/s, corresponding to a translational temperature of 5.48 K. The error bars in the graph denote statistical errors.

Figure 3

The Stark shifts of the lowest rotational energies of ${\mathrm{CH}}_3\mathrm{F}$ as a function of the applied electric field $E$. The five most abundant states $(J,K,M)$ are indicated. The Stark shifts are obtained by numerically diagonalizing the Stark Hamiltonian $J=0–30$.

Figure 4

(a) The dependence of the guided signal of ${\mathrm{CH}}_3\mathrm{F}$ on the injected flux of helium. As the injected molecule flux is set to be 1.00, 2.00, and 4.00 SCCM, respectively, with an increase of the injected flux of helium from 0.05 to 5.00 SCCM, the signal of ${\mathrm{CH}}_3\mathrm{F}$ detected by the QMS increases quickly and then drops slowly; the maximum QMS signal can be obtained with helium flux of 0.25 SCCM, which corresponds to the helium density of $5\times {10}^{14}{\mathrm{cm}}^{-3}$ inside the cell. The error bars in the graph denote statistical errors. (b) The dependence of the signal of ${\mathrm{CH}}_3\mathrm{F}$ on the injected flux of helium without the quadrupole guide. The inputted flux of ${\mathrm{CH}}_3\mathrm{F}$ is 2.00 SCCM, even when the injected helium flux is increased to 5.00 SCCM; the free flight signal of ${\mathrm{CH}}_3\mathrm{F}$ detected by the QMS is still increasing with the increase of the inputted helium flux.

Figure 5

Relative population (royal blue hexagon in the upper right corner) of WFS states of ${\mathrm{CH}}_3\mathrm{F}$ vs Stark shift for the field strength of 80 kV/cm; the black squares, red circles, and blue triangles show the relative population of WFS states of ${\mathrm{CH}}_3\mathrm{F}$ via the rotational energy level for $J=0–30$ at rotational temperatures of 5, 50, and 215 K, respectively.

Figure 6

The dependence of the Stark shift of the WFS state ${\mathrm{CH}}_3\mathrm{F}$ molecule in 80 kV/cm external electric field on the rotational energy for the rotational quantum number of $J=0–30$.

Figure 7

(a) Monte Carlo simulated results show that for the ${\mathrm{CH}}_3\mathrm{F}$ molecule beam, above 15 K the guiding efficiency of molecules in the quadrupole field is nearly not varied, but below 15 K the guiding efficiency decays quickly. (b) The relation between the rotational temperature and collision times. The data is obtained by comparing the experimental values with theoretical simulation results. Error bars in the graph denote statistical errors, and the curve is obtained by fitting $T_{\text{rot}}\left(N\right)=T_{\text{lrot}}+(T_{\text{irot}}-T_{\text{lrot}})\times e^{-N/\gamma \kappa }$.

Figure 8

Normalized velocity distribution of the ${\mathrm{CH}}_3\mathrm{F}$ molecular beam with the injected ${\mathrm{CH}}_3\mathrm{F}$ flux of 2.00 SCCM. When the injected helium flux is 0.05 SCCM, the velocity distribution is a typical effusive beam. As the injected helium flux is increased to 0.20 SCCM, cooling and slowing effects are obvious. With further increasing the injected helium flux to 2.00 SCCM, the ${\mathrm{CH}}_3\mathrm{F}$ molecular beam is moving to the high speed region caused by the boosting effect.