Could somebody provide the proof (or reference to some accessible literature) of relation $$S(E) = 1 + 2πiW^{†} (H_M − E − iπW W^{†} )−1 W \tag{2}$$$$S(E) = 1 + 2πiW^{†} (H_M − E − iπW W^{†} )^{−1} W \tag{2}$$
of arXiv:0806.4889, which relates $S$-matrix to an effective Hamiltonian?
People usually refer to the book
"Shell-model approach to nuclear reactions" by Mahaux, Claude; Weidenmüller, Hans A
which I do not have access to.