Isotone Chain Study of $\bar{p}$-atom spectroscopy and Strong Spin-orbit splittings

Abstract

Antiprotonic atoms have served as a pivotal tool for investigating the properties of baryon-baryon interactions, including their spin dependence. Examining the spin-orbit splittings induced by their strong interactions also could help clarify the nature of the $\bar{p}$-nucleus interactions and their fraction mediated by scalar and vector mesons. Although the strong spin-orbit splittings for a certain nucleus have been observed experimentally, thorough theoretical investigations have not yet been conducted. In this study, theoretical calculations based on the Dirac equation are systematically performed for nuclei along several isotone ``chains''. As a result, it is found that the magnitude of the strong spin-orbit splittings exhibits a significant dependence not only on the corresponding level shifts and widths almost linearly, but also on whether the optical potential enters as a vector or scalar potential. A simple perturbative analysis indicates that the relativistic corrections have a dominant effect the magnitude of the splittings. These results are expected to provide deeper insights into $\bar{p}$-nucleus interactions, and by extension baryon-baryon interactions, as well as into the properties of the mesons that mediate them.

Figures (5)

• Figure 1: The level widths of the main-chain nuclei as functions of their (a) charge radii and (b) wave function overlaps with the optical potential. In the left panel, the target nucleus is specified for each plotted point.
• Figure 2: The calculated strong spin-orbit splitting as a function of the level shifts (left panel) and widths (right panel). In both panels, results for $N=28$ chain nuclei with vector potential, $N=28$ with scalar potential, $N=50$ with vector potential, $N=50$ with scalar potential are indicated by red circles, blue crosses, green upward triangles, violet downward triangles, respectively.
• Figure 3: Calculated strong spin-orbit splitting as a function of the (a) strong shift and (b) level width. In both panels, results in the case where the optical potential enters as a vector (scalar) potential are indicated by red circles (green triangles). For the optical potential the Friedman potential is used. The black dotted and dash-dotted lines indicate the results of the linear fitting for the vector and scalar sequences, while the blue dashed line shows the prediction when the scalar-vector proportion in the optical potential is in accord with the standard relativistic mean-field (RMF) model.
• Figure 4: Same with Fig. \ref{['fig:shift_width_split_swave']}, but for the Wycech potential.
• Figure B1: Calculated strong spin-orbit splittings as a function of corresponding level widths, based on the simple non-relativistic model. The results when the optical potential enters as vector and scalar potentials are indicated by the blue circles and violet triangles, respectively.