Neutrino neutral current isoscalar excitations in 12C-isospin mixing, II

The neutrino-neutral current isoscalar excitation of 12C( (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, within 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 12C( (1+; T = 0; 12.71 MeV) from the 12C( (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 12C 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