Longitudinal and transverse scaling functions within the coherent density fluctuation model

We extend our previous description of the superscaling phenomenon in inclusive electron scattering within the coherent density fluctuation model (CDFM). This model is a natural extension to finite nuclei of the relativistic Fermi gas (RFG) model within which the scaling variable ψ' was introduced. In this work we propose a new modified CDFM approach to calculate the total, longitudinal, and transverse scaling functions built up from the hadronic tensor and the longitudinal and transverse response functions in the RFG model. We test the superscaling behavior of the new CDFM scaling functions by calculating the cross sections of electron scattering (in quasielastic and Δ regions for nuclei with 12≤A≤208 at different energies and angles) and comparing to available experimental data. The new modified CDFM approach is extended to calculate charge-changing neutrino and antineutrino scattering on 12C at 1 GeV incident energy.