Remarks on the connection between conventional reaction theories and the integral-equation approach to few-particle scattering

On the relation between the method of coupled channels and the truncated channel coupling array formalism for rearrangement reactions

“…We conclude that a CRC calculation of the wavefunction in a definite model space is likely to be more accurate than a corresponding BSCCA calculation, in which the same basis functions are used but the Green's functions are only projected on to individual arrangements. This conclusion agrees with previous statements by J. Schwager [9]. Our conclusion favors CRC over the corresponding truncated BSCCA on grounds of accuracy% It is also '~ Related criticisms of BSCCA are given by Adhikari, S.K.…”

“…We explore the correspondence of CRC to BSCCA through a common model space. A previous wavefunction discussion by Schwager [9] does not stress the importance of model space to the extent that we do, it also does not relate CRC to the use of components ~, ~. In the approximations discussed here the model wavefunctions consist of intrinsic wavefunctions of the clusters, combined with wavefunctions of relative motion.…”

“…Let us first consider how such representations would be used in complete analyses of (9). We employ two alternative complete sets, constructed in terms of the eigenfunctions of (6), and consisting of all basis functions of the form…”

“…(Cotanch and Vincent [7] considered CRC as the definition of "model space" approximation, but we use the same term in a broader sense as described above.) The CCA formalism we discuss here is expressed in terms of component wavefunctions [8,9], each of which corresponds to a definite partition of the system into clusters. In the particular system we consider there are only two two-body partitions, ~ and fi, to which component wavefunctions ~ and correspond, so that the wavefunction of the total system is given by From CCA, coupled equations for ~ and ~ can be derived [2,3].…”