Nonlocal Nucleon-Nucleon Interaction

D. A. Giltinan; R. M. Thaler

doi:10.1103/PhysRev.131.805

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Nonlocal Nucleon-Nucleon Interaction

D. A. Giltinan

R. M. Thaler

Case Institute of Technology, Cleveland, Ohio

Case Institute of Technology, Cleveland, Ohio and Lewis Research Laboratory, National Aeronautics and Space Administration, Cleveland, Ohio

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Phys. Rev. 131, 805 – Published 15 July, 1963

DOI: https://doi.org/10.1103/PhysRev.131.805

Abstract

It has been explicitly demonstrated that the proton-proton scattering data require that the singlet even parity nucleon-nucleon interaction be nonlocal. This result comes from an examination of the energy dependence of both the ${}^{1}S_{0}$ and ${}^{1}D_{2}$ phase shifts. A nonlocal singlet even parity potential of the form $V (r, r^{'}) = \frac{V {(r)}^{\frac{1}{2}} V {(r^{'})}^{\frac{1}{2}} R^{- 3} [\exp (- R^{- 1} | r - r^{'} |)]}{(4 π R^{- 1} | r - r^{'} |)}$ is examined. The potential function $V (r)$ is taken to have the form of a monotonic attraction outside a "hard core." The radius of the "hard core," the depth and range of $V (r)$ , and the nonlocal distance $R$ provide four parameters which can be adjusted to fit the experimental values of the singlet scattering length and effective range, and the 310-MeV ${}^{1}S_{0}$ and ${}^{1}D_{2}$ phase shifts. For a long-range attractive potential function, such as the Yukawa, the energy dependence of the ${}^{1}S_{0}$ and ${}^{1}D_{2}$ phase shifts is strikingly similar to that suggested by the phase-shift analysis of the Yale group. Although the radius of the "hard core" is decreased somewhat from the local value, a "hard core" is still required.

References (7)

H. P. Stapp, T. J. Ypsilantis, and N. Metropolis, Phys. Rev. 105, 302 (1957)
G. Breit, M. H. Hull, Jr., K. E. Lassila, and K. D. Pyatt, Jr., Phys. Rev. 120, 2227 (1960)
J. L. Gammel and R. M. Thaler, in Proceedings of the Seventh Annual Rochester Conference on High-Energy Nuclear Physics, 1957 (Interscience Publishers, Inc., New York, 1957)
J. L. Gammel and R. M. Thaler, in Progress in Elementary Particle and Cosmic-Ray Physics, edited by J. G. Wilson and S. A. Wouthuysen (North-Holland Publishing Company, Amsterdam, 1960), Vol. V, p. 99
O. Chamberlain, E. Segrè, R. D. Tripp, C. Wiegand, and T. Ypsilantis, Phys. Rev. 105, 288 (1957)
C. Lee, J. L. Gammel, and R. M. Thaler, in Nuclear Forces and the Few Nucleon Problem, edited by T. C. Griffith and E. A. Power (Pergamon Press Inc., New York, 1960), p. 43
O. Rojo and L. M. Simmons, Phys. Rev. 125, 273 (1960)

[c1] H. P. Stapp, T. J. Ypsilantis, and N. Metropolis, Phys. Rev. 105, 302 (1957)

[c2] G. Breit, M. H. Hull, Jr., K. E. Lassila, and K. D. Pyatt, Jr., Phys. Rev. 120, 2227 (1960)

[c3] J. L. Gammel and R. M. Thaler, in Proceedings of the Seventh Annual Rochester Conference on High-Energy Nuclear Physics, 1957 (Interscience Publishers, Inc., New York, 1957)

[c4] J. L. Gammel and R. M. Thaler, in Progress in Elementary Particle and Cosmic-Ray Physics, edited by J. G. Wilson and S. A. Wouthuysen (North-Holland Publishing Company, Amsterdam, 1960), Vol. V, p. 99

[c5] O. Chamberlain, E. Segrè, R. D. Tripp, C. Wiegand, and T. Ypsilantis, Phys. Rev. 105, 288 (1957)

[c6] C. Lee, J. L. Gammel, and R. M. Thaler, in Nuclear Forces and the Few Nucleon Problem, edited by T. C. Griffith and E. A. Power (Pergamon Press Inc., New York, 1960), p. 43

[c7] O. Rojo and L. M. Simmons, Phys. Rev. 125, 273 (1960)

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Nonlocal Nucleon-Nucleon Interaction

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