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

TL;DR

This paper presents systematic theoretical calculations of strong spin-orbit splittings in antiprotonic atoms along isotone chains, revealing their dependence on potential types and relativistic effects, to deepen understanding of baryon interactions.

Contribution

It provides the first thorough theoretical analysis of spin-orbit splittings in antiprotonic atoms using Dirac equation calculations across isotone chains, highlighting the impact of potential types and relativistic corrections.

Findings

Spin-orbit splittings depend linearly on level shifts and widths.

Splittings vary significantly with scalar or vector potential entries.

Relativistic corrections dominate the magnitude of 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.