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arXiv:1809.09140 · Physical Review A

Scattering of cold He4 on He4Li6,7 and He4Na23 molecules

M. A. Shalchi, A. Delfino, T. Frederico, Lauro Tomio

Published Sep 24, 2018• 4 citations
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Abstract

We predict $s$-wave elastic cross-sections $\ensuremath{\sigma}$ for low-energy atom-molecule collisions with kinetic energies up to 40 mK for the $^{4}\mathrm{He}$ collision with weakly bound diatomic molecules formed by $^{4}\mathrm{He}$ with $^{7}\mathrm{Li},\phantom{\rule{0.28em}{0ex}}^{6}\mathrm{Li}$, and $^{23}\mathrm{Na}$. Our scattering calculations are performed by using diatomic and triatomic molecular binding energies obtained from several available realistic models as input in a renormalized zero-range model as well as a finite-range one-term separable potential in order to quantify the relevance of range corrections to our predictions. Of particular relevance for possible experimental realization, we show the occurrence of a zero in $\ensuremath{\sigma}$ for the collision of cold $^{4}\mathrm{He}$ on a $^{4}\mathrm{He}\phantom{\rule{0.16em}{0ex}}^{23}\mathrm{Na}$ molecule below 20 mK. Also our results for the elastic collision $^{4}\mathrm{He}$ on $^{4}\mathrm{He}\phantom{\rule{0.16em}{0ex}}^{6,7}\mathrm{Li}$ molecules suggest that $\ensuremath{\sigma}$ varies considerably for the realistic models studied. As the chosen molecules are weakly bound and the scattering energies are very low, our results are interpreted on the light of the Efimov physics, which explains the model independence and robustness of our predictions despite some sensitivity on the potential range.

DOI
10.1103/physreva.98.032705

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We predict sss-wave elastic cross-sections \ensuremathσ\ensuremath{\sigma}\ensuremathσ for low-energy atom-molecule collisions with kinetic energies up to 40 mK for the 4He^{4}\mathrm{He}4He collision with weakly bound diatomic molecules formed by 4He^{4}\mathrm{He}4He with 7Li,6Li^{7}\mathrm{Li},\phantom{\rule{0.28em}{0ex}}^{6}\mathrm{Li}7Li,6Li, and 23Na^{23}\mathrm{Na}23Na. Our scattering calculations are performed by using diatomic and triatomic molecular binding energies obtained from several available realistic models as input in a renormalized zero-range model as well as a finite-range one-term separable potential in order to quantify the relevance of range corrections to our predictions. Of particular relevance for possible experimental realization, we show the occurrence of a zero in \ensuremathσ\ensuremath{\sigma}\ensuremathσ for the collision of cold 4He^{4}\mathrm{He}4He on a 4He23Na^{4}\mathrm{He}\phantom{\rule{0.16em}{0ex}}^{23}\mathrm{Na}4He23Na molecule below 20 mK. Also our results for the elastic collision 4He^{4}\mathrm{He}4He on 4He6,7Li^{4}\mathrm{He}\phantom{\rule{0.16em}{0ex}}^{6,7}\mathrm{Li}4He6,7Li molecules suggest that \ensuremathσ\ensuremath{\sigma}\ensuremathσ varies considerably for the realistic models studied. As the chosen molecules are weakly bound and the scattering energies are very low, our results are interpreted on the light of the Efimov physics, which explains the model independence and robustness of our predictions despite some sensitivity on the potential range.
Atom-dimer exchange and dissociation reaction rates are predicted for different combinations of two 4He^{4}\mathrm{He}4He atoms and one of the alkaline species among 6Li,7Li^{6}\mathrm{Li}, ^{7}\mathrm{Li}6Li,7Li, and 23Na^{23}\mathrm{Na}23Na, by using three-body scattering formalism with short-range two-body interactions. Our study was concerned with low-energy reaction rates in which the sss-, ppp-, and ddd-wave contributions are the relevant ones. The 4He^{4}\mathrm{He}4He is chosen as one of the atoms in the binary mixture, in view of available previous investigations and laboratory accessibilities. Focusing on possible experimental cold-atom realizations with two-atomic mixtures, in which information on atom-dimer reaction rates can be extracted, we predict the occurrence of a dip in the elastic reaction rate for colliding energies smaller than 20 mK, when the dimer is the 4He23Na^{4}\mathrm{He}^{23}\mathrm{Na}4He23Na molecule. We are also anticipating a zero in the elastic ppp-wave contribution for the 4He+4He7Li^{4}\mathrm{He}+^{4}\mathrm{He}^{7}\mathrm{Li}4He+4He7Li and 4He+4He23Na^{4}\mathrm{He}+^{4}\mathrm{He}^{23}\mathrm{Na}4He+4He23Na reaction processes. With weakly bound molecules reacting with atoms at very low colliding energies, we interpret our results in the light of Efimov physics which supports model independence and robustness of our predictions. Specific sensitivities on the effective range were evidenced, highlighted by the particular inversion role of the ppp- and ddd-waves in the atom exchange and dissociation processes.
Atom-molecule collisions in helium--helium--alkali-metal triatomic systems at cold energies are studied using the adiabatic hyperspherical representation. We consider the elastic collision processes $^{4}\mathrm{He}X+^{4}\mathrm{He}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}^{4}\mathrm{He}X+^{4}\mathrm{He}$ and $^{4}\mathrm{He}_{2}+X\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}^{4}\mathrm{He}_{2}+X$, as well as the reactive collision processes $^{4}\mathrm{He}X+^{4}\mathrm{He}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightleftharpoons}^{4}\mathrm{He}_{2}+X$, where XXX is one of the bosonic alkali-metal atoms: 7Li^{7}\mathrm{Li}7Li, 23Na^{23}\mathrm{Na}23Na, 39K^{39}\mathrm{K}39K, 85Rb^{85}\mathrm{Rb}85Rb, or 133Cs^{133}\mathrm{Cs}133Cs. The elastic and reactive collision cross sections are calculated at nonzero collision energies by including not only zero atom-molecule relative angular momentum, L=0L=0L=0, processes but also L>0L>0L>0 processes. The total cross section for $^{4}\mathrm{He}X+^{4}\mathrm{He}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}^{4}\mathrm{He}X+^{4}\mathrm{He}$ is found to increase with the scattering length between 4He^{4}\mathrm{He}4He and XXX, while the other collision processes are not found to have any systematic dependence on the alkali-metal species XXX.
We have measured integral elastic cross sections for ground state $^{4}\mathrm{\ensuremath{-}}^{4}$He scattering at collision energies from 1.35 to 0.5 K using a novel atomic beam apparatus built into a dilution refrigerator. Scattering is almost pure s wave, and is predicted to be enormous due to a possibly bound state near the continuum. The effective integral cross section ranges from 20 to 1000 A˚2{\mathrm{\r{}}}^{2}˚2 as collision energy is reduced in our experiment. These cross sections are in agreement with the values predicted using the latest analytical potential of Aziz and Slaman.
Using the HFDHE2 He-He potential of Aziz et al. [J. Chem. Phys. 90, 4330 (1979)] with the Faddeev-Yakubovsky theory, we have calculated the 4He^{4}\mathrm{He}4He atom-triatom scattering length and found it to be - 116 \AA{}. We reduced the sss-wave two-body ttt matrix to a separable form through the unitary-pole approximation and did the same for the sss-wave [3+1] and [2+2] subamplitudes with the energy-dependent-pole approximation in our work. Also, the binding energies of all the states in the trimer and tetramer, and the atom-diatom scattering length, already determined in our previous work with other potentials, were recalculated for the new interaction. We found an excited trimer bound state, apparently not an Efimov state, near the atom-diatom threshold and an atom-diatom scattering length of 195 \AA{}. A feature of our results was the absence of an excited state in the tetramer, but in its place, was a resonancelike state which led to the large atom-triatom scattering length.
The best available intermolecular potential for helium by Aziz, Nain, Carley, Taylor, and McConville is shown here for the first time to have a 4He2 bound state. Two numerical analyses, namely, eigenvalue solution and effective range theory, are used to support this conclusion. Unlike usual chemically bound species, the binding energy of this very weakly bound level is found to be only 8.3×10−4 K, which is four orders of magnitude smaller than the potential well depth ε = 10.8 K. The scattering length for He+He collisions, determined from effective range theory, is used to calculate the elastic cross section in the very low energy limit. The results (1.878×105 Å2 for 4He+4He and 6.035×102 Å for 3He+3He) are consistent with measurements at the lowest velocities yet attained. In terms of the estimated uncertainties of the parameters of the potential of Aziz and co-workers, it is shown that it is very likely that a bound state of the 4He2 molecule does in fact exist.
The calculations of the elastic scattering properties for collisions between two 23Na atoms at ultra-cold temperatures are reported and compared with experimental and theoretical results in the detail. We present a parametric model potential for the triplet molecular state of the 23Na molecule, and calculate the scattering length ɑ(subscript t) and the effective range r(subscript e) by using the semiclassical and Numerov methods, respectively. The shape resonances occur in the collisions at low energies, and resonance positions and widths are computed by Briet-Wigner formula. In addition, we also present other results that include differential cross sections at zero energy limit.