_{2}+ O

_{2}collisions in a magnetic field: On the role of the potential energy surface

^{1}, José Campos-Martínez

^{1}and Marta I. Hernández

^{1,a)}

### Abstract

The collision dynamics of ^{17} in the presence of a magnetic field is studied within the close-coupling formalism in the range between 10 nK and 50 mK. A recent global *ab initio* potential energy surface (PES) is employed and its effect on the dynamics is analyzed and compared with previous calculations where an experimentally derived PES was used [T. V. Tscherbul *et al.*, New J. Phys134, 055021 (2009)]. Compared to the results using the older PES, magnetic-field dependence of the low-field-seeking state in the ultracold regime is characterized by a very large background scattering length, *a* _{ bg }, and cross sections exhibit broader and more pronounced Feshbach resonances. The marked resonance structure is somewhat surprising considering the influence of inelastic scattering but it can be explained by resorting to the analytical van der Waals theory, where the short-range amplitude of the entrance channel wavefunction is enhanced by the large *a* _{ bg }. This strong sensitivity to the short range of the *ab initio* PES persists up to relatively high energies (10 mK). After this study and despite quantitative predictions are very difficult, it can be concluded that the ratio between elastic and spin relaxationscattering is generally small, except for magnetic fields which are either low or close to an asymmetric Fano-type resonance. Some general trends found here, such as a large density of quasibound states and a propensity toward large scattering lengths, could be also characteristic of other anisotropic molecule–molecule systems.

We are indebted to Roman V. Krems for encouragement and for giving us essential insight along several stages of this work. We wish to thank M. H. Alexander, D. E. Manolopoulos, and J. M. Hutson for the use of the Hybrid Propagator routines of the MOLSCAT code, and to M. Bartolomei, E. Carmona-Novillo, and R. Hernández-Lamoneda for the use of the *ab initio* PES. J.P.-R. acknowledges hospitality in the Departmtent of Chemistry of UBC (Canada) and support from a predoctoral JAE CSIC grant. The work has been funded by Ministerio de Ciencia e Innovación (Spain, Grant Nos. CTQ2007-62898-BQU and FIS2010-22064-C02-02). We also thank CESGA (Spain) for allocation of computing time.

I. INTRODUCTION

II. THEORY

III. COMPUTATION DETAILS

IV. RESULTS AND DISCUSSION

A. Magnetic-field dependence at 1 μK

B. Translational energy dependence

V. CONCLUDING DISCUSSION

### Key Topics

- Ab initio calculations
- 29.0
- Magnetic fields
- 22.0
- Elasticity
- 19.0
- Inelastic scattering
- 10.0
- Magnetic resonance
- 10.0

## Figures

Internal energies of ^{17} as functions of magnetic field. In this work, molecules are considered to be initially in their *lfs* states |ζ_{ a }, ζ_{ b }〉 = |3, 3〉. Open and closed symbols indicate critical values of the field for which *d* and *g* barriers, respectively, become open for the different outgoing channels. Note also that calculations of Fig. 4 refer to the *hfs* state |1, 1〉.

Internal energies of ^{17} as functions of magnetic field. In this work, molecules are considered to be initially in their *lfs* states |ζ_{ a }, ζ_{ b }〉 = |3, 3〉. Open and closed symbols indicate critical values of the field for which *d* and *g* barriers, respectively, become open for the different outgoing channels. Note also that calculations of Fig. 4 refer to the *hfs* state |1, 1〉.

Comparison of the *ab initio* and Perugia potential matrix elements among the fragment states |3, 3〉 and |3, 1〉 for a magnetic field *B* = 100 G. The long-range behavior is compared in the inset. Note that orbital angular momentum for the entrance (|3, 3〉) and outgoing (|3, 1〉) channels are 0 and 2, respectively.

Comparison of the *ab initio* and Perugia potential matrix elements among the fragment states |3, 3〉 and |3, 1〉 for a magnetic field *B* = 100 G. The long-range behavior is compared in the inset. Note that orbital angular momentum for the entrance (|3, 3〉) and outgoing (|3, 1〉) channels are 0 and 2, respectively.

Magnetic-field dependence for collisions of ^{17} in the initial *lfs* state |3, 3〉 and translational energy of 1 μK. (a) Elastic cross sections; (b) total inelastic cross sections; and (c) ratio γ between elastic and inelastic (untrapping) cross sections. Blue and red colors correspond to using the *ab initio* (Ref. 32) and the Perugia (Ref. 26) PESs, respectively.

Magnetic-field dependence for collisions of ^{17} in the initial *lfs* state |3, 3〉 and translational energy of 1 μK. (a) Elastic cross sections; (b) total inelastic cross sections; and (c) ratio γ between elastic and inelastic (untrapping) cross sections. Blue and red colors correspond to using the *ab initio* (Ref. 32) and the Perugia (Ref. 26) PESs, respectively.

Total cross section vs magnetic-field for the *hfs* state |1, 1〉 at a translational energy of 1 μK and using the *ab initio* PES. Note that only the elastic channel is open. The result can be compared with Fig. 4 of Ref. 25, corresponding to the Perugia PES.

Total cross section vs magnetic-field for the *hfs* state |1, 1〉 at a translational energy of 1 μK and using the *ab initio* PES. Note that only the elastic channel is open. The result can be compared with Fig. 4 of Ref. 25, corresponding to the Perugia PES.

Effect of the long-range anisotropy of the *ab initio* PES: Magnetic-field dependence of elastic and total inelastic cross sections for the *lfs* state |3, 3〉 at 10 μK. Thick lines joined by filled squares show results using the correct long-range anisotropy (Refs. 32 and 33) while dashed lines joined by open squares correspond to calculations where the long-range anisotropy of the interaction has been switched off.

Effect of the long-range anisotropy of the *ab initio* PES: Magnetic-field dependence of elastic and total inelastic cross sections for the *lfs* state |3, 3〉 at 10 μK. Thick lines joined by filled squares show results using the correct long-range anisotropy (Refs. 32 and 33) while dashed lines joined by open squares correspond to calculations where the long-range anisotropy of the interaction has been switched off.

Translational energy dependence of the collisional processes for the *lfs* state |3, 3〉: a comparison between *ab initio* and Perugia PESs for different values of magnetic field. (a) Elastic cross sections; (b) Total inelastic cross sections; and (c) Elastic-to-inelastic ratio γ.

Translational energy dependence of the collisional processes for the *lfs* state |3, 3〉: a comparison between *ab initio* and Perugia PESs for different values of magnetic field. (a) Elastic cross sections; (b) Total inelastic cross sections; and (c) Elastic-to-inelastic ratio γ.

Same as Fig. 6 but for different values of magnetic field near the 32 G resonance of the calculations with the *ab initio* PES.

Same as Fig. 6 but for different values of magnetic field near the 32 G resonance of the calculations with the *ab initio* PES.

Study of the sensitivity of the elastic-to-inelastic ratio γ to the anisotropy of the *ab initio* PES. All terms of the spherical harmonic expansion are multiplied by β except the isotropic one. The effect is shown for different translational energies and magnetic fields.

Study of the sensitivity of the elastic-to-inelastic ratio γ to the anisotropy of the *ab initio* PES. All terms of the spherical harmonic expansion are multiplied by β except the isotropic one. The effect is shown for different translational energies and magnetic fields.

## Tables

Energies (in K) and coefficients [in the basis of Eq. (5)] of the three lowest states of ^{17} [Eq. (2)] for a magnetic field *B* = 100 G.

Energies (in K) and coefficients [in the basis of Eq. (5)] of the three lowest states of ^{17} [Eq. (2)] for a magnetic field *B* = 100 G.

Parameters associated with the long-range behavior of the *ab initio* and Perugia potentials: isotropic vdW coefficient , scale length (), and energy () of the analytical vdW theory (Ref. 46), and height of the *d*-wave centrifugal barrier. is the critical magnetic field for which the |3, 3〉 − |3, 1〉 Zeeman splitting becomes larger than the *d*-wave barrier.

Parameters associated with the long-range behavior of the *ab initio* and Perugia potentials: isotropic vdW coefficient , scale length (), and energy () of the analytical vdW theory (Ref. 46), and height of the *d*-wave centrifugal barrier. is the critical magnetic field for which the |3, 3〉 − |3, 1〉 Zeeman splitting becomes larger than the *d*-wave barrier.

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