For elastic scattering of 133 Cs atoms by 85 Rb and 87 Rb atoms, interacting via the X 1 Σ + and a 3 Σ + molecular states of RbCs, calculations are presented of the scattering length and the effective range and also of two volume parameters, one for low energy p-wave scattering and one for the energy of an ensemble of fermions. The calculations are performed by various methods, with several representations of the interatomic potentials, including new ab initio potentials presented here. It is shown how the calculated data may be corrected to include the influence of the long range interactions, thus removing the need for numerical solutions of the radial Schrödinger equation at very large interatomic separations. The sensitivity of the results to the choice of potentials, to the van der Waals dispersion coefficient C 6 and to the reduced mass of the colliding atoms is explored, and is found to be great.
We calculate the s-wave scattering length and effective range and the p-wave scattering volume for 7 Li atoms interacting with 133 Cs atoms via the X 1 Σ + molecular potential. The length and volume are found by fitting the log-derivative of the zero energy wave function evaluated at short range to a long range expression that accounts for the leading van der Waals dispersion potential and then incorporating the remaining long range dispersion contributions to first order. The effective range is evaluated from a quadrature formula. The calculated parameters are checked from the zero energy limits of the scattering phase shifts. We comment on ill-conditioning in the calculated s-wave scattering length.
We present ab initio potentials for ground state lithium, sodium, potassium and rubidium atoms interacting with ground state chromium atoms via the 6 Σ + and 8 Σ + states of the corresponding dimers. Each potential is matched to the leading van der Waals dispersion energy − C 6 / R 6 − C 8 / R 8 and an exchange energy; we list the values of C 6 , C 8 and the exchange fitting parameters. We present calculated values from quantal and semi-classical approximations for the s-wave scattering length and effective range and the p-wave scattering volume for collisions of each of the alkali-metal atoms lithium, sodium, potassium and rubidium with 52 chromium atoms and comment on s-wave scattering by 53 chromium atoms.
The calculation of the elastic scattering properties of mixtures composed by rubidium and potassium atoms is reported and compared with experimental results in detail. The improved potentials for both molecular states the singlet and the triplet of the RbK are presented, and the scattering lengths a_{t} and the effective range r_{e} are calculated with the help of this potential using WKB and Numerov methods for Rb-K in the triplet and singlet state. In addition, the convergence of these scattering properties as the depending on a K_{0} parameter is investigated using Quantum Defect Theory. The evaporative cooling other results that include the cross section and the spin-charge cross section, the rate coefficient as a function of the energy and the ultra-low temperature are also presented in this study.
We report the calculation of the same-species elastic scattering properties for the ultracold rubidium–rubidium ( 85 Rb– 85 Rb) system and the results are compared with other theoretical and experimental results in detail. We present an improved potential for triplet ground states of the Rb 2 molecule, and calculate the scattering lengths a t and the effective range r e using WKB and Numerov methods for two rubidium-85 collisions in the triplet state. Also, we investigate the convergence of these scattering properties, i.e. the dependence on core radius and K 0 parameter using quantum defect theory and the analytic calculations of scattering length obtained by Szmytkowski. In addition, we present evaporative cooling and other results that include phase shift and cross section at zero energy limit.
The calculation of the elastic scattering properties of mixtures composed of ultracold Rb–K atoms is reported and compared with experimental results in detail. The improved potentials for both the singlet and triplet molecular states of Rb–K are presented, and the scattering lengths a t and the effective range r e are calculated with numeric and semiclassical methods for Rb–K in the triplet and singlet state. In addition, the convergence of these scattering properties depending on a K 0 parameter is investigated using quantum defect theory. Other results of the evaporative cooling that include the cross section and the spin–charge cross section, the rate coefficient as a function of the energy and ultralow temperature are also presented in this study.
We model the binding energies of rovibrational levels of the RbYb molecule using experimental data from two-color photoassociation spectroscopy in mixtures of ultracold
87Rb with various Yb isotopes. The model uses a theoretical potential based on state-of-the-art ab initio potentials, further improved by least-squares fitting to the experimental data. We have fixed the number of bound states supported by the potential curve, so that the model is mass scaled, that is, it accurately describes the bound-state energies for all measured isotopic combinations. Such a model enables an accurate prediction of the
s-wave scattering lengths of all isotopic combinations of the RbYb system. The reduced mass range is broad enough to cover the full scattering lengths range from $\ensuremath{-}\ensuremath{\infty}$ to $+\ensuremath{\infty}$. For example, the
87Rb
174Yb system is characterized by a large positive scattering length of
+880(120) a.u., while
87Rb
173Yb has $a=\ensuremath{-}626(88)$ a.u. On the other hand
87Rb
170Yb has a very small scattering length of $\ensuremath{-}11.5(2.5)$ a.u. confirmed by the pair's extremely low thermalization rate. For isotopic combinations including
85Rb the variation of the interspecies scattering lengths is much smoother ranging from
+39.0(1.6) a.u. for
85Rb
176Yb to
+230(12) a.u. in the case of
85Rb
168Yb. Hyperfine corrections to these scattering lengths are also given. We further complement the fitted potential with interaction parameters calculated from alternative methods. The recommended value of the van der Waals coefficient is
C6=2837(13) a.u. agrees with but is more precise than the current state-of-the-art theoretical predictions [M. S. Safronova, S. G. Porsev, and C. W. Clark, Phys. Rev. Lett. 109, 230802 (2012)].