The relativistic effective mass M * , and Fermi momentum, kF , are important ingredients in the determination of the nuclear equation of state, but they have rarely been extracted from experimental data below saturation density where translationally invariant nuclear matter becomes unstable against clusterization into the existing atomic nuclei. Using a novel kind of superscaling analysis of the quasielastic cross section electron scattering data involving a suitable selection criterion and 12 C as a reference nucleus, the global scaling properties of the resulting set of data for 21 nuclei ranging from 2 H to 238 U are then analyzed. We find that a subset of a third of the about 20000 data approximately scales to an universal superscaling function with a more constrained uncertainty band than just the reference 12 C case and provides M * as a function of kF .

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We reanalyze the scaling properties of inclusive quasielastic electron scattering from 12 C by subtracting from the data the effects of two-particle emission. A model of relativistic meson-exchange currents (MEC) is employed within the mean field theory of nuclear matter, with scalar and vector potentials that induce an effective mass and a vector energy to the nucleons. A new phenomenological quasielastic scaling function is extracted from a selection of the data after the subtraction of the 2p-2h contribution. The resulting superscaling approach with relativistic effective mass (SuSAM*) can be used to compute the genuine quasielastic cross section without contamination of the 2p-2h channel that can then be added separately to obtain the total quasielastic plus two-nucleon emission response.

A semiempirical formula for the inclusive electroweak response functions in the two-nucleon emission channel is proposed. The method consists in expanding each one of the vector-vector, axial-axial, and vector-axial responses as sums of six subresponses. These correspond to separating the meson-exchange currents as the sum of three currents of similar structure and expanding the hadronic tensor as the sum of the separate contributions from each current plus the interferences between them. For each subresponse, we factorize the coupling constants, the electroweak form factors, the phase space, and the delta propagator, for the delta-forward current. The remaining spin-isospin contributions are encoded in coefficients for each value of the momentum transfer, q. The coefficients are fitted to the exact results in the relativistic mean field model of nuclear matter, for each value of q. The dependence on the energy transfer ω is well described by the semiempirical formula. The q-dependency of the coefficients of the subresponses can be parametrized or can be interpolated from the provided tables. The description of the five theoretical responses is quite good. The parameters of the formula, the Fermi momentum, number of particles, relativistic effective mass, vector energy, the electroweak form factors, and the coupling constants, can be modified easily. This semiempirical formula can be applied to the cross section of neutrinos, antineutrinos, and electrons.

We use a recent scaling analysis of the quasielastic electron scattering data from 12 C to predict the quasielastic charge-changing neutrino scattering cross sections within an uncertainty band. We use a scaling function extracted from a selection of the (e, e ′ ) cross section data, and an effective nucleon mass inspired by the relativistic mean-field model of nuclear matter. The corresponding super-scaling analysis with relativistic effective mass (SuSAM*) describes a large amount of the electron data lying inside a phenomenological quasielastic band. The effective mass incorporates the enhancement of the transverse current produced by the relativistic mean field. The scaling function incorporates nuclear effects beyond the impulse approximation, in particular meson-exchange currents and short range correlations producing tails in the scaling function. Besides its simplicity, this model describes the neutrino data as reasonably well as other more sophisticated nuclear models.