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Journal of the Physical Society of Japan

Calculation of Elastic Scattering Properties in Ultracold Fermi–Bose and Bose–Bose Rb–K Vapor

Mustafa Kemal Öztürk, Süleyman Özçelik

Published Mar 14, 2006• 0 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.75.034301

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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.
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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 calculations of the elastic scattering properties of ultracold-francium isotopes are reported in the detail. A parametric model potential for the triplet molecular states of the Fr2_{2}2​ is represented, and the scattering lengths at and the effective range rer_{e}re​ are calculated using WKB and Numerov methods for Fr-Fr in the triplet state. The convergence of these scattering properties as the depending on a K0K_{0}K0​ parameter and core radius is also investigated using two method as Quantum Defect Theory and analytical formula of symskovisky.
The elastic scattering properties in a mixture of sodium and cesium atoms are investigated at cold and ultracold temperatures. Based on the accurate interatomic potential for the NaCs mixture, the interspecies s-wave scattering lengths, the effective ranges and the p-wave scattering lengths are calculated by the quantal method and the semiclassical method, respectively. The s-wave scattering lengths are 512.7 a 0 for the singlet state and 33.4 a 0 for the triplet state. In addition, the spin-change and elastic cross sections are also calculated, and the g-wave shape resonance is found in the total elastic cross sections.
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.
Based on the accurate singlet and triplet state interatomic potentials for Na2, a theoretical study of elastic scattering properties of sodium atoms at ultracold temperatures is reported in this paper. The s-wave scattering length, effective range, the p-wave scattering length and the number of bound states are calculated. The singlet and triplet elastic scattering cross section between sodium aotms at ultracold temperatures are dominated by s-wave scattering, and shape resonances occur with collision energy increasing. There exist pronounced f-wave and i-wave shape resonances for the singlet and triplet cross section. In addition, s-wave scattering length is calculated by using the degenerate internet state approximation for selected hyperfine states of sodium atoms. The results are in agreement with calculated values obtained by close-coupling method.