Nucleon momentum distributions of complex nuclei from inclusive electron scattering

TL;DR

This work addresses inconsistencies in nucleon momentum distributions extracted from inclusive electron scattering by refining the residual excitation-energy treatment within a relativistic Fermi gas model. It introduces a momentum-dependent excitation energy $E^{*\text{RFG}}_{A-1}$ that unifies Fermi motion and SRC effects, ensuring continuity at the Fermi momentum $k_F$. The authors demonstrate that the resulting $n(k)$ agrees with ab initio calculations across a wide range of nuclei, capturing both the low-momentum plateau and the high-momentum SRC tail. This work provides a practical experimental perspective on the interplay between Fermi motion and SRCs and offers a robust framework for analyzing energy and momentum dependence in scattering experiments.

Abstract

Nucleon momentum distributions (NMDs) reveal essential information about Fermi motion and short-range correlations (SRCs). In extracting NMDs from inclusive electron scattering data, theoretical analyses, such as the scaling analysis, are typically employed. For complex nuclei, consistently treating the excitation energy of the residual system is a complicated task, leading to discrepancies between existing extracted NMDs and ab initio calculations, particularly around the Fermi momentum $k_F$. To address this issue, we introduce an improved description of the excitation energy in the framework of the relativistic Fermi gas (RFG) model. With this treatment, the extracted NMDs of complex nuclei show better agreement with ab initio calculations across the low- and high-momentum range, especially around $k_F$, successfully reproducing both the behaviors of Fermi motion and SRCs. These results provide a new experimental perspective on the interplay between Fermi motion and SRCs in complex nuclei.

Figures (6)

• Figure 1: (a) Illustration of the one-nucleon knockout process in electron-nucleus scattering under the PWIA assumption. The residual $A-1$ system is left in an excited state after a nucleon with momentum $\bf{k}$ is knocked out. For (b) independent nucleon knockout, removing a nucleon creates a single hole below the Fermi energy $\varepsilon_F$, and the $A-1$ nucleus recoils with corresponding $-\bf{k}$. For (c) SRC nucleon knockout process, its partner nucleon carries an approximately back-to-back momentum $-\bf{k}$, and the remaining $A-2$ system stays nearly at rest.
• Figure 2: (a) $y$-scaling functions $F(y)$ and (b) nucleon momentum distributions $n(k)$ of $^{12}$C extracted from the inclusive cross section with the incident electron energy $E_e=3.356$ GeV and the scattering angle $\theta=25^\circ$Zhang2025. Red squares indicate the extractions with RFG excitation energy, and green circles indicate the extractions without excitation energy. The $F(y_{\text{CW}})$ results (shaded area) Ciofi2009, extractions by Ciofi degli Atti et al. (black squares) Ciofi1991, and QMC calculations (lines) with different $NN+3N$ interactions are presented for comparison Wiringa2014.
• Figure 3: The RFG excitation energy $E^{*\text{RFG}}_{A-1}$ as a function of $k$ for $^{12}$C with the Fermi momentum setting as $k_F=285$ MeV/c.
• Figure 4: Nucleon momentum distributions $n(k)$ of $^{12}$C extracted from the experimental cross sections measured at ($E_e,\theta$)=(3.356 GeV, 25$^{\circ}$), (4.045 GeV, 23$^{\circ}$), (4.045 GeV, 30$^{\circ}$), (5.766 GeV, 18$^{\circ}$), and (5.766 GeV, 22$^{\circ}$). The $Q^2$ values at the quasielastic peak are also given.
• Figure 5: Nucleon momentum distributions $n(k)$ of $^{4}$He extracted from the experimental cross sections measured at ($E_e,\theta$)=(3.595 GeV, 20$^{\circ}$), (3.356 GeV, 21$^{\circ}$), (3.356 GeV, 25$^{\circ}$), (5.766 GeV, 18$^{\circ}$), and (5.766 GeV, 22$^{\circ}$). The $Q^2$ values at the quasielastic peak are also given.