Longitudinal Component of the Weak Vector Current
of Spin-1/2 Nuclear Isodoublets

M. I. Krivoruchenko^{a, b, c}, F. Šimkovic^{c, d}, and S. Kovalenko^e

^aInstitute for Theoretical and Experimental Physics, Moscow, 117218 Russia

e-mail: mikhail.krivoruchenko@itep.ru

^bMoscow Institute of Physics and Technology, Dolgoprudny, Moscow oblast, 141700 Russia

^cBogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia

^dDepartment of Nuclear Physics and Biophysics, Comenius University, SK-842 48 Bratislava, Slovakia

^eUniversidad Tecnica Federico Santa Maria, Centro Cientifico Tecnologico de Valparaiso, Valparaiso, Chile

Abstract—The generalized Ward identity is derived for the vertex function of the weak vector current (VC) of
nucleons within an effective theory with account of the isotopic symmetry breaking. The generalized Ward
identity establishes a relationship between the form factor of the longitudinal weak VC component and the mass
difference and the charge radii of an isotopic doublet on the mass shell. This relationship can be used to evaluate
the form factors of both nucleons and nuclei with spin J = 1/2 and isospin I = 1/2. The reactions with large trans-
ferred momenta involving isotopic doublets, in which the mass splitting is maximized, offer the greatest prom-
ise for measuring the form factor. Numerical estimates of the form factor of the longitudinal weak VC compo-
nent of a nucleon pair and eight nuclear isodoublets are presented.

DOI: 10.1134/S1547477115050088

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