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Communications in Theoretical Physics

Elastic Scattering of Ultracold 133 Cs and 85 Rb Atoms in Triplet State

Sun Jin-Feng, Hu Qiu-Bo, Zunlue Zhu, Wang Xiao-Fei, Zhang Ji-Cai

Published Jun 1, 2007• 3 citations
Publisher

Abstract

Elastic scattering properties of the ultracold interaction for the triplet state of 133 Cs and 85 Rb atoms are studied using two kinds of potentials by the same phase . One is the interpolation potential, and another is Lennard-Jones potential (LJ12,6). The radial Schrodinger equation is also solved using two computational methods, the semiclassical method (WKB), and the Numerov method. Our results are found to be in an excellent agreement with the more recent theoretical values. It shows that the two potentials and methods are applicable for studying ultracold collisions between the mixing alkali atoms.

DOI
10.1088/0253-6102/47/6/030

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Elastic scattering properties of the ultracold interaction for the triplet state of 133 Cs and 85 Rb atoms are studied using two kinds of potentials by the same phase . One is the interpolation potential, and another is Lennard-Jones potential (LJ12,6). The radial Schrodinger equation is also solved using two computational methods, the semiclassical method (WKB), and the Numerov method. Our results are found to be in an excellent agreement with the more recent theoretical values. It shows that the two potentials and methods are applicable for studying ultracold collisions between the mixing alkali atoms.
The elastic scattering properties between ultracold 23 Na and 85 Rb atoms for the triplet state (a 3 Σ + u ) are researched. The s-wave scattering lengths of 23 Na and 85 Rb are calculated by the Numerov and semiclassical method with two kinds of interatomic potentials, which are the interpolation potential and Lennard—Jones potential (LJ 12,6 ) by the same phase Φ. Shape resonances appear clearly in the l = 5 partial waves for the a 3 Σ + u state. Moreover, the s-wave scattering cross section, total cross section and energy positions of shape resonances are also discussed.
The elastic scattering properties of ultracold 133Cs2 triplet state are investigated in detail. We construct a potential curve of the 133Cs2 triplet state, based on the latest ab initio molecular potential data and show how the scattering parameters are obtained by using three methods: the Numerov method, the semiclassical method and the variable phase method, where the scattering lengths of the 133Cs2 triplet state, i.e. 301.79a0, 300.67a0 and 310.81a0 are obtained respectively, with a0 being the Bohr radius. We also calculate the effective range and the number of bound states for the 133Cs2 triplet state. Our results are in agreement with the recent experimental data and the theoretical calculations. This confirms that the results of the scattering properties of the ultracold 133Cs2 triplet state, calculated by using these three methods, are reliable.
Elastic scattering properties of the ultracold interaction for the triplet state of 39 K have been studied using a potential composed of short-range and long-range terms, where the long-range term has a multiplier: “cutoff function”. For governing the decrease of the cutoff function, the “cutoff radius ” has been adjusted by comparing it to experimental energy values. The scattering properties have then been found using the solutions of the radial equation for two methods, the WKB and the Numerov method. The obtained results have been compared in detail with the experimental and other theoretical results. PACS numbers: 32.80.Cy, 34.20.Cf, 34.50.Pi I.
The elastic scattering properties for collisions between cold and ultracold 39 K atoms in a triplet state are investigated. Based on the recent theoretical and experimental results, the improved hybrid potential is presented for a triplet a 3 ∑ u + ground state of K 2 . Our calculated value of the s-wave scattering length a by using the Numerov method for the triplet state is 79.578 a 0 and found to be in good agreement with the previous ones. The numbers of bound states are supported by the molecular potential. Pronounced shape resonances appear for the l = 3 partial waves for the a 3 ∑ u + state. Furthermore, the s-wave scattering cross section, the total cross section and energy positions of shape resonances for the a 3 ∑ u + state are calculated.
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 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.