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تسجيل مستخدم جديدRelativistic effects in quasielastic electron scattering
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تأليف
Maria B. Barbaro
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The impact of pionic correlations and meson-exchange currents on the quasi-elastic electromagnetic response functions is studied in a fully relativistic framework.
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The experimental data from quasielastic electron scattering from $^{12}$C are reanalyzed in terms of a new scaling variable suggested by the interacting relativistic Fermi gas with scalar and vector interactions, which is known to generate a relativi
stic effective mass for the interacting nucleons. By choosing a mean value of this relativistic effective mass $m_N^* =0.8 m_N$, we observe that most of the data fall inside a region around the inverse parabola-shaped universal scaling function of the relativistic Fermi gas. This suggests a method to select the subset of data that highlight the quasielastic region, about two thirds of the total 2,500 data. Regardless of the momentum and energy transfer, this method automatically excludes the data that are not dominated by the quasielastic process. The resulting band of data reflects deviations from the perfect universality, and can be used to characterize experimentally the quasielastic peak, despite the manifest scaling violation. Moreover we show that the spread of the data around the scaling function can be interpreted as genuine fluctuations of the effective mass $M^* equiv m^*_N/m_N sim 0.8 pm 0.1$. Applying the same procedure we transport the scaling quasielastic band into a theoretical prediction band for neutrino scattering cross section that is compatible with the recent measurements and slightly more accurate.
The electromagnetic responses obtained from Greens function Monte Carlo (GFMC) calculations are based on realistic treatments of nuclear interactions and currents. The main limitations of this method comes from its nonrelativistic nature and its comp
utational cost, the latter hampering the direct evaluation of the inclusive cross sections as measured by experiments. We extend the applicability of GFMC in the quasielastic region to intermediate momentum transfers by performing the calculations in a reference frame that minimizes nucleon momenta. Additional relativistic effects in the kinematics are accounted for employing the two-fragment model. In addition, we developed a novel algorithm, based on the concept of first-kind scaling, to compute the inclusive electromagnetic cross section of $^4$He through an accurate and reliable interpolation of the response functions. A very good agreement is obtained between theoretical and experimental cross sections for a variety of kinematical setups. This offers a promising prospect for the data analysis of neutrino-oscillation experiments that requires an accurate description of nuclear dynamics in which relativistic effects are fully accounted for.
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.
We present a global analysis of the inclusive quasielastic electron scattering data with a superscaling approach with relativistic effective mass. The SuSAM* model exploits the approximation of factorization of the scaling function $f^*(psi^*)$ out o
f the cross section under quasifree conditions. Our approach is based on the relativistic mean field theory of nuclear matter where a relativistic effective mass for the nucleon encodes the dynamics of nucleons moving in presence of scalar and vector potentials. Both the scaling variable $psi^*$ and the single nucleon cross sections include the effective mass as a parameter to be fitted to the data alongside the Fermi momentum $k_F$. Several methods to extract the scaling function and its uncertainty from the data are proposed and compared. The model predictions for the quasielastic cross section and the theoretical error bands are presented and discussed for nuclei along the periodic table from $A=2$ to $A=238$: $^2$H, $^3$H, $^3$He, $^4$He, $^{12}$C, $^{6}$Li, $^{9}$Be, $^{24}$Mg, $^{59}$Ni, $^{89}$Y, $^{119}$Sn, $^{181}$Ta, $^{186}$W, $^{197}$Au, $^{16}$O, $^{27}$Al, $^{40}$Ca, $^{48}$Ca, $^{56}$Fe, $^{208}$Pb, and $^{238}$U. We find that more than 9000 of the total $sim 20000$ data fall within the quasielastic theoretical bands. Predictions for $^{48}$Ti and $^{40}$Ar are also provided for the kinematics of interest to neutrino experiments.
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 selectio
n 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.
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