Scattering lengths and effective ranges for He-He and spin-polarized H-H and D-D scattering

The modifications of effective-range theory, necessitated by the long-range nature of interatomic dispersion and relativistic retardation forces, are discussed. A numerical comparison is given of parameters describing ${}_{}{}^3{}_{}{}^{}\mathrm{-}_{}^3{}_{}{}^{}$He, ${}_{}{}^3{}_{}{}^{}\mathrm{-}_{}^4{}_{}{}^{}$He, and ${}_{}{}^4{}_{}{}^{}\mathrm{-}_{}^4{}_{}{}^{}$He scattering at very low energies calculated with several recently published interaction potentials. The effect of relativistic retardation on these parameters and on the calculated binding energies of the ${}_{}{}^4{}_{}{}^{}\mathrm{-}_{}^4{}_{}{}^{}$He dimer is shown. It is demonstrated that all of these quantities are extremely sensitive to the potential. Scattering lengths and effective ranges for the lowest triplet interactions of H-H and D-D are also reported.