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Influence of the Exclusion Principle on the Scattering Theory of Nonlocal, Separable Interactions
Phys. Rev. 136, B49 – Published 12 October, 1964
DOI: https://doi.org/10.1103/PhysRev.136.B49
Abstract
For a nonlocal, separable interaction which describes low-energy nucleon-nucleon scattering, the scattering-theory solution to the Brueckner-Bethe-Goldstone (BBG) equation is obtained analytically. The associated scattering amplitudes are evaluated for all momenta of the interacting pair. The off-energy-shell amplitudes are defined by analytic continuation to complex values of the relative momentum of the pair. The positions of singularities in the amplitudes are investigated for various values of both the two-body kinematical parameters and the density of the passive BBG Fermi gas. A comparison of the amplitudes calculated with and without incorporating the effects of the exclusion principle indicates that even for repulsive interactions the latter may differ from the former by as much as 50% for Fermi-gas densities as low as of the observed nuclear density.
References (20)
- J. Goldstone, Proc. Roy. Soc. (London) A239, 267 (1957) N. M. Hugenholtz, Physica 23, 481 (1957) J. Hubbard, Proc. Roy. Soc. (London) A240, 539 (1957) V. Galitskii and A. B. Migdal, Zh. Eksperim. i Teor. Fiz. 34, 139 (1958) [English transl.: Soviet Phys.—JETP 7, 96 (1958)] L. D. Landau, Zh. Eksperim. i Teor. Fiz. 30, 1058 (1956) ibid.32, 58 (1957) ibid.30, 97 (1958) [English transl.: Soviet Phys.—JETP 3, 920 (1957) Soviet Phys.—JETP 5, 101 (1957) Soviet Phys.—JETP 8, 70 (1959)] D. F. Dubois, Ann. Phys. (N. Y.) 7, 174 (1959) C. B. Duke, Ph.D. thesis, Princeton University, 1963 (unpublished) A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, R. A. SilvermanMethods of Quantum Field Theory in Statistical Physics, translated by (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1963), Chap. 2
- N. M. Hugenholtz, Physica 23, 533 (1957)
- V. M. Galitskii, Zh. Eksperim. i Teor. Fiz. 34, 151 (1958) [English transl.: Soviet Phys.—JETP 7, 104 (1958)]
- L. Van Hove, Physica 25, 849 (1959) Lectures on the Many-Body Problem, edited by E. R. Caianiello (Academic Press Inc., New York, 1962), p. 5
- L. D. Gomez, J. D. Walecka, and V. F. Weisskopf, Ann. Phys. (N. Y.) 3, 241 (1958) A. Deshalit and V. F. Weisskopf, ibid. 5, 282 (1958)
- H. A. Bethe and J. Goldstone, Proc. Roy. Soc. (London) A238, 551 (1957)
- J. A. Wheeler, Phys. Rev. 50, 675 (1936)
- Y. Yamaguchi, Phys. Rev. 95, 1628 (1954)
- L. Verlet and J. Gavoret, Nuovo Cimento 10, 505 (1958)
- K. A. Brueckner and W. Wada, Phys. Rev. 103, 1008 (1956) C. T. DeDominicis, University of Birmingham, Ph.D. thesis, 1957 (unpublished) C. DeDominicis and P. C. Martin, Phys. Rev. 105, 1419 (1957) J. Goldstone, Cambridge University, Ph.D. thesis, 1958 (unpublished) M. L. Mehta, Nucl. Phys. 12, 333 (1959) J. S. R. Chisholm and E. J. Squires, ibid. 13, 165 (1959) P. C. Sood and S. A. Moszkowski, ibid. 21, 582 (1960) J. Dabrowski and J. Sawicki, ibid. 22, 318 (1961)
- R. D. Puff, Ann. Phys. (N. Y.) 13, 317 (1961)
- K. A. Brueckner and W. Wada, Phys. Rev. 103, 1008 (1956)
- J. M. Blatt and V. F. Weisskopf, Theoretical Nuclear Physics (John Wiley & Sons, Inc., New York, 1952), p. 153
- P. A. M. Dirac, The Principles of Quantum Mechanics (The Clarendon Press, Oxford, 1958), p. 58
- C. B. Duke, General Electric Research Laboratory Report 64-RL-(3604M) (unpublished)
- R. Courant and D. Hilberg, Methods of Mathematical Physics (Interscience Publishers, Inc., New York, 1955), Vol. I, Chap. 3
- L. H. Schick, Rev. Mod. Phys. 33, 608 (1961)
- D. G. Ravenhall, Rev. Mod. Phys. 30, 430 (1958)
- H. A. Bethe and P. Morrison, Elementary Nuclear Theory (John Wiley & Sons, Inc., New York, 1956), 2nd ed., Chap. 10
- R. L. Becker, Phys. Rev. 127, 1328 (1962)