^{1,a)}, Pavel Soldán

^{1,b)}, Jeremy M. Hutson

^{1}, Pascal Honvault

^{2,c)}and Jean-Michel Launay

^{2}

### Abstract

A potential energy surface for the lowest quartet electronic state of lithium trimer is developed and used to study spin-polarized collisions at ultralow kinetic energies. The potential energy surface allows barrierless atom exchange reactions. Elastic and inelastic cross sections are calculated for collisions involving a variety of rovibrational states of . Inelastic collisions are responsible for trap loss in molecule production experiments. Isotope effects and the sensitivity of the results to details of the potential energy surface are investigated. It is found that for vibrationally excited states, the cross sections are only quite weakly dependent on details of the potential energy surface.

One of the authors (M.T.C.) is grateful for sponsorship from the University of Durham and Universities UK.

I. INTRODUCTION

II. QUARTET POTENTIAL ENERGY SURFACES FOR

A. Electronic states overview

B. Basis set convergence

C. The surface

1. Representation of the surface

2. Choice of grid

3. Fitting and interpolation

4. The long-range potential

III. SCATTERING CALCULATIONS

A. Methodology

B. Computational details

C. Ultracold collisions

D. Cold collisions

E. Potential sensitivity

F. Isotope effects

G. Reactions in isotopic mixtures

IV. CONCLUSIONS

### Key Topics

- Elasticity
- 35.0
- Potential energy surfaces
- 24.0
- Basis sets
- 17.0
- Ground states
- 13.0
- Elastic collisions
- 12.0

## Figures

CASSCF quartet potentials of at geometries for states that correlate with the atomic and asymptotic limits. The interatomic distances are , , and .

CASSCF quartet potentials of at geometries for states that correlate with the atomic and asymptotic limits. The interatomic distances are , , and .

CASSCF quartet potentials of at geometries for states that correlate with the atomic and asymptotic limits. The interatomic distances are .

CASSCF quartet potentials of at geometries for states that correlate with the atomic and asymptotic limits. The interatomic distances are .

Triplet potential energy curves of from the atomic and dissociation limits.

Triplet potential energy curves of from the atomic and dissociation limits.

Correlation diagram of quartet potentials of that correlate with the atomic dissociation limit. Note that the energy is shown relative to this limit and the state correlating with is not shown. The first panel connects the states with the atom-diatom limit, with one interatomic distance fixed at and symmetry preserved. The second panel connects the atom-diatom limit with states, with one interatomic distance fixed at and symmetry preserved. The third panel connects and terms, with two interatomic distances fixed at and the angle between them, , varied.

Correlation diagram of quartet potentials of that correlate with the atomic dissociation limit. Note that the energy is shown relative to this limit and the state correlating with is not shown. The first panel connects the states with the atom-diatom limit, with one interatomic distance fixed at and symmetry preserved. The second panel connects the atom-diatom limit with states, with one interatomic distance fixed at and symmetry preserved. The third panel connects and terms, with two interatomic distances fixed at and the angle between them, , varied.

Comparison of different fitted potentials with the *ab initio* energies for the quartet ground state of at geometries.

Comparison of different fitted potentials with the *ab initio* energies for the quartet ground state of at geometries.

The fitted quartet ground-state potential of lithium trimer for a bond angle of 60°. Contours are labeled in .

The fitted quartet ground-state potential of lithium trimer for a bond angle of 60°. Contours are labeled in .

The fitted quartet ground-state potential of lithium trimer for a bond angle of 120°. Contours are labeled in .

The fitted quartet ground-state potential of lithium trimer for a bond angle of 120°. Contours are labeled in .

The fitted quartet ground-state potential of lithium trimer for a bond angle of 150°. Contours are labeled in .

The fitted quartet ground-state potential of lithium trimer for a bond angle of 150°. Contours are labeled in .

Energy dependence of elastic cross sections for (, ). The energy-dependent scattering length is shown in the inset.

Energy dependence of elastic cross sections for (, ). The energy-dependent scattering length is shown in the inset.

Energy dependence of elastic and inelastic cross sections for (, ). The complex energy-dependent scattering length is shown in the inset.

Energy dependence of elastic and inelastic cross sections for (, ). The complex energy-dependent scattering length is shown in the inset.

Energy dependence of the phase shift for (, ).

Energy dependence of the phase shift for (, ).

Energy dependence of elastic and sum of inelastic probabilities, , for (, ).

Energy dependence of elastic and sum of inelastic probabilities, , for (, ).

Eigenphase sum (upper panel) and individual eigenphases (lower panel) for (, ).

Eigenphase sum (upper panel) and individual eigenphases (lower panel) for (, ).

Final rotational distributions for (, ) at .

Final rotational distributions for (, ) at .

Elastic probabilities, , as a function of total angular momentum for (, ).

Elastic probabilities, , as a function of total angular momentum for (, ).

Inelastic probabilities, , as a function of total angular momentum for (, ).

Inelastic probabilities, , as a function of total angular momentum for (, ).

(Color online) Elastic and total inelastic cross sections for (, ) on the uncontracted cc-pV5Z and aug-cc-pCVTZ basis set potentials and the inelastic cross sections in the Langevin model.

(Color online) Elastic and total inelastic cross sections for (, ) on the uncontracted cc-pV5Z and aug-cc-pCVTZ basis set potentials and the inelastic cross sections in the Langevin model.

Final rotational distributions for (, ). Top panel: statistical prediction; center panel: ultracold regime ; bottom panel: collision energy of .

Final rotational distributions for (, ). Top panel: statistical prediction; center panel: ultracold regime ; bottom panel: collision energy of .

Center-of-mass differential cross sections for (, ) at a collision energy of . Differential cross sections are integrated through the azimuthal angle and summed over the final states in each vibrational manifold.

Center-of-mass differential cross sections for (, ) at a collision energy of . Differential cross sections are integrated through the azimuthal angle and summed over the final states in each vibrational manifold.

Dependence of the elastic cross sections for (, ) on the scaling factor of the nonadditive part of the potential.

Dependence of the elastic cross sections for (, ) on the scaling factor of the nonadditive part of the potential.

Dependence of the elastic cross sections for (, ) on the scaling factor of the nonadditive part of the potential.

Dependence of the total inelastic cross sections for (, ) on the scaling factor of the nonadditive part of the potential.

Dependence of the total inelastic cross sections for (, ) on the scaling factor of the nonadditive part of the potential.

Final rotational distributions for (, ) at a collision energy in the Wigner regime.

Final rotational distributions for (, ) at a collision energy in the Wigner regime.

Final rotational distributions for (, ) at a collision energy of .

Final rotational distributions for (, ) at a collision energy of .

Center-of-mass differential cross sections for (, ) at a collision energy of . Differential cross sections are integrated through the azimuthal angle and summed over the final states in each vibrational manifold and overall.

Center-of-mass differential cross sections for (, ) at a collision energy of . Differential cross sections are integrated through the azimuthal angle and summed over the final states in each vibrational manifold and overall.

The low-lying energy rotational levels of , , and for , relative to the potential minimum. Only levels with even are shown for and only levels with odd are shown for .

The low-lying energy rotational levels of , , and for , relative to the potential minimum. Only levels with even are shown for and only levels with odd are shown for .

Energy dependence of eigenphase sum (top panel), elastic cross section (center panel), and inelastic/reactive cross section (bottom panel) for collisions of (, ) with .

Energy dependence of eigenphase sum (top panel), elastic cross section (center panel), and inelastic/reactive cross section (bottom panel) for collisions of (, ) with .

## Tables

Convergence tests for Li basis sets. For atoms, static polarizability and excitation energy. For triplet dimers, dissociation energy , position of the minimum , BSSE evaluated at , scattering length , and energy of the highest vibrational level for the molecule. For quartet trimers, dissociation energy and position of the minimum for . All calculations except the “best available theory” are from the present work and used RCCSD(T) calculations.

Convergence tests for Li basis sets. For atoms, static polarizability and excitation energy. For triplet dimers, dissociation energy , position of the minimum , BSSE evaluated at , scattering length , and energy of the highest vibrational level for the molecule. For quartet trimers, dissociation energy and position of the minimum for . All calculations except the “best available theory” are from the present work and used RCCSD(T) calculations.

Elastic and total inelastic cross sections and rate coefficients for at a collision energy of for different initial states of the molecule.

Elastic and total inelastic cross sections and rate coefficients for at a collision energy of for different initial states of the molecule.

Elastic and total inelastic cross sections and rate coefficients for at a collision energy of for different initial states of the molecule.

Cross sections and related parameters for at a collision energy of for different initial states of the molecule.

Cross sections and related parameters for at a collision energy of for different initial states of the molecule.

Cross sections and related parameters for at a collision energy of for different initial states of the molecule.

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