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 Virtual State Partial Cross Section Resonance Pole
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- 6.Gel’fand and Shilov (1964), Vol. 1.Google Scholar
- 8.Cf. the discussion in Section II.9.Google Scholar
- 9.One obtains dispersion relations when these analytic properties are expressed in terms of integral relations between different matrix elements for real values of the variables.Google Scholar
- 10.Taylor (1972), Chapter 12.Google Scholar
- 13.For more on this subject, see Nussenzveig (1972).Google Scholar
- 17.This derivation is based on Goldberger and Watson (1964), Section 8.5.Google Scholar
- 20.Cf. Appendix XVII.A.Google Scholar
- 21.In addition to their other quantum numbers like l,Google Scholar
- 22.We did not give a complete proof of the statements in Section XVIII.5, but argued that causality, the finiteness of the binding energies for possible bound states, and the finite range of the interaction are sufficient, though certainly much less is necessary.Google Scholar
- 26.G. Bialkowski has helped me with the writing of this section.Google Scholar