Meson Dynamics and the Nuclear Many-Body Problem. I. The Free-Nucleon Problem

W. D. Brown; R. D. Puff; L. Wilets

doi:10.1103/PhysRevC.2.331

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Meson Dynamics and the Nuclear Many-Body Problem. I. The Free-Nucleon Problem

W. D. Brown^*, R. D. Puff, and L. Wilets

University of Washington, Seattle, Washington 98105

^*Present address: Department of Physics and Astronomy, and Center for Theoretical Physics, University of Maryland, College Park, Maryland.

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Phys. Rev. C 2, 331 – Published 1 August, 1970

DOI: https://doi.org/10.1103/PhysRevC.2.331

Abstract

Relativistic nucleon-meson field theory is cast in a form appropriate to the nuclear many-body problem. Martin-Schwinger thermodynamic Green's functions are employed. The $n$ -nucleon Green's functions satisfy a set of coupled equations which is formally identical to those of the usual potential many-body problem. Here, however, the two-body potential is replaced by a time-dependent interaction in which the mesons are formally eliminated in favor of higher-order nucleon correlations. A general program of increasing complexity for obtaining approximate solutions to the equations is discussed. It is necessary to solve the "vacuum" (one-, two-, etc., nucleon propagator) first. This has been done in the "Hartree-Fock" approximation which sums all diagrams containing a single continuous nucleon line with all possible uncrossed $π$ and $ω$ meson lines. Peaks in the spectral function are identified with masses of known $N^{*}$ resonances. The appearance of ghost states, which arise in the process of mass and wave-function renormalization, is discussed. The resultant Green's function is used to calculate the magnetic moment of the nucleon, yielding a significantly better isovector component of the magnetic moment than the usual perturbation theory, although the isoscalar component is poor in both cases.

References (24)

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H. A. Bethe, in Proceedings of the International Congress on Nuclear Physics, Paris, France, 1964, edited by P. Gugenbeiger (Centre National de la Recherche Scientifique, Paris, France, 1964), Vol. I, pp. 120-122 G. E. Brown, A. M. Green, and W. J. Gerace, Nucl. Phys. A115, 435 (1968)
International Conference on the Nucleon-Nucleon Interaction, Rev. Mod. Phys. 39, 495 (1967)
P. C. Martin and J. Schwinger, Phys. Rev. 115, 1342 (1959)
R. D. Puff, Ann. Phys. (N.Y.) 13, 317 (1961)
R. D. Puff, A. S. Reiner, and L. Wilets, Phys. Rev. 149, 778 (1966) T. C. Foster, 149, 784 (1966)
E. Fiset, Ph.D. thesis, University of Washington, 1967 (unpublished) Phys. Rev. C 2, 85 (1970)
C. B. Dover and R. H. Lemmer, Phys. Rev. 165, 1105 (1968) C. B. Dover, Ann. Phys. (N.Y.) 50, 449 (1968) Phys. Rev., to be published E. Nyman, to be published
Omitted endnote
G. Källen, Helv. Phys. Acta 25, 417 (1952) H. Lehmann, Nuovo Cimento 11, 342 (1954)
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[c1] B. D. Day, Rev. Mod. Phys. 39, 719 (1967) A. G. Petschek, Ann. Rev. Nucl. Sci. 14, 29 (1964) [3]

[c2] R. Rajaraman and H. A. Bethe, Rev. Mod. Phys. 39, 745 (1967)

[c3] B. H. Brandow, Rev. Mod. Phys. 39, 771 (1967)

[c4] H. A. Bethe, in Proceedings of the International Congress on Nuclear Physics, Paris, France, 1964, edited by P. Gugenbeiger (Centre National de la Recherche Scientifique, Paris, France, 1964), Vol. I, pp. 120-122 G. E. Brown, A. M. Green, and W. J. Gerace, Nucl. Phys. A115, 435 (1968)

[c5] International Conference on the Nucleon-Nucleon Interaction, Rev. Mod. Phys. 39, 495 (1967)

[c6] P. C. Martin and J. Schwinger, Phys. Rev. 115, 1342 (1959)

[c7] R. D. Puff, Ann. Phys. (N.Y.) 13, 317 (1961)

[c8] R. D. Puff, A. S. Reiner, and L. Wilets, Phys. Rev. 149, 778 (1966) T. C. Foster, 149, 784 (1966)

[c9] E. Fiset, Ph.D. thesis, University of Washington, 1967 (unpublished) Phys. Rev. C 2, 85 (1970)

[c10] C. B. Dover and R. H. Lemmer, Phys. Rev. 165, 1105 (1968) C. B. Dover, Ann. Phys. (N.Y.) 50, 449 (1968) Phys. Rev., to be published E. Nyman, to be published

[c11] Omitted endnote

[c12] G. Källen, Helv. Phys. Acta 25, 417 (1952) H. Lehmann, Nuovo Cimento 11, 342 (1954)

[c13] D. S. Falk, Phys. Rev. 115, 1069 (1959)

[c14] P. J. Redmond, Phys. Rev. 112, 1404 (1958)

[c15] K. W. Ford, Phys. Rev. 105, 320 (1957)

[c16] P. A. M. Dirac, Proc. Roy. Soc. (London) A180, 1 (1942) E. C. G. Sudarshan, in Proceedings of the Fourteenth Solvay Conference, Brussels, Belgium, 1967 (John Wiley & Sons Inc., New York)

[c17] T. D. Lee and G. C. Wick, Nucl. Phys. B9, 209 (1969)

[c18] N. N. Bogolyubov, A. A. Logunov, and D. V. Shirkow, Zh. Eksperim. i Theor. Fiz. 37, 805 (1959) [transl.: Soviet Phys.-JETP 10, 574 (1960)]

[c19] E. C. G. Stuckelberg, Helv. Phys. Acta 11, 225 (1938) P. T. Mathews, Phys. Rev. 26, 1254 (1949) A. Salam, 127, 331 (1962) Nucl. Phys. 18, 681 (1960) A. SalamA. Komar 21, 624 (1960) (with ) S. Kamefuchi, 18, 691 (1960) S. KamefuchiH. Umezawa23, 399 (1961) (with ibid.) P. A. Ionides, 28, 662 (1961) M. Veltman, B7, 637 (1968) D. Boulware, Ann. Phys. (N.Y.) 56, 140 (1970)

[c20] J. C. Ward, Phys. Rev. 78, 182 (1950)

[c21] H. Lehmann, K. Symanzik, and W. Zimmermann, Nuovo Cimento 2, 425 (1955)

[c22] N. R. Lipshutz, Phys. Rev. 158, 1491 (1967)

[c23] B. Fried, Phys. Rev. 88, 1142 (1952)

[c24] S. D. Drell and H. R. Pagels, Phys. Rev. 140, B397 (1965)

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Meson Dynamics and the Nuclear Many-Body Problem. I. The Free-Nucleon Problem

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