Relationships among the coupled-states, P-helicity decoupling and effective potential methods

Abstract

Block diagonalization of the space-fixed close-coupled (SF CC) equations, without reference to any internal coordinate system, yields both the body-fixed ( R-helicity) and P-helicity scattering equations; thereby re-establishing the equivalence of the two representations. If the centrifugal barrier plays an unimportant role in the collision dynamics, then the off-diagonal centrifugal coupling terms may be neglected, leading to the coupled-states (CS) and P-helicity decoupling equations. Alternatively, the CS method is equivalent to an “average- I” approximation within a SF frame. The relation between the transformed and untransformed CS S-matrices is discussed. For the first time, the effective potential equations are derived by a weighted averaging of the CS equations; other effective potentials arise from different averaging procedures.