The Effective Range of Nuclear Forces II. Photo-Disintegration of the Deuteron

H. A. Bethe; Conrad Longmire

doi:10.1103/PhysRev.77.647

Access by Xinjiang University

The Effective Range of Nuclear Forces II. Photo-Disintegration of the Deuteron

H. A. Bethe^*

Conrad Longmire^†

Cornell University, Ithaca, New York

Columbia University, New York, New York

^*A part of this investigation was made while the first author was at Columbia University as a Visiting Professor.
^†Now at Los Alamos Scientific Laboratory, Los Alamos, New Mexico.

PDF

Phys. Rev. 77, 647 – Published 1 March, 1950

DOI: https://doi.org/10.1103/PhysRev.77.647

Abstract

The theory of the effective range is applied to the photo-disintegration of the deuteron. For the photoelectric effect, the only important influence of the range is through the normalization of the ground state wave function. We find that this is given by an energy-independent factor ( ${(1 - γ r_{0 t})}^{- 1}$ , where $r_{0 t}$ is the effective range of the forces in the triplet state, and $γ$ is related to the binding energy of the deuteron. With the most likely experimental constants, this factor is 1.58, irrespective of the shape of the nuclear potential.

In the photomagnetic case, the effect of the range on the matrix element nearly compensates that on the normalization. The cross section is thus nearly the same as for zero range of the forces. However, the cross section is sensitive to the difference of the effective ranges for triplet and singlet state, and can thus be used to determine the latter ( $r_{0 s}$ ). The capture of slow neutrons by protons gives $r_{0 s} \approx 2.6 \pm 0.6 \times 10^{- 13}$ cm, in good agreement with the proton-proton scattering results.

In the last section, we show that the effect of tensor forces is unimportant.

References (17)

Phys. Rev. 76, 38 (1949)
J. M. Blatt and J. D. Jackson, Phys. Rev. 76, 18 (1949)
H. A. Bethe and R. Peierls, Proc. Roy. Soc. A148, 146 (1935)
H. A. Bethe and R. F. Bacher, Rev. Mod. Phys. 8, 82 (1936) ibid.8(p. 125)
R. E. Bell and L. G. Elliot, Phys. Rev. 74, 1552 (1948)
R. S. Christian and E. W. Hart, Phys. Rev. 77, 441 (1950)
G. F. Chew, Phys. Rev. 74, 809 (1948)
J. D. Jackson (private communication)
Hadley, Kelly, Leith, Segrè, Wiegand, and York, Phys. Rev. 75, 351 1949 private communication from R. Serber
S. Flügge and E. Hückel, Phys. Rev. 73, 520 (1948)
Omitted endnote
W. J. Whitehouse and G. A. R. Graham, Can. J. Research A25, 261 (1947)
E. Fermi and L. Marshall, Phys. Rev. 72, 193 (1947)
Sutton, McDaniel, Anderson, and Lavatelli, Phys. Rev. 71, 272 (1947)
F. Villars, Phys. Rev. 72, 256 (1947)
A. Pais, Kgl. Danske Vid. Sels. Math.-Fys. Medd. 20, No. 17 (1943)
W. Rarita and J. Schwinger, Phys. Rev. 59, 436, 556 (1941)

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

[c2] J. M. Blatt and J. D. Jackson, Phys. Rev. 76, 18 (1949)

[c3] H. A. Bethe and R. Peierls, Proc. Roy. Soc. A148, 146 (1935)

[c4] H. A. Bethe and R. F. Bacher, Rev. Mod. Phys. 8, 82 (1936) ibid.8(p. 125)

[c5] R. E. Bell and L. G. Elliot, Phys. Rev. 74, 1552 (1948)

[c6] R. S. Christian and E. W. Hart, Phys. Rev. 77, 441 (1950)

[c7] G. F. Chew, Phys. Rev. 74, 809 (1948)

[c8] J. D. Jackson (private communication)

[c9] Hadley, Kelly, Leith, Segrè, Wiegand, and York, Phys. Rev. 75, 351 1949 private communication from R. Serber

[c10] S. Flügge and E. Hückel, Phys. Rev. 73, 520 (1948)

[c11] Omitted endnote

[c12] W. J. Whitehouse and G. A. R. Graham, Can. J. Research A25, 261 (1947)

[c13] E. Fermi and L. Marshall, Phys. Rev. 72, 193 (1947)

[c14] Sutton, McDaniel, Anderson, and Lavatelli, Phys. Rev. 71, 272 (1947)

[c15] F. Villars, Phys. Rev. 72, 256 (1947)

[c16] A. Pais, Kgl. Danske Vid. Sels. Math.-Fys. Medd. 20, No. 17 (1943)

[c17] W. Rarita and J. Schwinger, Phys. Rev. 59, 436, 556 (1941)

Physical Review Journals Archive

Export citation

Export citation

The Effective Range of Nuclear Forces II. Photo-Disintegration of the Deuteron

Abstract

References (17)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation