On the role of the magnetic dipolar interaction in cold and ultracold collisions: Numerical and analytical results for NH(${}^3{\Sigma }^{-}$) + NH(${}^3{\Sigma }^{-}$)

Abstract

We present a detailed analysis of the role of the magnetic dipole-dipole interaction in cold and ultracold collisions. We focus on collisions between magnetically trapped NH molecules, but the theory is general for any two paramagnetic species for which the electronic spin and its space-fixed projection are (approximately) good quantum numbers. It is shown that dipolar spin relaxation is directly associated with magnetic-dipole induced avoided crossings that occur between different adiabatic potential curves. For a given collision energy and magnetic field strength, the cross-section contributions from different scattering channels depend strongly on whether or not the corresponding avoided crossings are energetically accessible. We find that the crossings become lower in energy as the magnetic field decreases, so that higher partial-wave scattering becomes increasingly important \textit{below} a certain magnetic field strength. In addition, we derive analytical cross-section expressions for dipolar spin relaxation based on the Born approximation and distorted-wave Born approximation. The validity regions of these analytical expressions are determined by comparison with the NH + NH cross sections obtained from full coupled-channel calculations. We find that the Born approximation is accurate over a wide range of energies and field strengths, but breaks down at high energies and high magnetic fields. The analytical distorted-wave Born approximation gives more accurate results in the case of s-wave scattering, but shows some significant discrepancies for the higher partial-wave channels. We thus conclude that the Born approximation gives generally more meaningful results than the distorted-wave Born approximation at the collision energies and fields considered in this work.

Accepted by Eur. Phys. J. D for publication in Special Issue on Cold Quantum Matter - Achievements and Prospects (2011)

References in corpus (17)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Laser cooling of a diatomic molecule
• Precision measurement of gravity with cold atoms in an optical lattice and comparison with a classical gravimeter
• Magnetic trapping and Zeeman relaxation of imidogen (NH X-triplet-Sigma)
• Low-energy molecular collisions in a permanent magnetic trap
• The radiative lifetime of metastable CO ($a^3\Pi ,v=0$)
• Continuous loading of an electrostatic trap for polar molecules
• Cold N+NH Collisions in a Magnetic Trap
• Ultracold atom-molecule collisions and bound states in magnetic fields: tuning zero-energy Feshbach resonances in He-NH (3Sigma-)
• OH hyperfine ground state: from precision measurement to molecular qubits
• Time-Domain Measurement of Spontaneous Vibrational Decay of Magnetically Trapped NH
• Mechanism of Collisional Spin Relaxation in Triplet-Sigma Molecules
• Cold and ultracold NH--NH collisions in magnetic fields
• Cold collisions of N atoms and NH molecules in magnetic fields
• Cold and ultracold NH--NH collisions: The field-free case
• Collisional properties of cold spin-polarized nitrogen gas: theory, experiment, and prospects as a sympathetic coolant for trapped atoms and molecules

Cited by in corpus (11)

• Quantum reactive scattering of ultracold NH($X{}^3{\Sigma }^{-}$) radicals in a magnetic trap
• Atom-molecule collisions, spin relaxation, and sympathetic cooling in an ultracold spin-polarized Rb(${}^2\mathrm{S}$)-SrF${(}^2{\Sigma }^{+})$ mixture
• Cold collisions of heavy ${}^2\Sigma$ molecules with alkali-metal atoms in a magnetic field: Ab initio analysis and prospects for sympathetic cooling of SrOH${(}^2\Sigma )$ by Li(${}^2$S)
• Multistage Zeeman deceleration of NH $X{}^3{\Sigma }^{-}$ radicals
• Full-dimensional quantum scattering calculations on ultracold atom-molecule collisions in magnetic fields: The role of molecular vibrations
• Sympathetic cooling of fluorine atoms with ultracold atomic hydrogen
• Cold collisions of an open-shell S-state atom with a ^2Pi molecule: N(^4S) colliding with OH in a magnetic field
• Elastic and inelastic collisions of ${}^2\Sigma$ molecules in a magnetic field
• Multichannel Quantum Defect Theory for cold molecular collisions with a strongly anisotropic potential energy surface
• Magnetic Feshbach resonances in collisions of non-magnetic closed-shell ${}^1\Sigma$ molecules
• Ultracold molecular collisions in magnetic fields: Efficient incorporation of hyperfine structure in the total rotational angular momentum representation