Concepts of multiparticle time delay

D. Bollé; T. A. Osborn

doi:10.1103/PhysRevD.13.299

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Concepts of multiparticle time delay

D. Bollé^*,†

T. A. Osborn

Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742
Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305

Department of Physics, Brooklyn College, Brooklyn, New York 11210
Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305

^*Onderzoeker IIKW Belgium.
^†On leave from Institute for Theoretical Physics, University of Leuven, B-3030 Heverlee, Belgium.

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Phys. Rev. D 13, 299 – Published 15 January, 1976

DOI: https://doi.org/10.1103/PhysRevD.13.299

Abstract

This paper studies two concepts of time delay in few-particle scattering. The first is a global time delay that refers to the total advancement or retardation of the entire wave-packet motion owing to the presence of interactions not contained in the asymptotic Hamiltonian. The second type, the angular time delay, is the early or late arrival of a particle in a counter subtending an angle $θ$ with respect to the incident beam direction. In the two-body problem the magnitude of this time delay is known to be $(\frac{d}{d E}) f (E, θ)$ , where $f (E, θ)$ is the scattering amplitude at energy $E$ . We discuss the definition of these two kinds of time delay in the three-body problem. We provide a generalization of the relation between angular time delay and the scattering amplitude that is valid for elastic, rearrangement, and breakup scattering. The interdependence of these two kinds of multichannel time delay is established. Possible physical applications of the resulting theory are discussed.

References (35)

L. D. Faddeev, Mathematical Aspects of the Three-Body Problem (Davey, New York, 1965)
F. T. Smith, Phys. Rev. 118, 349 (1960)
M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, New York, 1964), p. 485
J. M. Jauch and J. P. Marchand, Helv. Phys. Acta 40, 217 (1967)
D. Bollé and T. A. Osborn, Phys. Rev. D 11, 3417 (1975)
L. E. Eisenbud, Ph.D. thesis, Princeton Univ., 1948 (unpublished) E. P. Wigner, Phys. Rev. 98, 145 (1955)
W. Brenig and R. Haag, Fortschr. Phys. 7, 183 (1959)
M. Froissart, M. L. Goldberger, and K. M. Watson, Phys. Rev. 131, 2820 (1963)
F. Goldrich and E. P. Wigner, in Magic without Magic: John Archibald Wheeler, a Collection of Essays in Honor of His 60th Birthday, edited by John R. Klauder (Freeman, San Francisco, 1972), p. 147
H. M. Nussenzveig, Phys. Rev. D 6, 1534 (1972)
M. G. Krein, Mat. Sb. 33, 597 (1953) M. S. Birman and M. G. Krein, Dokl. Acad. Nauk SSSR 144, 268 (1962) [Sov. Math. Dokl. 3, 707 (1962)]
V. S. Buslaev, in Spectral Theory and Wave Process, edited by M. S. Birman (Consultants Bureau, London, 1972)
J. M. Jauch, K. B. Sinha, and B. N. Misra, Helv. Phys. Acta 45, 398 (1972)
T. Y. Tsang and T. A. Osborn, Nucl. Phys. A247, 43 (1975)
F. T. Smith, J. Chem. Phys. 38, 1304 (1963) Phys. Rev. 131, 2803 (1963) J. Chem. Phys. 57, 5562 (1972)
R. Dashen, S. Ma, and H. Bernstein, Phys. Rev. 187, 345 (1969)
F. T. Smith, Phys. Rev. 130, 394 (1963)
U. Bar-Gadda, Physica 62, 321 (1972)
Ph. A. Martin, Ecole Polytechnique Federale report, Lausanne, Switzerland, 1975 (unpublished)
R. Jackiw and G. Woo, Phys. Rev. D 12, 1643 (1975)
R. A. Van Santen, J. Chem. Phys. 57, 5571 (1972)
J. Nowakowski and T. A. Osborn, Nucl. Phys. A249, 301 (1975)
R. Fong, Phys. Rev. 140, B762 (1965)
R. H. Dalitz and R. G. Moorehouse, Proc. R. Soc. London A318, 279 (1970)
T. A. Osborn and D. Bollé, Phys. Lett. 52B, 13 (1974) J. Math. Phys. 16, 1533 (1975)
[1], Chap. 10
J. D. Dollard, Commun. Math. Phys. 12, 193 (1969)
T. A. Osborn and D. Bollé, Phys. Rev. C 8, 1198 (1973)
[25]
[28]
S. Yoshida, Phys. Lett. 45B, 324 (1973)
K. Yazaki and S. Yoshida, Nucl. Phys. A232, 249 (1974)
L. Schwartz, Theorie des Distributions (Hermann, Paris, 1951), Vol. II
J. A. Donaldson, A. G. Gibson, and R. Hersh, J. Funct. Anal. 14, 131 (1973)
T. Kato, Perturbation Theory for Linear Operators (Springer, New York, 1966), p. 533

[c1] L. D. Faddeev, Mathematical Aspects of the Three-Body Problem (Davey, New York, 1965)

[c2] F. T. Smith, Phys. Rev. 118, 349 (1960)

[c3] M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, New York, 1964), p. 485

[c4] J. M. Jauch and J. P. Marchand, Helv. Phys. Acta 40, 217 (1967)

[c5] D. Bollé and T. A. Osborn, Phys. Rev. D 11, 3417 (1975)

[c6] L. E. Eisenbud, Ph.D. thesis, Princeton Univ., 1948 (unpublished) E. P. Wigner, Phys. Rev. 98, 145 (1955)

[c7] W. Brenig and R. Haag, Fortschr. Phys. 7, 183 (1959)

[c8] M. Froissart, M. L. Goldberger, and K. M. Watson, Phys. Rev. 131, 2820 (1963)

[c9] F. Goldrich and E. P. Wigner, in Magic without Magic: John Archibald Wheeler, a Collection of Essays in Honor of His 60th Birthday, edited by John R. Klauder (Freeman, San Francisco, 1972), p. 147

[c10] H. M. Nussenzveig, Phys. Rev. D 6, 1534 (1972)

[c11] M. G. Krein, Mat. Sb. 33, 597 (1953) M. S. Birman and M. G. Krein, Dokl. Acad. Nauk SSSR 144, 268 (1962) [Sov. Math. Dokl. 3, 707 (1962)]

[c12] V. S. Buslaev, in Spectral Theory and Wave Process, edited by M. S. Birman (Consultants Bureau, London, 1972)

[c13] J. M. Jauch, K. B. Sinha, and B. N. Misra, Helv. Phys. Acta 45, 398 (1972)

[c14] T. Y. Tsang and T. A. Osborn, Nucl. Phys. A247, 43 (1975)

[c15] F. T. Smith, J. Chem. Phys. 38, 1304 (1963) Phys. Rev. 131, 2803 (1963) J. Chem. Phys. 57, 5562 (1972)

[c16] R. Dashen, S. Ma, and H. Bernstein, Phys. Rev. 187, 345 (1969)

[c17] F. T. Smith, Phys. Rev. 130, 394 (1963)

[c18] U. Bar-Gadda, Physica 62, 321 (1972)

[c19] Ph. A. Martin, Ecole Polytechnique Federale report, Lausanne, Switzerland, 1975 (unpublished)

[c20] R. Jackiw and G. Woo, Phys. Rev. D 12, 1643 (1975)

[c21] R. A. Van Santen, J. Chem. Phys. 57, 5571 (1972)

[c22] J. Nowakowski and T. A. Osborn, Nucl. Phys. A249, 301 (1975)

[c23] R. Fong, Phys. Rev. 140, B762 (1965)

[c24] R. H. Dalitz and R. G. Moorehouse, Proc. R. Soc. London A318, 279 (1970)

[c25] T. A. Osborn and D. Bollé, Phys. Lett. 52B, 13 (1974) J. Math. Phys. 16, 1533 (1975)

[c26] [1], Chap. 10

[c27] J. D. Dollard, Commun. Math. Phys. 12, 193 (1969)

[c28] T. A. Osborn and D. Bollé, Phys. Rev. C 8, 1198 (1973)

[c29] [25]

[c30] [28]

[c31] S. Yoshida, Phys. Lett. 45B, 324 (1973)

[c32] K. Yazaki and S. Yoshida, Nucl. Phys. A232, 249 (1974)

[c33] L. Schwartz, Theorie des Distributions (Hermann, Paris, 1951), Vol. II

[c34] J. A. Donaldson, A. G. Gibson, and R. Hersh, J. Funct. Anal. 14, 131 (1973)

[c35] T. Kato, Perturbation Theory for Linear Operators (Springer, New York, 1966), p. 533

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