Density dependence of 2p-2h meson-exchange currents

We analyze the density dependence of the contribution of meson-exchange currents to the lepton-nucleus inclusive cross section in the two-particle two-hole channel. The model is based on the relativistic Fermi gas, where each nucleus is characterized by its Fermi momentum $k_F$. We find that the 2p-2h nuclear response functions at their peaks scale as $A{k}_F^2$ for Fermi momentum going from 200 to 300 MeV/$c$ and momentum transfer $q$ from $2k_F$ to 2 $\mathrm{GeV}/c$. This behavior is different from what is found for the quasielastic response, which scales as $A/k_F$. Additionally, the deep scaling region is also discussed and there the usual scaling behavior is found to be preferable.

Figure 1

The 2p-2h MEC response of [10] plotted versus $\omega$ for three values of the Fermi momentum $k_F$ and for different values of the momentum transfer $q=200$, ..., 1000 MeV/$c$ (left panel) and 1100, ..., 2000 MeV/$c$ (right panel), increasing from left to right.

Figure 2

Upper panels: The 2p-2h MEC response (a) and the reduced response defined by Eq. (3) (b) plotted versus $\omega$ for $q=800\mathrm{MeV}/c$ and Fermi momentum $k_F$ varying between 200 (lower curve) and 300 (upper curve) MeV/$c$. Lower panels: The corresponding scaled 2p-2h MEC response defined by Eq. (5) plotted versus the scaling variables ${\psi }_{\mathrm{MEC}}^{\prime }$ (c) and ${\psi }_{\mathrm{QE}}^{\prime }$ (d).

Figure 3

The scaled 2p-2h MEC response defined by Eq. (5) (left panel) and the corresponding superscaling function defined by Eq. (6) (right panel) plotted versus the scaling variable ${\psi }_{\mathrm{QE}}^{\prime }$ for $q=2\mathrm{GeV}/c$.

Figure 4

As for Fig. 2, but now for different values of $q$.

Figure 5

The 2p-2h MEC transverse response $R_{\mathrm{MEC}}^T$ and the separate $\mathrm{\Delta }\mathrm{\Delta }$-, $\pi \pi$-, and $\pi \mathrm{\Delta }$-interference components plotted versus $\omega$. The free RFG transverse response (red curves) is also shown for reference.

Figure 6

The scaled 2p-2h MEC response ${\tilde{F}}_{\mathrm{MEC}}^T$ defined in Eq. (5) and the separate $\mathrm{\Delta }\mathrm{\Delta }$-, $\pi \pi$-, and $\pi \mathrm{\Delta }$-interference components plotted versus ${\psi }_{\mathrm{MEC}}^{\prime }$ for $q=800\mathrm{MeV}/c$ and $k_F=200$ and $300\mathrm{MeV}/c$.

Figure 7

The scaled 2p-2h MEC response ${\tilde{F}}_{\mathrm{MEC}}^T$ defined in Eq. (5) and the separate $\mathrm{\Delta }\mathrm{\Delta }$-, $\pi \pi$-, and $\pi \mathrm{\Delta }$-interference components plotted versus ${\psi }_{\mathrm{QE}}^{\prime }$ for $q=800\mathrm{MeV}/c$ and $k_F=200$ and $300\mathrm{MeV}/c$.

Figure 8

The 2p-2h MEC response (first column), the corresponding scaled response ${\tilde{F}}_{\mathrm{MEC}}^T$ defined by Eq. (5) (second column), and the superscaling function defined by Eq. (6) (third column) for four nuclei and three values of momentum transfer $q$.