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Dalitz, R. H.; Thacker, T.W.

doi:10.1103/physrevlett.15.334.3

Cited by 1 publication

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“…is r e s? I t is also well known (Amati 1963;Dalitz & Rajasekaran 1963;Eden & Taylor 1963;Nauenberg & Nearing 1964;Ross 1963) th a t a resonance in the neighbour hood of an isolated threshold E t is characterized by two pole two unphysical sheets which are reached from the physical sheets by passing across the physical E axis either above or below E t, as shown on figure 4 . Both of these resonance eigenstates are characterized by the boundary condition (2.2), but the two eigenstates correspond to the two choices of branch possible for the momenta & ,• appropriate to the channel with threshold E t, the value of being + \kj\ (on the real E axis) for the path crossing above E t, and + i|&J (on the real E axis) for the path crossing below E t. Both of these poles may contribute significantly to the properties of the resonance scattering when the resonance energy is close to E t ; otherwise, the only pole of importance is th a t lying closest to the physical sheet.…”

Section: Whatmentioning

confidence: 90%

“…W ith this assumption, it is also the case th a t the phases of the (7,are associated with the non-resonant background scattering in these channels, as we shall now discuss. We should remark first th a t the relation given by Dalitz (1963) and by Dalitz & Moorhouse (1965) between the phase of ((7,(7,) and the background scattering phase (namely th a t all Cj have the same phase where denotes the background scattering phase for the resonant eigenstate (Q)) is valid only in exceedingly…”

Section: Solated Resonance Statementioning

confidence: 99%

“…Now, Dalitz (1963) and Dalitz & Moorhouse (1965) considered the eigenphases 8a and eigenstates < f)a of the unitary m atrix 8 , as is certainly always permissible. I t then appeared plausible th a t the (real) resonance energy corresponded to one of these eigenphases increasing rapidly through | tt (the corresponding eigenvalue of the reaction m atrix K = i(S -l) 1(8 + 1) then has a pole a t thi 1961)).…”

Section: What Is Res? 281mentioning

confidence: 99%

“…For the situation where the background phases are energy-independent, the only exception to this last remark is the case where all the background eigenphases are equal. In this case one eigenphase can resonate and increase by tt without crossing any of the other eigenphases (modTr).f The formulae of Dalitz (1961Dalitz ( , 1963 are then correct if all the background phases 8a are mad 8a, in the eigenphase which resonates. However, we should emphasize also th a t the eigenphase representation is a perfectly acceptable and economical representa tion of the 8 matrix in situations where the eigenphases vary slowly and do not cross.…”

Section: What Is Res? 281mentioning

confidence: 99%

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What is resonance?

Dalitz

Moorhouse

1970

Proc. R. Soc. Lond. A

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The concept of duality, discussed in the previous paper by Dr C. Schmid, refers to the notion that the analysis of an S matrix amplitude in terms of s channel resonances and its analysis in terms of t channel (and u channel) reggeon exchanges are not independent, but represent alternative descriptions, the former being the more appropriate in the low energy domain and the latter being the more appropriate in the low t (or low u ) domain for high energy interactions. Hence, at the time when this Discussion meeting was planned, it appeared necessary to attempt to clarify the notion of resonance , since there was then a good deal of discussion about how partial wave analyses of scattering data should be interpreted in terms of resonance states (Bransden, O’Donnell & Moorhouse 1965; Lovelace 1968; Donnachie 1968), and even whether such an interpretation was necessarily the case at all (Schmid 1968 a,b ; Collins, Johnson & Squires 1968; Alessandrini & Squires 1968; Alessandrini, Freund, Oehme & Squires 1968; Collins, Johnson & Ross 1968; Kreps & Logan 1969). However, in the actual use of duality in this meeting and in the model amplitudes which have been discussed thus far for the illustration of duality, there is really no controversy about the nature of resonance, since these models are still confined to the cases of resonances with zero width, characterized by poles on the real s axis, and there is essentially no ambiguity about the relation between resonances and poles in this limiting case. All the same, it still seems worthwhile to take a few moments to draw attention to a number of points about the description of resonance, which deserve to be more widely known.

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Section: Whatmentioning

confidence: 90%

Section: Solated Resonance Statementioning

confidence: 99%