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Coupled Integral Equations for the Nucleon and Pion Electromagnetic Form Factors

Baker, M. and Zachariasen, F. (1960) Coupled Integral Equations for the Nucleon and Pion Electromagnetic Form Factors. Physical Review, 119 (1). pp. 438-448. ISSN 0031-899X. http://resolver.caltech.edu/CaltechAUTHORS:20120813-134042840

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Abstract

The dispersion relations for the nucleon isotopic vector form factors and the pion form factor which take into account contributions from both the 2π and NN intermediate states become a set of coupled integral equations for the form factors if the four amplitudes (ππ|NN) (ππ|ππ) (NN|ππ) (NN|NN) are assumed known. If these four amplitudes are replaced by their Born approximation values and spin and certain kinematic factors are neglected, the resulting set of coupled singular integral equations can be solved exactly. Comparison of these exact solutions with the form factors obtained from the usual approximation of retaining only the lowest mass state (i.e., the 2π state) confirms the hope that high-mass states do not contribute much to dispersion integrals. It is also of interest that these solutions are obtained from dispersion relations without subtractions and satisfy the necessary conditions that they vanish at infinite momentum transfer and take on the value e at the origin for all values of the coupling parameters appearing in the equations.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRev.119.438 DOIUNSPECIFIED
http://link.aps.org/doi/10.1103/PhysRev.119.438PublisherUNSPECIFIED
Additional Information:© 1960 The American Physical Society. Received February 2, 1960. Supported in part by the U. S. Air Force through the Air Force Office of Scientific Research.
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Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Record Number:CaltechAUTHORS:20120813-134042840
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120813-134042840
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33133
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:14 Aug 2012 17:35
Last Modified:26 Dec 2012 15:57

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