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Journal of Physics B Atomic Molecular and Optical Physics

Rotational cooling of molecular gases by positron impact at vanishing collision energies

J Sabin Del Valle, Enrico Bodo, Franco Antonio Gianturco

Published Jun 14, 2005• 5 citations
Publisher

Abstract

The behaviour of the rotationally inelastic cross sections for ultracold positrons injected in molecular gases is examined computationally by considering the ambient molecules to be rotationally 'hot' ( j = 10) and by letting the relative translational energies tend to zero. The size of the corresponding state-to-state transitions are obtained from an exact quantum calculation carried out in the space-frame representation, using non-empirical model interactions between e + and the target test molecules (H 2 , N 2 , O 2 , Li 2 ). The structural features of the molecules are related, via the dynamical coupling effects, to the size and efficiency of the cooling process along the above series of target gases. It is shown that positron projectiles can provide a possible route to the cooling of molecular rotations for simple homonuclear diatomics within the framework of ultracold dynamical conditions.

DOI
10.1088/0953-4075/38/13/001

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The behaviour of the rotationally inelastic cross sections for ultracold positrons injected in molecular gases is examined computationally by considering the ambient molecules to be rotationally 'hot' ( j = 10) and by letting the relative translational energies tend to zero. The size of the corresponding state-to-state transitions are obtained from an exact quantum calculation carried out in the space-frame representation, using non-empirical model interactions between e + and the target test molecules (H 2 , N 2 , O 2 , Li 2 ). The structural features of the molecules are related, via the dynamical coupling effects, to the size and efficiency of the cooling process along the above series of target gases. It is shown that positron projectiles can provide a possible route to the cooling of molecular rotations for simple homonuclear diatomics within the framework of ultracold dynamical conditions.
Quantum mechanical methods are employed to obtain superelastic cross sections involving H 2 and N 2 molecules, in excited rotational states, colliding with electrons at the very low collision energies which are encountered in cold trap experiments. This computational analysis intends to explore the feasibility of cold electrons for the collisional quenching of molecular gases down to the nanokelvin regimes. The results are obtained using rigorous coupled-channel (CC) calculations in the laboratory frame of reference which allows one to correctly describe the cross section behaviour at ultralow energies. The results are analysed down to the ultracold region of validity of Wigner's law, where it is found that electron-driven collisions exhibit substantial efficiency for the quenching of rotational populations in molecular gases involving the title systems.
Measurements of positron temperature as a function of time are presented when a positron gas, confined in an electromagnetic trap at an elevated temperature ( K), is cooled by interactions with the molecular gases , or CO at 300 K. A simple model describing positron thermalization by coupling to vibrational and rotational modes is presented, with cooling-rate predictions calculated in the Born approximation. Comparisons to the measured positron cooling-rate curves permit estimates of the magnitudes of the relevant cross sections. The results are compared with experiment for the case of vibrational excitation, where direct measurements exist; and they provide estimates of the rotational excitation cross sections where direct measurements are not currently possible. Positron cooling rates are compared for these gases at 300 K, and estimates of their effectiveness in cooling positrons to cryogenic temperatures are discussed.
Cold collisions involving highly rotationally excited diatomic molecules are investigated. As the translational energy is lowered, the total inelastic cross section decreases sharply for specific channels where quasiresonant transitions are no longer energetically allowed. Rate coefficients are given for collisional quenching of rotationally excited H2,D2,T2,{\mathrm{H}}_{2},{\mathrm{D}}_{2},{\mathrm{T}}_{2},H2​,D2​,T2​, and O2{\mathrm{O}}_{2}O2​ at zero temperature. The specific rotational states that are stable against collisional relaxation would be interesting prospects for cooling and trapping. The application of collisional cooling methods together with recently developed schemes for producing rotationally hot molecules may allow high densities of ultracold ``super rotors'' to be achieved.
The translational and internal level cooling of atoms and molecules in ultracold gases results from a combination of elastic and inelastic collisional processes. While elastic collisions lead to rapid thermalization, exoergic inelastic collisions may lead to heating and trap loss. To date, most collisional studies have targeted low-lying levels of diatomic molecules. Here we investigate inelastic quenching and elastic scattering of rotationally excited linear (H2{}_{2}2​, HD, CO, O2{\mathrm{O}}_{2}O2​, and CO2{}_{2}2​) and nonlinear (H2{}_{2}2​O and NH3{}_{3}3​) molecules in ultracold collisions with He and report the corresponding complex scattering lengths. It has been found that the ratio of the imaginary component $\ensuremath{\beta}$ to the real component $\ensuremath{\alpha}$ of the scattering length generally increases with decreasing rotational constant for linear molecules. With the exception of CO, $\ensuremath{\beta}$ becomes significantly smaller than $\ensuremath{\alpha}$ as the energy gap for rotational transitions increases. In all cases, $\ensuremath{\beta}$ decreases with rotational energy gap for relatively large rotational excitation, allowing for convenient fits to an exponential energy gap formula. Excited rotational levels of H2{\mathrm{H}}_{2}H2​ and HD appear to be collisionally stable due to the very low values of $\ensuremath{\beta}/\ensuremath{\alpha}$. Rotationally excited H2{\mathrm{H}}_{2}H2​O also appears to be a viable candidate for He buffer gas cooling due to relatively small values of $\ensuremath{\beta}$.
The study of molecular inelastic collision processes at cold and ultracold temperatures is of considerable interest as schemes are currently being developed to efficiently cool and trap neutral polar molecules. In this work, quantum-mechanical scattering calculations are presented for the quenching of rotationally excited CO due to collisions with H, He and H 2 for collision energies between 10 −5 and 10 cm −1 . The calculations were performed using the close-coupling approach and the coupled-states approximation. Cross sections for the quenching of the j = 1–10, 20, 30 and 40 levels of CO are presented and mechanism and trends of energy transfer in these systems are discussed.
A close coupling quantum-mechanical calculation is performed for rotational energy transfer in a HD+HD collision at very low energy, down to the ultracold temperatures: $T\ensuremath{\sim}{10}^{\ensuremath{-}8}$ K. A global six-dimensional H2{}_{2}2​-H2{}_{2}2​ potential-energy surface is adopted from a previous work [Boothroyd et al., J. Chem. Phys. 116, 666 (2002)]. State-resolved integral cross sections ${\ensuremath{\sigma}}_{ij\ensuremath{\rightarrow}{i}^{\ensuremath{'}}{j}^{\ensuremath{'}}}({\ensuremath{\varepsilon}}_{\text{kin}})$ of different quantum-mechanical rotational transitions $ij\ensuremath{\rightarrow}{i}^{\ensuremath{'}}{j}^{\ensuremath{'}}$ in the HD molecules and corresponding state-resolved thermal rate coefficients ${k}_{ij\ensuremath{\rightarrow}{i}^{\ensuremath{'}}{j}^{\ensuremath{'}}}(T)$ have been computed. Additionally, for comparison, H2{}_{2}2​+H2{}_{2}2​ calculations for a few selected rotational transitions have also been performed. The hydrogen and deuterated hydrogen molecules are treated as rigid rotors in this work. A pronounced isotope effect is identified in the cross sections of these collisions at low and ultracold temperatures.