The dependence of scattering length on van der Waals interaction and reduced mass of the system in two-atomic collision at cold energies

The static exchange model (SEM) and the modified static exchange model (MSEM) recently introduced by Ray in Pramana – J. Phys.83, 907 (2014) are used to study the elastic collision between two hydrogen-like atoms when both are in ground states by considering the system as a four-body Coulomb system in the centre of mass frame, in which all the Coulomb interaction terms in direct and exchange channels are treated exactly. The SEM includes the non-adiabatic short-range effect due to electron exchange. The MSEM added in it, the long-range effect due to induced dynamic dipole polarizabilities between the atoms e.g., the van der Waals interaction. Applying the SEM code in different H-like two-atomic systems, a reduced mass (μ) dependence on the scattering length is observed. Again, applying the MSEM code on H(1s)–H(1s) elastic scattering and varying the minimum values of interatomic distance R₀, the dependence of scattering length on the effective interatomic potential consistent with the existing physics is observed. Both these basic findings in low and cold energy atomic collision physics are quite useful and are being reported for the first time.