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arXiv:1009.1322 · Physical Chemistry Chemical Physics

Cold collisions of N ( 4 S) atoms and NH ( 3 Σ) molecules in magnetic fields

Piotr Szymon Żuchowski, Jeremy M. Hutson

Published Dec 24, 2010• 38 citations
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Abstract

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.

DOI
10.1039/c0cp01447h

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•Jan 1, 2011•0 citations
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.
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 present elastic and inelastic spin-changing cross sections for cold and ultracold NH(X (3)Σ(-)) + NH(X (3)Σ(-)) collisions, obtained from full quantum scattering calculations on an accurate ab initio quintet potential-energy surface. Although we consider only collisions in zero field, we focus on the cross sections relevant for magnetic trapping experiments. It is shown that evaporative cooling of both fermionic (14)NH and bosonic (15)NH is likely to be successful for hyperfine states that allow s-wave collisions. The calculated cross sections are very sensitive to the details of the interaction potential, due to the presence of (quasi)bound state resonances. The remaining inaccuracy of the ab initio potential-energy surface therefore gives rise to an uncertainty in the numerical cross-section values. However, based on a sampling of the uncertainty range of the ab initio calculations, we conclude that the exact potential is likely to be such that the elastic-to-inelastic cross-section ratio is sufficiently large to achieve efficient evaporative cooling. This likelihood is only weakly dependent on the size of the channel basis set used in the scattering calculations.
Sympathetic cooling is one of the most promising techniques for producing ultracold molecules from precooled molecules. Previous researches have shown that it is inadequate to use the ultracold alkali-metal atoms as coolant for sympathetic cooling. To explore the possibility of ultracold alkali-earth-metal atoms as coolant, in this paper a theoretical investigation is performed of the cold collision dynamics for Xe-NH(X3∑-) system in magnetic fields. The interaction potential energies of Xe-NH complex are calculated respectively by using the single and double excitation coupled-cluster theory with the noniterative treatment of triple excitations[CCSD(T)] method and complete basis set limit extrapolated method. An analytic express of potential energy surface (PES) is given for the first time. A single global minimum value occurs at R=7.14a0, θ=102.76° with an energy of-153.54 cm-1, and the PES has a weak anisotropy. Combine the ab initio PES with quantum scattering theory, then the cold collisional dynamics of Xe-NH system in a magnetic field will be studied. The elastic and inelastic transition cross sections and their ratios of NH molecules in the lowest low-field following state (n=0, mj=1) under different magnetic fields and collisional energies are calculated. The results show that the elastic cross section is independent of magnetic field, and the inelastic cross section changes with magnetic field, especially at an ultracold temperature. A common rule of thumb is that to successfully implement cooling, the ratio of elastic cross section to inelastic cross section needs to reach 100 at least. The results suggest that it is likely to be a challenging work to perform sympathetic cooling of NH molecule by ultracold Xe atom.
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.
In this work we investigate the potential of controlling cold (O(K)−mK) and ultracold (mK-μK) atom-molecule collisions by tuning scattering states across Feshbach resonances using magnetic fields. We are interested in particular in the prospect of suppressing the often undesirable inelastic collisions. The He-O_2 system provides the vehicle for our study. We calculate bound and quasi-bound states of several isotopic combinations, including their Zeeman structure, to reveal the underlaying pattern for easier characterization of quasi-bound states in terms of rigorous and approximately good quantum numbers. These calculations also help us locate the fields at which zero-energy resonances will occur. Scattering calculations are then performed for collisions of 3^He and 4^He with {16}^O_2 at fixed (1 μK) energy but varying magnetic field. The field is varied to sweep the scattering state across resonance. At low and ultralow energies we enter the Wigner threshold regime where the S-partial wave dominates the wavefunction. The cross sections, and the real and imaginary parts of the scattering length, vary dramatically across resonance. Their profiles are used to analyze the resonances. In a highlight of our results we show that dramatic suppression of inelastic cross sections occur for 4^He-{16}^O_2 . The resonances are relatively wide (of order 100 Gauss), with suppression of inelastic scattering over a similarly wide range of fields and for temperatures ranging from 10 mK down to 1 μK. We conclude that under certain conditions it is possible to almost completely eliminate inelastic collisions. This is potentially very important for cooling techniques, such as evaporative and sympathetic cooling, that require efficient elastic cross sections. Suppression of inelastic collisions can not only increase thermalization efficiency but it can also result in longer trap-lifetimes by reducing transitions to untrapable states.