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E. Clementel, G. Poiani andC. Villi:Nuovo Cimento,2, 389 (1955). This paper will be quoted here as I and the same notation will be used.
In terms of the quantitiesA, B andC, i.e. ofall the nine experimental coefficients, the determination of phaseshifts forT=1/2 state could therefore be carried out using the Ashkin and Vosko graphical method for positive scattering [Phys. Rev.,91, 1248 (1953)].
The mathematical condition is given by cos 2α i ≥1−2A i . For the upper and lower values of αi, the pointsQ 2 andQ 3 coincide, making Fermi and Yang solutions identical, as it has been found analyrically in ref. (1).
R. Karrlus andM. A. Ruderman:Phys. Rev.,93, 771 (1955);M. Goldberger, H. Miyazawa andR. Oehme: in press. We thankDr. R. Oehme for making available to us this paper prior to publication.
H. L. Anderson, W. C. Davidon andU. E. Cruse: in press. We thank Prof.Anderson for the opportunity to read this paper prior to publication.
See in this connection section 8 of the paper:F. de Hoffmann et al.:Phys. Rev.,95, 1586 (1954).
SeeG. F. Chew andF. E. Low’s communications presented at theRochester Conference, 1955, and related papers on this subject. The equalityα 31=α 11, following from the still provisional form of the cut-off theory, is not necessarily required by the scattering relations.
If one assumesα 11=α 13=0, from the third of Eqs. (7) one gets cos 2α 1=1 — 2A, which corresponds to Eq. (6) used in a previous note [E. Clementel, G. Poiani andC. Villi:Nuovo Cimento,2, 352 (1955)].
H. A. Bethe andF. de Hoffmann:Mesons and Felds (New-York, 1955), p. 79.
The illustrative curves (1) and (2) have been calcuated using the coefficients given in Table XVI of ref. (7). With these coefficients it is found that the analyzer excludes positive values ofα 3 for energies higher than ∼ 170 MeV. Assuming the following linear dependenceα 3=9.5° − 17.1°η ofα 3 on the relative momentum η valid in the energy region where the equation λ 2+ (k)− μ+(k) is expected to hold, the crossing point ofα (+)33 andα (−)33 is found to be somewhere between 170 and 180 MeV.
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Clementel, E., Villi, C. On pion-nucleon scattering. Nuovo Cim 2, 845–849 (1955). https://doi.org/10.1007/BF02725046
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DOI: https://doi.org/10.1007/BF02725046