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A singular integral equation in the theory of meson-nucleon scattering

Published online by Cambridge University Press:  24 October 2008

R. H. Dalitz ,
M. K. Sundaresen ,
H. A. Bethe  and
N. F. Mott
R. H. Dalitz
Affiliation:
Laboratory of Nuclear StudiesCornell UniversityIthaca, N.Y.
M. K. Sundaresen
Affiliation:
Laboratory of Nuclear StudiesCornell UniversityIthaca, N.Y.
H. A. Bethe
Affiliation:
Laboratory of Nuclear StudiesCornell UniversityIthaca, N.Y.
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Abstract

The Tamm-Dancoff theory of meson-nucleon scattering (pseudoscalar coupling) leads to a series of singular integral equations. The asymptotic behaviour of the solutions of these equations is obtained here for all scattering states. For attractive states there is a critical coupling constant beyond which no normalizable solutions exist for these equations; for repulsive states another critical coupling constant appears, beyond which the solutions oscillate infinitely often but are still normalizable. It is concluded that the renormalization procedures proposed previously (3) are consistent and successfully define finite vertex-functions, and that the equations obtained for these vertex-functions have satisfactory properties for numerical work.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 2 , April 1956 , pp. 251 - 272
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

REFERENCES

(1)Chew, G. F.Phys. Rev. (2), 89 (1953), 591 and 95 (1954), 1669.CrossRefGoogle Scholar
(2)Cutkosky, R. E.Phys. Rev. (2), 96 (1954), 1135.CrossRefGoogle Scholar
(3)Dalitz, R. H. and Dyson, F. J.Phys. Rev. (2), 99 (1955), 301.CrossRefGoogle Scholar
(4)Dyson, F. J.Proceedings of the third Rochester conference (1953), p. 80.Google Scholar
(5)Dyson, F. J., Ross, M., Salpeter, E. E., Schweber, S. S., Sundaresen, M. K., Visscher, W. M. and Bethe, H. A.Phys. Rev. (2), 95 (1954), 1644.CrossRefGoogle Scholar
(6)Edwards, S. F.Phys. Rev. (2), 90 (1953), 284.CrossRefGoogle Scholar
(7)Feldman, G.Proc. roy. Soc. A, 223 (1954), 112.Google Scholar
(8)Gammel, J. L.Phys. Rev. (2), 95 (1954), 209.CrossRefGoogle Scholar
(9)Goldstein, J. S.Phys. Rev. (2), 91 (1953), 1516.CrossRefGoogle Scholar
(10)Levy, M.Phys. Rev. (2), 84 (1951), 441 and 88 (1952), 72.CrossRefGoogle Scholar
(11)Salpeter, E. E. and Bethe, H. S.Phys. Rev. (2), 84 (1951), 1232.CrossRefGoogle Scholar
(12)Smithies, F.Duke math. J. 8 (1941), 107.CrossRefGoogle Scholar
(13)Visscher, W. M.Phys. Rev. (2), 96 (1954), 788.CrossRefGoogle Scholar
(14)Wick, G. C.Phys. Rev. (2), 96 (1954), 1124.CrossRefGoogle Scholar