Two-Channel Separable <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Λ</mi><mi>N</mi></math></span> Potentials

L. H. Schick; N. K. Tyagi

doi:10.1103/PhysRevD.5.1794

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Two-Channel Separable $Λ N$ Potentials

L. H. Schick

N. K. Tyagi

University of Wyoming, Laramie, Wyoming 82070

University of Southern California, Los Angeles, California 90007

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Phys. Rev. D 5, 1794 – Published 1 April, 1972

DOI: https://doi.org/10.1103/PhysRevD.5.1794

Abstract

An attempt is made to use a two-channel $YN$ potential with a single nonlocal separable (NLS) form in each of the four potential matrix elements to represent the low-energy $S$ -wave $Λ N$ interaction. For each spin state equations are developed for expressing the $Λ$ -channel, $Σ$ -channel, and cross-channel potential strengths in terms of the values of the $Λ N$ scattering length and effective range both for full and for no suppression of the $Σ$ channel with general forms for the NLS potential shapes. The condition that there be no resonance due to a bound state in the uncoupled $Σ$ channel is developed. The combined results are proposed as a method for determining which combinations of $Λ$ -channel and $Σ$ -channel NLS potential shapes may be eliminated as not capable of representing a meson-theoretic potential model of the low-energy $Λ N$ interaction. Application of the results is made to the meson-theoretic potential of Brown, Downs, and Iddings. With Yamaguchi forms for both NLS shapes a ${}^{1}S_{0}$ resonance below the $Σ$ -channel threshold due to an uncoupled $Σ$ -channel bound state is always obtained.

References (11)

E. Satoh and Y. Nogami, Phys. Letters 32B, 243 (1970)
A. R. Bodmer, Phys. Rev. 141, 1387 (1966)
A. R. Bodmer and D. M. Rote, report (Univ. of Illinois Chicago Circle), 1970 (unpublished)
J. T. Brown, B. W. Downs, and C. K. Iddings, Ann. Phys. (N.Y.) 60, 148 (1970) B. W. Downs, in Proceedings of the International Conference on Hypernuclear Physics, Argonne National Laboratory, 1969, edited by A. R. Bodmer and L. G. Hyman (Argonne National Laboratory, Argonne, Ill., 1969), p. 51
Y. Yamaguchi, Phys. Rev. 95, 1628 (1954)
L. H. Schick and Alan J. Toepfer, Phys. Rev. 170, 946 (1968)
R. C. Herndon and Y. C. Tang, Phys. Rev. 159, 853 (1967) Y. C. Tang, in Proceedings of the International Conference on Hypernuclear Physics, Argonne National Laboratory, 1969, edited by A. R. Bodmer and L. G. Hyman ([4]), p. 276
B. Sechi-Zorn, B. Kehoe, J. Twitty, and R. A. Burnstein, Phys. Rev. 175, 1735 (1968)
G. Alexander, in Proceedings of the International Conference on Hypernuclear Physics, Argonne National Laboratory, 1969, edited by A. R. Bodmer and L. G. Hyman ([4]), p. 5
T. R. Mongan, Phys. Rev. 180, 1514 (1969)
A. N. Kamal and H. J. Kreuzer, Phys. Rev. D 2, 2033 (1970)

[c1] E. Satoh and Y. Nogami, Phys. Letters 32B, 243 (1970)

[c2] A. R. Bodmer, Phys. Rev. 141, 1387 (1966)

[c3] A. R. Bodmer and D. M. Rote, report (Univ. of Illinois Chicago Circle), 1970 (unpublished)

[c4] J. T. Brown, B. W. Downs, and C. K. Iddings, Ann. Phys. (N.Y.) 60, 148 (1970) B. W. Downs, in Proceedings of the International Conference on Hypernuclear Physics, Argonne National Laboratory, 1969, edited by A. R. Bodmer and L. G. Hyman (Argonne National Laboratory, Argonne, Ill., 1969), p. 51

[c5] Y. Yamaguchi, Phys. Rev. 95, 1628 (1954)

[c6] L. H. Schick and Alan J. Toepfer, Phys. Rev. 170, 946 (1968)

[c7] R. C. Herndon and Y. C. Tang, Phys. Rev. 159, 853 (1967) Y. C. Tang, in Proceedings of the International Conference on Hypernuclear Physics, Argonne National Laboratory, 1969, edited by A. R. Bodmer and L. G. Hyman ([4]), p. 276

[c8] B. Sechi-Zorn, B. Kehoe, J. Twitty, and R. A. Burnstein, Phys. Rev. 175, 1735 (1968)

[c9] G. Alexander, in Proceedings of the International Conference on Hypernuclear Physics, Argonne National Laboratory, 1969, edited by A. R. Bodmer and L. G. Hyman ([4]), p. 5

[c10] T. R. Mongan, Phys. Rev. 180, 1514 (1969)

[c11] A. N. Kamal and H. J. Kreuzer, Phys. Rev. D 2, 2033 (1970)

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Two-Channel Separable $Λ N$ Potentials

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Two-Channel Separable ΛN Potentials

Abstract

References (11)

Two-Channel Separable $Λ N$ Potentials