  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.

Atomic Physics