Resonances in Multichannel Systems
In the present chapter we discuss resonances in scattering processes from an initial state into several possible final states, where the internal quantum numbers of the resonances are, in general, different from the quantum numbers of the initial state and the final states. In Section XX.2 we first discuss, in detail, the case of a single multichannel resonance and then the case of a double multichannel resonance (which occurs if there are two resonances with different internal quantum numbers in the same partial wave, with both the resonances coupling to initial and final states). In Section XX.3 the Argand diagrams for inelastic resonances are described.
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- 1.See, e.g., A. Lichnerowicz (1967) or V. I. Smirnov (1964), Vol. III, Part 1, Section 42.Google Scholar
- 2.These rapid energy variations follow from Wigner’s eigenphase repulsion theorem : The eigenphases δl(K) do not cross (modulo π). As a consequence, near the resonance energy in the channel kR the eigenphases in all other channels k must also vary. This is assured by the existence of branch cuts in the individual eigenphases (and the corresponding transition matrix elements <k M > which are also functions of E) which are in the complex energy plane much closer to the real axis than the resonance pole. These branch cuts do not occur in the complete S matrix and therefore do not have physical significance. The occurrence of these branch cuts in the <K (Ir > and y1(K) must be just such that all these branch cuts cancel out in the background term (2.16), which can be a slowly varying function of energy. A discussion of these singularities of the individual eigenphases is given in C. J. Goebel, K. W. McVoy Phys. Rev. 164,1932 (1967);ADSCrossRefGoogle Scholar
- 11.Figures 3.1, 3.2, and 3.3 are from Barbaro-Galtieri (1968).Google Scholar