Resonance phenomena constitute some of the most interesting and striking features of scattering experiments. This chapter discusses in detail the connection between quasistationary states and resonance phenomena, and culminates in the derivation of the Breit-Wigner formula. In Section XVIII.2 the concept of “time delay” is introduced and its relation to the phase shift derived. Various formulations of causality are given in Section XVIII.3. In Section XVIII.4 the causality condition is used to derive certain analyticity properties of the S-matrix. These properties are discussed further in Section XVIII.5. In Section XVIII.6, the central section of this chapter, the connection between quasistationary states, defined by a large time delay, and resonances, defined by characteristic structures in the cross section, is derived. Section XVIII.7 describes the observable effects of virtual states. Section XVIII.8 discusses the effect resonances have on the Argand diagram. The actual appearance of resonances in experimental data when the effects of the resonant phase shift, the nonresonant background, and the limited resolution of the apparatus are taken into account is discussed in Section XVIII.9.
KeywordsPartial Wave Causality Condition Resonance Phenomenon Virtual State Partial Cross Section
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- 2a.Time delay has been introducted previously in a similar way by F.T. Smith: Phys. Rev. fff, 349(1960). Time delay funvtions computed for particular potentials are given in R. J. LeRoy, R. B. Bernstein: J. Chem. Phys. 54, 5114 (1971).Google Scholar
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