Optical potential for elastic scattering when rearrangements are present

The problem of constructing an optical potential for the elastic scattering when rearrangement processes can occur is considered in two stages. First an ``arrangement channel optical potential'' is constructed using a coupled channel T operator formalism describing a general scattering process. This complex potential is shown to have the properties necessary to describe nonreactive scattering in the presence of rearrangements. Second the usual elastic and inelastic nonreactive projectors P and Q are employed in obtaining an optical potential for just elastic scattering. An explicit expression for the channel optical potential is obtained which permits easy interpretation. The two-stage approach thus has the advantage of completely avoiding nonorthogonality difficulties.