On the equivalence between the space fixed and the body fixed formulations of the j z-conserving approximation

It is shown that space fixed and the body fixed formulations of the jz-conserving approximation are equivalent if the partial wave parameter ? is chosen equal to the final orbitral angular momentum l′. We also examine the replacement of ? by l, the initial orbital angular momentum in the space fixed formulation. Only these two choices of ? give simple expressions for the scattering amplitude.