Calculation of the elastic scattering parameters in an ultra-cold Fermi-Bose and Bose-Bose Fr vapor

Abstract

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 Fr${}_2$ is represented, and the scattering lengths at and the effective range $r_e$ 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 $K_0$ parameter and core radius is also investigated using two method as Quantum Defect Theory and analytical formula of symskovisky.

arXiv comment6 pages, 6 tables and 2 figures