Neutrino neutral current reactions in 12C

The differential and total cross sections for the nuclear reaction v/sub μ/+12C (g.s.)→12C* (1+; T = 1, 15.1 MeV)+v/sub μ/ are investigated for values of 50< or =E/sub v//sub μ/< or =300 MeV. An effective Hamiltonian for the above nuclear reaction is constructed from the neutrino-quark neutral current weak interaction, by first constructing the neutrino-nucleon neutral current interation and then using the impulse approximation along with the non-relativistic reduction procedure. The Weinberg-Salam model is the basis of the calculations. Detailed expressions for the differential cross sections are derived including the nucleon momentum-dependent terms. The numerical results are obtained using the general 2p-shell wavefunctions of Cohen and Kurath. The sensitivity of the total cross sections to the nuclear models and to the Weinberg angle is studied. The corresponding anti-neutrino reaction is also investigated. The ratio R = (sigma/sub T//sub v/μ-sigma/sub T//sup v//sub μ/) (sigma/sub T//sup v//sub μ/)+sigma/sub T//sup v//sub μ/) is found to be independent of the nuclear wavefunctions but very sensitive to the Weinberg angle. Thus this observable can be used to determine the free parameter theta/sub w/ in a nuclear reaction, thereby complementing the studies involving free nucleons. The recoil polarization of the final nucleus 12C*(1+; T = 1, 15.1 MeV) is also studied and its importance is pointed out