Abstract
The neutrino-neutral current isoscalar excitation of 12 C* (1 + ; T = 0; 12.71 MeV) is investigated systematically to examine the specific roles of the various pieces of the neutral current. An effective Hamiltonian for the (isoscalar) neutrino-nucleus neutral current interaction is derived, with in the context of the standard electroweak theory. The hadronic part of the neutral current interaction is found to be vectorial. Numerical results for the isoscalar total cross sections are found to satisfy the Primakoff inequality. The T = 1 admixture into the 12 C* (1 + ; T = 0; 12.71 MeV) from the 12 C* (1 + ; T = 1; 15.1 MeV) is taken into account. It is found that the isospin admixtures makes the total cross sections for the neutrino and antineutrino excitation of the 1 + ; 12.71 MeV in 12 C different. The asymmetry R is thus a direct measure of T = 1 admixture. When the T = 1 admixture is large (0.2), the Primakoff inequality is disturbed. Further effects of isospin mixing on the total cross sections are discussed.
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