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

TL;DR

This paper applies the dispersive optical model (DOM) to ($p$,$2p$) reactions within the distorted wave impulse approximation (DWIA) framework, comparing results with ($e$,$e'p$) data to improve nuclear spectroscopy analysis.

Contribution

It introduces the first application of the dispersive optical model to ($p$,$2p$) analysis within DWIA, highlighting discrepancies and uncertainties in spectroscopic factors.

Findings

DOM + DWIA yields a proton spectroscopic factor of 0.560 for $^{40}$Ca($p$,$2p$)$^{39}$K.

The spectroscopic factor from ($p$,$2p$) analysis is smaller than the DOM value consistent with ($e$,$e'p$).

Uncertainties from wave function choices and $p$-$p$ interactions do not explain the discrepancy.

Abstract

Both ($e$,$e'p$) 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 ($e$,$e'p$) 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. We apply the DOM wave functions to the traditional ($p$,$2p$) analysis and investigate the consistency of the DOM spectroscopic factor that describes the ($e$,$e'p$) 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 $p$-$p$ interaction is also investigated. We implement the DOM wave functions to the distorted wave impulse approximation (DWIA) framework for ($p$,$2p$) reactions. DOM + DWIA analysis on $^{40}$Ca($p$,$2p$)$^{39}$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 ($e$,$e'p$) analysis. Uncertainties arising from choices of single-particle wave function, optical potential, and $p$-$p$ interaction do not explain this inconsistency. The inconsistency in the spectroscopic factor suggests there is urgent need for improving the description of $p$-$p$ scattering in a nucleus and the resulting in-medium interaction with corresponding implications for the analysis of this reaction in inverse kinematics.