This paper clarifies the disagreement in the depth of the potential energy curve of the cesium dimer singlet ground state which has lasted for nearly a decade. We point out that the origin of this disagreement must be a technical misprint in the values of the three binding energies reported by Danzl et al. [Science 321, 1062 (2008)], while the X1Σg+ state potential reported by Coxon and Hajigeorgiou [J. Chem. Phys. 132, 094105 (2010)], based on experimental data by Amiot and Dulieu [J. Chem. Phys. 117, 5155 (2002)], is quite correct. We have recalculated the potential energy function of the triplet ground state a3Σu+ by using the available experimental data spanning both the attractive and the repulsive branches so that the potential energy function complies asymptotically with the singlet ground state X1Σg+ potential energy function by Coxon and Hajigeorgiou. This is important for the simulation of the near dissociation properties such as Feshbach resonances, which are typically observed in modern experiments with ultracold atoms and molecules.
We characterize Feshbach resonances in all isotopologues of the
Li−Li system with improved interaction potentials. Starting from spectroscopically accurate Morse/long-range (MLR) potential-energy curves for the singlet (
X1Σ+) and triplet (
a3Σ+) electronic states of
Li2, we apply small phenomenological inner-wall adjustments (following Julienne and Hutson, Phys. Rev. A 89, 052715 (2014), arXiv:1404.2623v3) and fit the resulting potentials to threshold measurements for the
6Li−6Li and
7Li−7Li isotopologues, including binding energies, scattering lengths, and Feshbach resonance positions. Using the optimized potentials in coupled-channels scattering calculations, we predict and characterize s-wave Feshbach resonances in the
6Li−7Li isotopologue. In its lowest-energy hyperfine channel, all resonances are narrow (
∼0.01−0.1 G), strongly closed-channel dominated, and predominantly triplet in electronic spin character, in marked contrast to the homonuclear systems. These results provide a foundation for designing Raman optical-transfer pathways to produce ultracold
Li2 molecules in deeply bound rovibrational levels of both the
X1Σ+ and
a3Σ+ potentials across all three isotopologues.
A modified semi-empirical Tang-Toennies potential model is used to describe the a3Σu+ potentials of the alkali dimers. These potentials are currently of interest in connection with the laser manipulation of the ultracold alkali gases. The fully analytical model is based on three experimental parameters, the well depth De, well location Re, and the harmonic vibrational frequency ωe of which the latter is only slightly optimized within the range of the literature values. Comparison with the latest spectroscopic data shows good agreement for Na2, K2, Rb2, and Cs2, comparable to that found with published potential models with up to 55 parameters. The differences between the reduced potential of Li2 and the conformal reduced potentials of the heavier dimers are analyzed together with why the model describes Li2 less accurately. The new model potential provides a test of the principle of corresponding states and an excellent first order approximation for further optimization to improve the fits to the spectroscopic data and describe the scattering lengths and Feshbach resonances at ultra-low temperatures.
We develop two schemes for tuning the scattering length on the ground triplet state of Cs2. First, an absolute value of the triplet scattering length of 133Cs2 is determined using the experimental data (Fioretti et al, Eur.Phys.J. 5, 389 (1999)). We demonstrate that the large scattering length can be made small and positive by coupling of the 3Σ + u (6S +6S) potential to the 3Πg state by strong off-resonant radiation. A weaker laser field coupling the 3Σ + u (6S + 6S) continuum to the lowest bound level of the excited 3Σ + g (6S + 6P) also leads to a small positive scattering length. In addition, the scattering length of the 135Cs isotope is found to be positive. The method used solves the Schrödinger equation for two electronic states coupled by an electromagnetic field with approximations employed. The scattering length is determined from calculated continuum wavefunctions of low energy. 1 A positive scattering length is a crucial ingredient in obtaining Bose-Einstein condensation from a gas of ultra-cold atoms. This parameter controls the long range repulsion
The presence of shape resonances due to tunneling through the centrifugal barrier modifies strongly the dynamics of cold atom scattering. As shown on the example of the ground and lowest triplet electronic states of the
85Rb133Cs molecule, the crucial parameter is, as usual for cold collisions, the scattering length. A general description of shape resonances of diatomic molecules is given from three simple single channel asymptotic models, whose respective performances are discussed. The first model, which consists of a ${R}^{\ensuremath{-}6}$ potential limited at short range by a repulsive wall, positioned to reproduce the
s-wave scattering length, accounts satisfactorily for the main system-independent properties of shape resonances. Introduction in the model of energy- and angular-momentum-dependent nodal lines specific to the inner part of the potential greatly improves its efficiency. When the energy and angular momentum dependence of the nodal lines cannot be deduced from full potential calculations or from experiment, a rough, but universal, estimate of these properties is obtained by extending the ${R}^{\ensuremath{-}6}$ behavior of the potential up to the origin.
In this article we extend the theory of ultra-long-range giant dipole molecules, formed by an atom in a giant dipole state and a ground-state alkali-metal atom, by angular-momentum couplings known from recent works on Rydberg molecules. In addition to
s-wave scattering, the next higher order of
p-wave scattering in the Fermi pseudopotential describing the binding mechanism is considered. Furthermore, the singlet and triplet channels of the scattering interaction as well as angular-momentum couplings such as hyperfine interaction and Zeeman interactions are included. Within the framework of Born-Oppenheimer theory, potential energy surfaces are calculated in both first-order perturbation theory and exact diagonalization. Besides the known pure triplet states, mixed-spin character states are obtained, opening up a whole new landscape of molecular potentials. We determine exact binding energies and wave functions of the nuclear rotational and vibrational motion numerically from the various potential energy surfaces.