First application of the dispersive optical model to $(p,2p)$ reaction analysis within the distorted-wave impulse approximation framework

Background: Both ($e,e^{\prime }p$) and ($p,2p$) reactions have been performed to study the proton single-particle character of nuclear states with its related spectroscopic factor. Recently, the dispersive optical model (DOM) was applied to the ($e,e^{\prime }p$) analysis revealing that the traditional treatment of the single-particle overlap function, distorted waves, and nonlocality must be further improved to achieve quantitative nuclear spectroscopy.

Purpose: We apply the DOM wave functions to the traditional ($p,2p$) analysis and investigate the consistency of the DOM spectroscopic factor that describes the ($e,e^{\prime }p$) cross section with the result of the ($p,2p$) analysis. Additionally, we make a comparison with a phenomenological single-particle wave function and optical potential. Uncertainty arising from a choice of $p\text{−}p$ interaction is also investigated.

Method: We implement the DOM wave functions to the nonrelativistic distorted-wave impulse approximation (DWIA) framework for ($p,2p$) reactions.

Results: DOM $+$ DWIA analysis on ${}^{40}\mathrm{Ca}(p,2p){}^{39}\mathrm{K}$ data generates a proton $0d_{3/2}$ spectroscopic factor of 0.560, which is meaningfully smaller than the DOM value of 0.71 shown to be consistent with the ($e,e^{\prime }p$) analysis. Uncertainties arising from choices of single-particle wave function, optical potential, and $p\text{−}p$ interaction do not explain this inconsistency.

Conclusions: The inconsistency in the spectroscopic factor suggests there is urgent need for improving the description of $p\text{−}p$ scattering in a nucleus and the resulting in-medium interaction with corresponding implications for the analysis of this reaction in inverse kinematics.

Figure 1

TDX with different optical potentials. The solid, dashed, and dotted lines are TDXs with the Koning-Delaroche optical potential (KD) and Dirac phenomenology (DP), respectively. The result with DOM ingredients is also shown as the dot-dashed line. All results reflect cross sections that are normalized with the spectroscopic factors shown in Table 1. The experimental data taken by the E258 experiment at RCNP [25] are also shown.

Figure 2

TDX with different $p\text{−}p$ effective interactions. The solid, dashed, and dotted lines are TDXs with the Franey-Love effective interaction [35] (FL), Melbourne $g$-matrix interaction at mean density [36] (Mel), and that at zero density (Mel free), respectively. The experimental data are the same as in Fig. 1.

Figure 3

Coordinate of the $(p,2p)$ three-body system.