  The static-exchange model (SEM) and the modified static-exchange model (MSEM)
recently introduced by Ray [1] is applied to study the elastic collision
between two hydrogen-like atoms when both are in ground states considering the
system as a four-body Coulomb problem in the center 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 dependence on scattering length is observed. Again applying the
MSEM code on H(1s)-H(1s) elastic scattering and varying the minimum values of
interatomic distance, the dependence of scattering length on the effective
interatomic potential consistent with the existing physics are observed. Both
these basic findings in low and cold energy atomic collision physics are quite
useful and are being reported for the first time.
