The Effective Range of Nuclear Forces. Effect of the Potential Shape

E. E. Salpeter

doi:10.1103/PhysRev.82.60

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The Effective Range of Nuclear Forces. Effect of the Potential Shape

E. E. Salpeter

Cornell University, Ithaca, New York

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Phys. Rev. 82, 60 – Published 1 April, 1951

DOI: https://doi.org/10.1103/PhysRev.82.60

Abstract

Corrections to the theory of the effective range, which take account of the shape of the neutron-proton potential, are discussed. The following quantities are calculated for a Yukawa, exponential, and square well potential: (a) various triplet ranges compatible with the value obtained for $ρ_{t} (0, - ε)$ from the latest experiments, (1.72±0.035)× $10^{- 13}$ cm. (b) The singlet effective range $r_{0 s}$ from neutron-proton scattering cross sections at energies up to 6 Mev. (c) $r_{0 s}$ from neutron absorption cross sections by hydrogen. (d) Photoelectric and photomagnetic disintegration cross sections for the deuteron for various $γ$ -rays.

It is shown that a comparison of the values obtained for $r_{0 s}$ from (b) and (c) could, with a slight increase in experimental accuracy, give an estimate of the potential shape. Present, very tentative, indications are for a short-tailed potential and a value for $r_{0 s}$ of about (2.7±0.5)× $10^{- 13}$ cm.

References (26)

H. A. Bethe, Phys. Rev. 76, 38 (1949)
H. A. Bethe and C. Longmire, Phys. Rev. 77, 647 (1950)
J. M. Blatt and J. D. Jackson, Phys. Rev. 76, 18 (1949)
R. E. Bell and L. G. Elliot, Phys. Rev. 79, 282 (1950)
R. C. Mobley and R. A. Laubenstein, Phys. Rev. 80, 309 (1950)
Taschek, Argo, Hemmendinger, and Jarvis, Phys. Rev. 76, 325 (1940)
Hornyak, Lauritsen, Morrison, and Fowler, Revs. Modern Phys. 22, 291 (1950)
T. R. Roberts and A. O. Nier, Phys. Rev. 77, 746 (1950)
Hughes, Burgy, and Ringo, Phys. Rev. 77, 291 (1950) 79, 227 (1950) and private communication
E. Melkonian, Phys. Rev. 76, 1744 (1949)
Smith, Barkas, Bishop, Bradner, and Gardner, Phys. Rev. 78, 86 (1950)
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W. J. Whitehouse and G. A. R. Graham, Can. J. Research A25, 261 (1947)
R. L. Walker, MDDC—414, unpublished
G. R. Bishop et al., Phys. Rev. 80, 211 (1950) ibid.81, 219 (1951)
J. E. Mack, Revs. Modern Phys. 22, 64 (1950)
N. Austern and R. G. Sachs, Phys. Rev. 81, 710 (1951)
E. P. Gray, private communication
H. Hall [Revs. Modern Phys. 8, 358 (1936)]
Omitted endnote
I. F. E. Hansson and L. Hulthén, Phys. Rev. 76, 1163 (1949) I. F. E. Hansson, 79, 909 (1950)
R. S. Christian and E. W. Hart, Phys. Rev. 77, 441 (1950) H. A. Bethe (unpublished work)
A. G. Prodell and P. Kusch, Phys. Rev. 79, 1009 (1950)
Smaller, Yasaitis, and Anderson, Phys. Rev. 80, 137 (1950)
F. Low, Phys. Rev. 77, 361 (1950)
A. Bohr, Phys. Rev. 73, 1109 (1948)

[c1] H. A. Bethe, Phys. Rev. 76, 38 (1949)

[c2] H. A. Bethe and C. Longmire, Phys. Rev. 77, 647 (1950)

[c3] J. M. Blatt and J. D. Jackson, Phys. Rev. 76, 18 (1949)

[c4] R. E. Bell and L. G. Elliot, Phys. Rev. 79, 282 (1950)

[c5] R. C. Mobley and R. A. Laubenstein, Phys. Rev. 80, 309 (1950)

[c6] Taschek, Argo, Hemmendinger, and Jarvis, Phys. Rev. 76, 325 (1940)

[c7] Hornyak, Lauritsen, Morrison, and Fowler, Revs. Modern Phys. 22, 291 (1950)

[c8] T. R. Roberts and A. O. Nier, Phys. Rev. 77, 746 (1950)

[c9] Hughes, Burgy, and Ringo, Phys. Rev. 77, 291 (1950) 79, 227 (1950) and private communication

[c10] E. Melkonian, Phys. Rev. 76, 1744 (1949)

[c11] Smith, Barkas, Bishop, Bradner, and Gardner, Phys. Rev. 78, 86 (1950)

[c12] Lampi, Freier, and Williams, Phys. Rev. 80, 853 (1950)

[c13] W. J. Whitehouse and G. A. R. Graham, Can. J. Research A25, 261 (1947)

[c14] R. L. Walker, MDDC—414, unpublished

[c15] G. R. Bishop et al., Phys. Rev. 80, 211 (1950) ibid.81, 219 (1951)

[c16] J. E. Mack, Revs. Modern Phys. 22, 64 (1950)

[c17] N. Austern and R. G. Sachs, Phys. Rev. 81, 710 (1951)

[c18] E. P. Gray, private communication

[c19] H. Hall [Revs. Modern Phys. 8, 358 (1936)]

[c20] Omitted endnote

[c21] I. F. E. Hansson and L. Hulthén, Phys. Rev. 76, 1163 (1949) I. F. E. Hansson, 79, 909 (1950)

[c22] R. S. Christian and E. W. Hart, Phys. Rev. 77, 441 (1950) H. A. Bethe (unpublished work)

[c23] A. G. Prodell and P. Kusch, Phys. Rev. 79, 1009 (1950)

[c24] Smaller, Yasaitis, and Anderson, Phys. Rev. 80, 137 (1950)

[c25] F. Low, Phys. Rev. 77, 361 (1950)

[c26] A. Bohr, Phys. Rev. 73, 1109 (1948)

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The Effective Range of Nuclear Forces. Effect of the Potential Shape

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