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CLASSIFICATION OF THE NATURAL MODES OF A COUPLED CHANNEL MODEL IN THE FRAMEWORK OF THE RIEMANN SURFACE APPROACH

By using the Riemann surface approach to the natural modes of a coupled channel model a S-matrix pole and the associated mode are classified by introducing new quantum numbers with topological meaning, namely the labels of the Riemann sheet and of its k-plane image to which the pole belongs. The Riemann surface approach allows not only studying each state separately, but also understanding the jump from a state to another state. As a result a new insight into the nature of the Feshbach and Fonda-Newton resonant states is obtained.