Multichannel Effective-Range Theory from theFormalism
- 10 May 1965
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 138 (3B), B702-B706
- https://doi.org/10.1103/physrev.138.b702
Abstract
An effective-range theory for systems of many coupled two-body channels is given using the formalism. The effective-range expansion is carried out in the amplitudes (where is essentially the matrix with the right-hand cut removed). Quite in analogy with the single-channel effective-range theory, the diagonal elements are given by an expression quadratic in , the relative momentum in channel . The effective ranges are given by certain principal-value integrals which depend on the position of the left-hand singularities in the corresponding channels and can be taken to be energy-independent to the same extent as in the one-channel theory. The nondiagonal elements , in general, have a weak energy dependence and can approximately be treated as constants. A two-channel computer experiment is performed to test these proposals in detail. Three different situations for the left-hand cut are considered: (i) a set of monopoles, (ii) a set of dipoles, and (iii) the left-hand cut produced by the exchange of scalar particles in the "crossed" reactions. For a large number of situations considered, the simple features proposed for the multichannel effective range theory were found to exist. The above formalism is similar to the multichannel effective-range theory of Ross and Shaw in the potential model.
Keywords
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