Gauge invariance, locality, and the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mo>−</mo><mn>2</mn><mn></mn></mrow></msub></mrow></math></span> photoabsorption sum rule

J. L. Friar; S. Fallieros

doi:10.1103/PhysRevC.15.365

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Gauge invariance, locality, and the $σ_{- 2}$ photoabsorption sum rule

J. L. Friar^* and S. Fallieros

Department of Physics, Brown University, Providence, Rhode Island 02912

^*Present address: Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87545.

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Phys. Rev. C 15, 365 – Published 1 January, 1977

DOI: https://doi.org/10.1103/PhysRevC.15.365

Abstract

The requirements of gauge invariance for the photoabsorption and Compton amplitudes are used to evaluate the $σ_{- 2}$ sum rule through terms of order (1/mass). This expression is shown to equal the derivative of the dispersive part of the forward Compton amplitude with respect to the squared photon energy. In the absence of "frozen" meson degrees of freedom this is equivalent to the derivative of the entire Compton amplitude. If static exchange currents or finite nucleon charge distributions are present, the seagull terms of our model are nonlocal and modify the sum rule.

NUCLEAR REACTIONS Calculated photoabsorption cross section and Compton amplitude. Tested $σ_{- 2}$ sum rule. Intrinsic form factors and exchange currents discussed.

References (17)

J. S. Levinger, Nuclear Photodisintegration (Oxford U.P. London, 1960)
H. A. Kramers, Atti. Congr. Int. Fisici, Como, 2, 545 (1927)
R. Kronig, J. Opt. Soc. Am. 12, 547 (1926)
R. Kronig, Physica 12, 543 (1946)
M. Gell-Mann, M. L. Goldberger, and W. E. Thirring, Phys. Rev. 95, 1612 (1954)
M. L. Goldberger and F. E. Low, Phys. Rev. 176, 1778 (1968)
S. J. Brodsky, F. E. Close, and J. F. Gunion, Phys. Rev. D 5, 1384 (1972)
J. L. Friar and S. Fallieros, Phys. Rev. C 11, 274 (1975)
J. L. Friar, Ann. Phys. (N.Y.) 95, 170 (1975)
J. L. Friar and M. Rosen, Ann. Phys. (N.Y.) 87, 289 (1974)
J. L. Friar, Phys. Rev. Lett. 36, 510 (1976)
J. L. Friar and S. Fallieros, Phys. Rev. C 11, 277 (1975)
T. Matsuura and K. Yazaki, Phys. Lett. 46B, 17 (1973)
J. Schwinger, Phys. Rev. Lett. 3, 296 (1959)
A. Martin, Nuovo Cim. Suppl. 2, 157 (1961)
R. J. Eden and J. Goldstone, Nucl. Phys. 49, 33 (1963)
M. Damashek and F. J. Gilman, Phys. Rev. D 1, 1319 (1970)

[c1] J. S. Levinger, Nuclear Photodisintegration (Oxford U.P. London, 1960)

[c2] H. A. Kramers, Atti. Congr. Int. Fisici, Como, 2, 545 (1927)

[c3] R. Kronig, J. Opt. Soc. Am. 12, 547 (1926)

[c4] R. Kronig, Physica 12, 543 (1946)

[c5] M. Gell-Mann, M. L. Goldberger, and W. E. Thirring, Phys. Rev. 95, 1612 (1954)

[c6] M. L. Goldberger and F. E. Low, Phys. Rev. 176, 1778 (1968)

[c7] S. J. Brodsky, F. E. Close, and J. F. Gunion, Phys. Rev. D 5, 1384 (1972)

[c8] J. L. Friar and S. Fallieros, Phys. Rev. C 11, 274 (1975)

[c9] J. L. Friar, Ann. Phys. (N.Y.) 95, 170 (1975)

[c10] J. L. Friar and M. Rosen, Ann. Phys. (N.Y.) 87, 289 (1974)

[c11] J. L. Friar, Phys. Rev. Lett. 36, 510 (1976)

[c12] J. L. Friar and S. Fallieros, Phys. Rev. C 11, 277 (1975)

[c13] T. Matsuura and K. Yazaki, Phys. Lett. 46B, 17 (1973)

[c14] J. Schwinger, Phys. Rev. Lett. 3, 296 (1959)

[c15] A. Martin, Nuovo Cim. Suppl. 2, 157 (1961)

[c16] R. J. Eden and J. Goldstone, Nucl. Phys. 49, 33 (1963)

[c17] M. Damashek and F. J. Gilman, Phys. Rev. D 1, 1319 (1970)

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Gauge invariance, locality, and the σ−2 photoabsorption sum rule

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References (17)

Gauge invariance, locality, and the $σ_{- 2}$ photoabsorption sum rule