Unitary four-body model

A. C. Fonseca; P. E. Shanley

doi:10.1103/PhysRevD.13.2255

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Unitary four-body model

A. C. Fonseca^* and P. E. Shanley

Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556

^*Work supported by Instituto de Alta Cultura, Portugal.

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Phys. Rev. D 13, 2255 – Published 15 April, 1976

DOI: https://doi.org/10.1103/PhysRevD.13.2255

Abstract

A field-theoretic model describing nonrelativistic four-body scattering processes is developed. The model is related to Bronzan's extended Lee model but the allowed interactions are restricted so that the resulting dynamical equations are as simple as possible, yet still exact. Two elementary particles $n$ and $a$ are introduced with the couplings $n + n \leftrightarrow D$ and $a + a \leftrightarrow C$ . Three-particle processes are generated by the additional coupling $D + a \leftrightarrow α$ , leading to the possible three-body reactions $D + a \to D + a$ and $D + a \to n + n + a$ . The four-body sector then involves the 2→2 reactions $a α \to a α$ and $a α \to CD$ , the 2→3 reactions $a α \to Daa$ and $a α \to Cnn$ , and the 2→4 reaction $a α \to nnaa$ . Off-shell integral equations are obtained for the 2→2 amplitudes, and from these, expressions for the 2→3 and 2→4 amplitudes are constructed. Possible applications and generalizations of the model are discussed.

References (10)

Few Body Problems in Nuclear and Particle Physics, Proceedings of the International Conference, Laval University, Quebec City, Canada, 1974, edited by R. J. Slabodrian, B. Cujec, and K. Ramavataram (Les Presses de l'Université Laval, Quebec, 1975)
R. D. Amado, Phys. Rev. 132, 485 (1963)
R. D. Amado, Phys. Rev. 122, 696 (1961)
R. Aaron, R. D. Amado, and Y. Y. Yam, Phys. Rev. 140, B1291 (1965) P. E. Shanley, ibid. 187, 1328 (1969)
E. O. Alt, P. Grassberger, and W. Sandhas, Phys. Rev. C 1, 85 (1970) V. F. Kharchenko and V. E. Kuzmichev, Phys. Lett. 42B, 328 (1972)
J. B. Bronzan, Phys. Rev. 172, 1429 (1968)
J. B. Bronzan, Phys. Rev. 139, B75 (1965)
L. Bianchi and L. Favella, Nuovo Cimento 34, 1825 (1964)
R. Aaron and R. D. Amado, Phys. Rev. 150, 857 (1966)
R. D. Amado, Phys. Rev. C 11, 719 (1975)

[c1] Few Body Problems in Nuclear and Particle Physics, Proceedings of the International Conference, Laval University, Quebec City, Canada, 1974, edited by R. J. Slabodrian, B. Cujec, and K. Ramavataram (Les Presses de l'Université Laval, Quebec, 1975)

[c2] R. D. Amado, Phys. Rev. 132, 485 (1963)

[c3] R. D. Amado, Phys. Rev. 122, 696 (1961)

[c4] R. Aaron, R. D. Amado, and Y. Y. Yam, Phys. Rev. 140, B1291 (1965) P. E. Shanley, ibid. 187, 1328 (1969)

[c5] E. O. Alt, P. Grassberger, and W. Sandhas, Phys. Rev. C 1, 85 (1970) V. F. Kharchenko and V. E. Kuzmichev, Phys. Lett. 42B, 328 (1972)

[c6] J. B. Bronzan, Phys. Rev. 172, 1429 (1968)

[c7] J. B. Bronzan, Phys. Rev. 139, B75 (1965)

[c8] L. Bianchi and L. Favella, Nuovo Cimento 34, 1825 (1964)

[c9] R. Aaron and R. D. Amado, Phys. Rev. 150, 857 (1966)

[c10] R. D. Amado, Phys. Rev. C 11, 719 (1975)

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Unitary four-body model

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