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Journal of Physics B Atomic Molecular and Optical Physics

Cold NH–NH collisions in a magnetic field: Basis set convergence versus sensitivity to the interaction potential

Yu. V. Suleimanov, Timur V. Tscherbul

Published Oct 4, 2016• 10 citations
Publisher

Abstract

Abstract We explore the combined effect of the uncertainties due to the interaction potential and basis set convergence on low-temperature collisional properties of spin-polarized NH molecules in a magnetic field. We show that quantum scattering calculations with different rotational basis sets and λ -scaled interaction potentials produce qualitatively different ratios of elastic to inelastic cross sections for collision energies above 10 −3 cm −1 , leading to favorable (unfavorable) prospects for sympathetic cooling of NH molecules depending on the basis set cutoff parameter N max . The physical reason behind this effect is that the resonance widths, which determine the maximum variation of the scattering cross sections with λ , tend to depend strongly on N max . At ultralow collision energies, all basis sets produce highly uncertain (and statistically indistinguishable) elastic and inelastic cross sections; however, their ratio γ is much less sensitive to small variations of the interaction potential. Our results highlight the importance of basis set convergence in quantum scattering calculations and establish the existence of parameter regimes where unconverged calculations can still be used to make qualitatively accurate predictions of scattering observables.

DOI
10.1088/0953-4075/49/20/204002

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Abstract We explore the combined effect of the uncertainties due to the interaction potential and basis set convergence on low-temperature collisional properties of spin-polarized NH molecules in a magnetic field. We show that quantum scattering calculations with different rotational basis sets and λ -scaled interaction potentials produce qualitatively different ratios of elastic to inelastic cross sections for collision energies above 10 −3 cm −1 , leading to favorable (unfavorable) prospects for sympathetic cooling of NH molecules depending on the basis set cutoff parameter N max . The physical reason behind this effect is that the resonance widths, which determine the maximum variation of the scattering cross sections with λ , tend to depend strongly on N max . At ultralow collision energies, all basis sets produce highly uncertain (and statistically indistinguishable) elastic and inelastic cross sections; however, their ratio γ is much less sensitive to small variations of the interaction potential. Our results highlight the importance of basis set convergence in quantum scattering calculations and establish the existence of parameter regimes where unconverged calculations can still be used to make qualitatively accurate predictions of scattering observables.
We calculate the interaction potential between N atoms and NH molecules and use it to investigate cold and ultracold collisions important for sympathetic cooling. The ratio of elastic to inelastic cross sections is large over a wide range of collision energy and magnetic field for most isotopic combinations, so that sympathetic cooling of NH molecules by N atoms is a good prospect. However, there are important effects due to a p-wave shape resonance that may inhibit cooling in some cases. We show that scaling the reduced mass used in the collision is approximately equivalent to scaling the interaction potential. We then explore the dependence of the scattering properties on the reduced mass and explain the resonant effects observed using angular-momentum-insensitive quantum defect theory.
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Elastic and spin-changing inelastic collision cross sections are presented for cold and ultracold magnetically trapped NH. The cross sections are obtained from coupled-channel scattering calculations as a function of energy and magnetic field. We specifically investigate the influence of the intramolecular spin-spin, spin-rotation, and intermolecular magnetic dipole coupling on the collision dynamics. It is shown that 15N^{15}\mathrm{N}15NH is a very suitable candidate for evaporative cooling experiments. The dominant trap-loss mechanism in the ultracold regime originates from the intermolecular dipolar coupling term. At higher energies and fields, intramolecular spin-spin coupling becomes increasingly important. Our qualitative results and conclusions are fairly independent of the exact form of the potential and of the size of the channel basis set.
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Ab initio calculations of cross sections and rate constants for elastic scattering and Zeeman relaxation in collisions of $\mathrm{NH}(X{}^{3}{\ensuremath{\Sigma}}^{\ensuremath{-}})$ molecules with 3He{}^{3}\mathrm{He}3He atoms in a magnetic field are presented and the mechanism for Zeeman transitions in ground-state ${}^{3}\ensuremath{\Sigma}$ molecules is established. The potential surface for He-NH interaction is obtained using all-electron coupled-cluster calculations with single, double, and noniterative triple excitations in a basis set augmented by bond functions. The ratio of the rates for elastic energy transfer and Zeeman relaxation in NH-3He{}^{3}\mathrm{He}3He collisions exceeds 105{10}^{5}105 at temperatures between 0.50.50.5 and 1 K.
We carry out quantum inelastic scattering calculations of collisions of Rb atoms with inverting NH3{\text{NH}}_{3}NH3​ and ND3{\text{ND}}_{3}ND3​ molecules in the energy range between 0 and $100\text{ }{\text{cm}}^{\ensuremath{-}1}$, which are important for experiments using velocity-controlled molecular beams to probe scattering resonances. We focus on molecules initially in the upper level of the ammonia inversion doublet for j=1j=1j=1, k=1k=1k=1, which is low-field seeking and can be controlled in a Stark decelerator. We calculate the integral elastic and state-to-state inelastic cross sections in the coupled-states approximation. We demonstrate the presence of both shape and Feshbach resonances in the elastic and inelastic cross sections at low collision energies and discuss their origin in terms of the bound states of the Rb-ND3{\text{ND}}_{3}ND3​ complex. We also consider elastic and inelastic cross sections in the ultracold regime, using close-coupling calculations, in order to assess the viability of sympathetic cooling of ND3{\text{ND}}_{3}ND3​ by Rb. The inelastic cross section for relaxation to the lower level of the inversion doublet is smaller than expected for such a strongly coupled system but is still likely to be too large to allow sympathetic cooling for ND3{\text{ND}}_{3}ND3​ in low-field-seeking states. However, there is a good prospect that sympathetic cooling will be possible for molecules in high-field-seeking states even when the collision partner is a magnetically trapped atom in a low-field-seeking state.