Quasifree ${\pi }^0$ and ${\pi }^{-}$ Electroproduction on ${}^4\mathrm{He}$ in the $\Delta$-Resonance Region

The reactions ${}^4\mathrm{He}(e,e^{\prime }p{}^3\mathrm{He}){\pi }^{-}$ and ${}^4\mathrm{He}(e,e^{\prime }p{}^3\mathrm{He}){\pi }^0$ were studied simultaneously, and for the first time, in a large kinematical domain including the $\Delta$-resonance region. This was achieved by detecting the recoiling ${}^3\mathrm{He}$ and ${}^3\mathrm{H}$ nuclei instead of the emitted pions. The dependences of the cross section on the recoil momentum $p_{\mathrm{rec}}$, the invariant mass $W_{\pi \mathrm{N}}$, and the direction ${\theta }_{\pi ,{\mathrm{q}}^{\prime }}$ and ${\varphi }_{\pi ,{\mathrm{q}}^{\prime }}$ of the produced pion, are globally well described by the results of (quasifree) distorted-wave impulse approximation calculations. However, in the $\Delta$-resonance region there are clear discrepancies, which point to medium modifications of the $\Delta$ in ${}^4\mathrm{He}$.

Figure 1

The cross section $d^8\sigma$ for the reactions ${}^4\mathrm{He}(e,e^{\prime }p{}^3\mathrm{H}){\pi }^0$ and ${}^4\mathrm{He}(e,e^{\prime }p{}^3\mathrm{He}){\pi }^{-}$ as a function of $p_{\mathrm{rec}}$.

Figure 2

The cross sections for ${\pi }^0$ and ${\pi }^{-}$ production as a function of $W_{\pi \mathrm{N}}$. Only events with $p_{\mathrm{rec}}\le 180\mathrm{MeV}/c$ are included.

Figure 3

Dependence of $d^8\sigma$ on ${\theta }_{\pi ,{\mathrm{q}}^{\prime }}$ for the reactions ${}^4\mathrm{He}(e,e^{\prime }p{}^3\mathrm{H}){\pi }^0$ and ${}^4\mathrm{He}(e,e^{\prime }p{}^3\mathrm{He}){\pi }^{-}$. The cross sections are shown for two $W_{\pi \mathrm{N}}$ bins: $W_{\pi \mathrm{N}}<1160\mathrm{MeV}$ (top) and $1160<W_{\pi \mathrm{N}}<1260\mathrm{MeV}$. Only events with $p_{\mathrm{rec}}\le 180\mathrm{MeV}/c$ are included.

Figure 4

The cross sections $d^8\sigma$ for the ${}^4\mathrm{He}(e,e^{\prime }p{}^3\mathrm{H}){\pi }^0$ and ${}^4\mathrm{He}(e,e^{\prime }p{}^3\mathrm{He}){\pi }^{-}$ reactions as a function of ${\varphi }_{\pi ,{\mathrm{q}}^{\prime }}$ (top), $\Phi$ (middle), and $\Delta \Phi$ (bottom). Only events with $p_{\mathrm{rec}}\le 180\mathrm{MeV}/c$ are included.