Complex Angular Momentum in Three-Particle Potential Scattering

James B. Hartle

doi:10.1103/PhysRev.134.B620

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Complex Angular Momentum in Three-Particle Potential Scattering

James B. Hartle^*

California Institute of Technology, Pasadena, California

^*National Science Foundation Predoctoral Fellow.

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Phys. Rev. 134, B620 – Published 11 May, 1964

DOI: https://doi.org/10.1103/PhysRev.134.B620

Abstract

In this paper we discuss the continuation of a class of three-particle potential scattering amplitudes to complex values of the total angular momentum. The class of amplitudes considered are those which describe a scattering in which a given pair of the particles is bound in the initial and final states. A nonrigorous discussion indicates that, except for simple kinematic factors, the only singularities present in the complex angular momentum plane are dynamical poles and possible isolated essential singularities. The Watson-Sommerfeld transformation of the full amplitude can be performed to display its large momentum-transfer behavior.

References (19)

C. Lovelace, Three-Particle Systems and Unstable Particles, Lectures at Edinburgh Summer School, 1963 (to be published)
A. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, New Jersey, 1957)
E. Hylleraas, Z. Physik 48, 469 (1928)
Omitted endnote
S. Mandelstam, Ann. Phys. (N. Y.) 19, 254 (1962)
J. Charap and E. Squires, Ann. Phys. (N. Y.) 20, 145 (1962) R. Newton, Phys. Rev. 129, 1437 (1963)
E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill Book Company, Inc., New York, 1955), Chap. 4
A. C. Zaanen, Linear Analysis (P. Noordhoff, Gronigen, 1953)
M. Jacob and G. Wick, Ann. Phys. (N. Y.) 7, 404 (1959)
R. Newton, J. Math. Phys. 1, 319 (1960)
J. Charap and E. Squires, Ann. Phys. (N. Y.) 21, 8 (1963)
G. C. Wick, Ann. Phys. (N. Y.) 18, 65 (1962)
R. Newton, Nuovo Cimento 29, 400 (1963) Phys. Letters 4, 11 (1963)
I. Drummond (to be published)
Omitted endnote
S. Mandelstam, Nuovo Cimento 30, 1148 (1963)
R. Boas, Entire Functions (Academic Press Inc., New York, 1954), p. 153
A. Erdelyi et al., Higher Transcendental Functions (McGraw-Hill Book Company, Inc., New York, 1953), Chap. VII
L. Favella and M. Reineri, Nuovo Cimento 23, 616 (1962)

[c1] C. Lovelace, Three-Particle Systems and Unstable Particles, Lectures at Edinburgh Summer School, 1963 (to be published)

[c2] A. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, New Jersey, 1957)

[c3] E. Hylleraas, Z. Physik 48, 469 (1928)

[c4] Omitted endnote

[c5] S. Mandelstam, Ann. Phys. (N. Y.) 19, 254 (1962)

[c6] J. Charap and E. Squires, Ann. Phys. (N. Y.) 20, 145 (1962) R. Newton, Phys. Rev. 129, 1437 (1963)

[c7] E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill Book Company, Inc., New York, 1955), Chap. 4

[c8] A. C. Zaanen, Linear Analysis (P. Noordhoff, Gronigen, 1953)

[c9] M. Jacob and G. Wick, Ann. Phys. (N. Y.) 7, 404 (1959)

[c10] R. Newton, J. Math. Phys. 1, 319 (1960)

[c11] J. Charap and E. Squires, Ann. Phys. (N. Y.) 21, 8 (1963)

[c12] G. C. Wick, Ann. Phys. (N. Y.) 18, 65 (1962)

[c13] R. Newton, Nuovo Cimento 29, 400 (1963) Phys. Letters 4, 11 (1963)

[c14] I. Drummond (to be published)

[c15] Omitted endnote

[c16] S. Mandelstam, Nuovo Cimento 30, 1148 (1963)

[c17] R. Boas, Entire Functions (Academic Press Inc., New York, 1954), p. 153

[c18] A. Erdelyi et al., Higher Transcendental Functions (McGraw-Hill Book Company, Inc., New York, 1953), Chap. VII

[c19] L. Favella and M. Reineri, Nuovo Cimento 23, 616 (1962)

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Complex Angular Momentum in Three-Particle Potential Scattering

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