Optical potentials Green’s function

Like we have done for the Green s function optical potential we can also evaluate the static part of Feshbach s optical Hamiltonian ... 

First we note that the matrices cancel with their inverse in Eq. (109), leaving the same single-particle part as for the Green s function optical potential. The interaction part however, differs from its Green s function analogue of Eq. (107) by involving the two-particle density... 

In order to implement the approximation to the optical potential we must choose a form for the potential Vopul (7.132) in which the Green s function is calculated (7.135). We choose different types of potential for the discrete and continuum channels of Q space, projected respectively by Q and Q+. For Q space we choose the average potential for the target state i). Its coordinate representation is obtained from (7.48,7.63,7.66)... 

In applying the distorted-wave second Born approximation we have the same difficulty as in calculating the optical potential. We must calculate the spectrum of the Green s function of (6.87). The first iteration of (6.87) is written as... 

The complex energy, 2 of Eq. (5) is normally understood in fhe context of resonance scattering theory as the complex pole in the Breit-Wigner amplitude, or in the S-matrix, or in the optical potential of Feshbach s fheory," or in the Green s function, e.g.. Refs. [2,6-8]. 

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