Interrelation between $\bar{p}$-Ca Atom Spectra and Nuclear Density Profiles

TL;DR

This study develops a Dirac-equation framework for $ar{p}$-Ca atoms that couples the Coulomb interaction with a density-folded optical potential, including isovector ($b_1$) and p-wave ($c_0$) terms and the anomalous magnetic moment. By employing both simple 3pF and realistic Skyrme-DFT density profiles, it demonstrates that strong shifts and level widths are highly sensitive to the density distribution and to the presence of non-isoscalar terms, with notable effects from deeply bound nuclear states. The results show that no single globally fitted potential can simultaneously reproduce $^{40}$Ca and $^{48}$Ca spectra, underscoring the importance of nucleus-specific analyses and realistic density inputs for interpreting antiprotonic-atom spectroscopy. The work highlights how experimental advances in high-resolution X-ray spectroscopy, together with refined density models, can yield deeper insights into nuclear structure and baryon–baryon interactions. Overall, incorporating isovector and p-wave contributions, along with realistic nuclear densities, is essential for accurately describing $ar{p}$-Ca spectra and extracting nuclear-density–dependent information.

Abstract

This work studies $\bar{p}$-Ca atom spectra in light of the strong shifts and level widths, using the optical model with several types of parametric coefficients. The spectroscopic quantities are obtained as the eigenvalues of the Dirac equation, where the nuclear densities computed via nuclear Density Functional Theory and the effect of the anomalous magnetic moment are incorporated. The results indicate that the isovector term's contribution to the optical potential is crucial for explaining the systematical differences in the strong shifts between $^{40}$Ca and $^{48}$Ca. Furthermore, it is found that both the strong shifts and the level widths exhibit significant dependence on the nuclear density profiles. These findings provide critical insights into the nuclear structures, particularly in the context of Calcium isotopes, by offering a more comprehensive understanding of the underlying nuclear-hadron properties.

Figures (4)

• Figure 1: The isovector density $\rho_1$ as a function of the radial coordinate, with respect to several density profiles. In the left panel, distribution of $^{40}$Ca is exhibited, and the right shows that of $^{48}$Ca.
• Figure 2: The real part of the optical potential with Type II parameters as a function of the radial coordinate, for several representative of the nuclear profiles. In the left panel, distribution of $^{40}$Ca is exhibited, and the right shows the counterpart of $^{48}$Ca.
• Figure 3: Scatter plots of the calculated values for $^{48}$Ca, with Type II parameter, as functions of the neutron skin thickness. Each point is labeled by used density profiles. The left and right panel demonstrates the result of shifts and widths, respectively.
• Figure 4: Level transition scheme in $\bar{p}^{40}$Ca and $\bar{p}^{48}$Ca.