NUMERICAL SOLUTION OF LIPPMANN-SCHWINGER EQUATION FOR ELECTRON AND H$_2^+$ ISOTOPE COLLISIONS Hidekazu Takagi Physics Laboratory, School of medicine, Kitasato University The Lippmann-Schwinger equation for electron and H$_2^+$ isotope collisions is solved numerically adopting an expansion by Chebyshev polynomial. The characteristic feature in the scattering by the configuration interaction is discussed and utilized for the numerical calculation. Applying those results to the multichannel quantum defect formalism, we investigated the dissociative recombination and rotational and vibrational transition of H$_2^+$ and HD$^+$.\\