Relativistic Calculation of Nucleon-Nucleon Phase Parameters

Alexander Gersten; Richard H. Thompson; A. E. S. Green

doi:10.1103/PhysRevD.3.2076

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Relativistic Calculation of Nucleon-Nucleon Phase Parameters

Alexander Gersten^*

Richard H. Thompson^† and A. E. S. Green

University of Florida, Gainesville, Florida 32601
Texas A & M University, College Station, Texas 77840

University of Florida, Gainesville, Florida 32601

^*Present address: University of Nijmegen, Nijmegen, The Netherlands.
^†Present address: Department of Physics, Drexel University, Philadelphia, Pa. 19104.

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Phys. Rev. D 3, 2076 – Published 1 May, 1971

DOI: https://doi.org/10.1103/PhysRevD.3.2076

Abstract

An approximate Bethe-Salpeter equation is used to calculate the $N - N$ phase parameters. The one-boson-exchange (OBE) hypothesis is invoked to approximate the left-hand singularity. A good fit to the existing data is obtained, and certain phase parameters ( ${}^{3}D_{2}$ , ${}^{1}D_{2}$ , and ${}^{3}P_{2}$ ), which are not fitted well by existing OBE-potential (OBEP) models, are much improved. The observables are not fitted directly, but rather an approximate procedure suggested by MacGregor et al. is used to minimize the experimental $χ^{2}$ . Comparisons are made with the nonrelativistic OBEP used in conjunction with the Schrödinger equation.

References (27)

T. Ueda and A. E. S. Green, Phys. Rev. 174, 1304 (1968)
R. A. Bryan and B. L. Scott, Phys. Rev. 177, 1435 (1969)
Richard H. Thompson, Phys. Rev. D 1, 110 (1970)
R. Blankenbecler and R. Sugar, Phys. Rev. 142, 1051 (1966)
E. E. Salpeter and H. A. Bethe, Phys. Rev. 84, 1232 (1951)
T. Sawada and A. E. S. Green, Bull. Am. Phys. Soc. 11, 383 (1966) UF-Nuclear Meson reports, 1968 (unpublished)
Richard H. Thompson, Alexander Gersten, and A. E. S. Green, Phys. Rev. D 3, 2069 (1971)
A. E. S. Green, Phys. Rev. 73, 26 (1948) ibid.75, 1926 (1949)
Angela Barbaro-Galtieri, Stephen E. Derenzo, Leroy R. Price, Alan Rittenberg, Arthur H. Rosenfeld, Naomi Barash-Schmidt, Claude Bricman, Matts Roos, Paul Söding, and Charles G. Wohl, Rev. Mod. Phys. 42, 87 (1970)
M. Jacob and G. C. Wick, Ann. Phys. (N.Y.) 7, 404 (1959)
M. L. Goldberger, M. T. Grisaru, S. W. MacDowell, and D. Y. Wong, Phys. Rev. 120, 2250 (1960)
M. E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957)
J. Goto and S. Machida, Progr. Theoret. Phys. (Kyoto) 25, 64 (1961)]
Omitted endnote
S. Ogawa, S. Sawada, T. Ueda, W. Watari, and M. Yonezawa, Progr. Theoret. Phys. (Kyoto) Suppl. 39, 140 (1967)
R. A. Arndt, R. A. Bryan, and M. H. MacGregor, Phys. Rev. 152, 1490 (1966) R. A. Bryan (private communication)
Omitted endnote
K. L. Kowalski, Phys. Rev. Letters 15, 798 (1965)
H. P. Noyes, Phys. Rev. Letters 15, 538 (1965)
R. E. Seamon, K. A. Friedman, and G. Breit, Phys. Rev. 145, 779 (1966)
M. H. MacGregor, R. A. Arndt, and R. M. Wright, Phys. Rev. 169, 1128 (1968) ibid.182, 1714 (1969)
R. W. Stagat, F. Riewe, and A. E. S. Green, Phys. Rev. (to be published)
Omitted endnote
Alexander Gersten and A. E. S. Green, Phys. Rev. 176, 1199 (1968)
G. Breit, in International Conference on Properties of Nuclear States, Montreal, 1969 (unpublished)
R. J. Oakes and J. J. Sakurai, Phys. Rev. Letters 19, 1266 (1967)
T. A. Griffy and L. I. Schiff, in High Energy Physics, edited by E. H. S. Burhop (Academic, New York, 1967), Vol. I

[c1] T. Ueda and A. E. S. Green, Phys. Rev. 174, 1304 (1968)

[c2] R. A. Bryan and B. L. Scott, Phys. Rev. 177, 1435 (1969)

[c3] Richard H. Thompson, Phys. Rev. D 1, 110 (1970)

[c4] R. Blankenbecler and R. Sugar, Phys. Rev. 142, 1051 (1966)

[c5] E. E. Salpeter and H. A. Bethe, Phys. Rev. 84, 1232 (1951)

[c6] T. Sawada and A. E. S. Green, Bull. Am. Phys. Soc. 11, 383 (1966) UF-Nuclear Meson reports, 1968 (unpublished)

[c7] Richard H. Thompson, Alexander Gersten, and A. E. S. Green, Phys. Rev. D 3, 2069 (1971)

[c8] A. E. S. Green, Phys. Rev. 73, 26 (1948) ibid.75, 1926 (1949)

[c9] Angela Barbaro-Galtieri, Stephen E. Derenzo, Leroy R. Price, Alan Rittenberg, Arthur H. Rosenfeld, Naomi Barash-Schmidt, Claude Bricman, Matts Roos, Paul Söding, and Charles G. Wohl, Rev. Mod. Phys. 42, 87 (1970)

[c10] M. Jacob and G. C. Wick, Ann. Phys. (N.Y.) 7, 404 (1959)

[c11] M. L. Goldberger, M. T. Grisaru, S. W. MacDowell, and D. Y. Wong, Phys. Rev. 120, 2250 (1960)

[c12] M. E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957)

[c13] J. Goto and S. Machida, Progr. Theoret. Phys. (Kyoto) 25, 64 (1961)]

[c14] Omitted endnote

[c15] S. Ogawa, S. Sawada, T. Ueda, W. Watari, and M. Yonezawa, Progr. Theoret. Phys. (Kyoto) Suppl. 39, 140 (1967)

[c16] R. A. Arndt, R. A. Bryan, and M. H. MacGregor, Phys. Rev. 152, 1490 (1966) R. A. Bryan (private communication)

[c17] Omitted endnote

[c18] K. L. Kowalski, Phys. Rev. Letters 15, 798 (1965)

[c19] H. P. Noyes, Phys. Rev. Letters 15, 538 (1965)

[c20] R. E. Seamon, K. A. Friedman, and G. Breit, Phys. Rev. 145, 779 (1966)

[c21] M. H. MacGregor, R. A. Arndt, and R. M. Wright, Phys. Rev. 169, 1128 (1968) ibid.182, 1714 (1969)

[c22] R. W. Stagat, F. Riewe, and A. E. S. Green, Phys. Rev. (to be published)

[c23] Omitted endnote

[c24] Alexander Gersten and A. E. S. Green, Phys. Rev. 176, 1199 (1968)

[c25] G. Breit, in International Conference on Properties of Nuclear States, Montreal, 1969 (unpublished)

[c26] R. J. Oakes and J. J. Sakurai, Phys. Rev. Letters 19, 1266 (1967)

[c27] T. A. Griffy and L. I. Schiff, in High Energy Physics, edited by E. H. S. Burhop (Academic, New York, 1967), Vol. I

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Relativistic Calculation of Nucleon-Nucleon Phase Parameters

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