Unified Description of Electron-Nucleus Scattering within the Spectral Function Formalism

The formalism based on factorization and nuclear spectral functions has been generalized to treat transition matrix elements involving two-nucleon currents, whose contribution to the nuclear electromagnetic response in the transverse channel is known to be significant. We report the results of calculations of the inclusive electron-carbon cross section, showing that the inclusion of processes involving two-nucleon currents appreciably improves the agreement between theory and data in the dip region, between the quasielastic and $\mathrm{\Delta }$-production peaks. The relation to approaches based on the independent particle of the nucleus and the implications for the analysis of flux-integrated neutrino-nucleus cross sections are discussed.

Figure 1

Free-space meson exchange current diagrams. The first two correspond to $\pi$-meson exchange: diagram (a) and the one obtained interchanging particle 1 and 2 represent the contact or seagull contribution, while diagram (b) is the pion-in-flight term. Diagrams (c) and (d), and the additional two resulting from the interchange $1\leftrightarrow 2$, involve a $\mathrm{\Delta }$-resonance excitation.

Figure 2

(a) Double differential cross section of the process $e+{}^{12}C\to e^{\prime }+X$ at beam energy $E_e=680\mathrm{MeV}$ and scattering angle ${\theta }_e=37.5$ deg. The solid line shows the result of the full calculation, while the dashed line has been obtained including the one-body current only. The contributions arising from two-nucleon currents are illustrated by the dot-dashed and dotted lines, corresponding to the pure two-body current transition probability and to the interference term, respectively. The experimental data are taken from Ref. [24]. (b) Same as (a) but for $E_e=1300\mathrm{MeV}$ and ${\theta }_e=37.5$ deg. The experimental data are taken from Ref. [25].

Figure 3

(a) Double differential electron-carbon cross section at beam energy $E_e=680\mathrm{MeV}$ and scattering angle ${\theta }_e=36$ deg. The dashed line corresponds to the result obtained neglecting FSI, while the solid line has been obtained within the approach of Ref. [15]. The experimental data are taken from Ref. [24]. (b) Same as (a) but for $E_e=1300\mathrm{MeV}$ and ${\theta }_e=37.5$ deg. The experimental data are taken from Ref. [25].