Neutrino-Nucleus Cross Sections by the Gross Theory of \(\beta \)-Decay

In the present work, we calculate the neutrino-nucleus cross sections, using the gross theory of \(\beta \)-decay (GTBD) for a set of nuclei of astrophysical interest. We work with A-even nuclei between \(12\leqslant A \leqslant 208\), preserving the allowed transitions for which our GTBD model is valid. Once the neutrino-nucleus cross sections within the GTBD model were obtained, we performed two phenomenological adjustments to these cross sections and then extrapolated the adjustment to nuclei that do not belong to the set. One of them corresponds to the usual polynomial adjustment already present in the literature. The other adjustment is of exponential type due to the behavior of the cross section with the incident neutrino energy. The exponential adjustment proved to be more effective than the polynomial adjustment. Some anomalies that existed in the calculations of the cross sections for a range of nuclei with \(36\leqslant Z \leqslant 50\) and \(44\leqslant N \leqslant 74\) were analyzed. We also carried out an extension of the cross sections for nuclei that do not belong to the ensemble and compared with other theoretical predictions from microscopic models and good agreements were achieved.