Coherency and incoherency in neutrino-nucleus elastic and inelastic scattering

Neutrino-nucleus scattering nu A -> nu A, in which the nucleus conserves its integrity, is considered. Our consideration follows a microscopic description of the nucleus as a bound state of its constituent nucleons described by a multiparticle wave function of a general form. We show that elastic interactions keeping the nucleus in the same quantum state lead to a quadratic enhancement of the corresponding cross section in terms of the number of nucleons. Meanwhile, the cross section of inelastic processes in which the quantum state of the nucleus is changed, essentially has a linear dependence on the number of nucleons. These two classes of processes are referred to as coherent and incoherent, respectively. Accounting for all possible initial and final internal states of the nucleus leads to a general conclusion independent of the nuclear model. The coherent and incoherent cross sections are driven by factors vertical bar F-p/n vertical bar(2) and (1 - vertical bar F-p/n vertical bar(2)), where vertical bar F-p/n vertical bar(2) is a proton/neutron form factor of the nucleus, averaged over its initial states. Therefore, our assessment suggests a smooth transition between regimes of coherent and incoherent neutrino-nucleus scattering. In general, both regimes contribute to experimental observables. The coherent cross-section formula used in the literature is revised and corrections depending on kinematics are estimated. Consideration of only those matrix elements which correspond to the same initial and final spin states of the nucleus and accounting for a nonzero momentum of the target nucleon are two main sources of the corrections. As an illustration of the importance of the incoherent channel, we considered three experimental setups with different nuclei. As an example, for Cs-133 and neutrino energies of 30-50 MeV, the incoherent cross section is about 10%-20% of the coherent contribution if the experimental detection threshold is accounted for. Experiments attempting to measure coherent neutrino scattering by solely detecting the recoiling nucleus, as is typical, might be including an incoherent background that is indistinguishable from the signal if the excitation gamma eludes its detection. However, as is shown here, the incoherent component can be measured directly by searching for photons released by the excited nuclei inherent to the incoherent channel. For a beam experiment these gammas should be correlated in time with the beam, and their higher energies make the corresponding signal easily detectable at a rate governed by the ratio of incoherent to coherent cross sections. The detection of signals due to the nuclear recoil and excitation gamma s provides a more sensitive instrument in studies of nuclear structure and possible signs of new physics.