Quantum calculation of the collision-induced line-shape effects in antiprotonic helium and the new accurate ab initio $\bar{p}$He$^{+}$-He potential energy surface

Abstract

We present the first fully ab initio calculations of collision-induced broadening and shift of spectral lines in antiprotonic helium ($\bar{p}$He$^{+}$) perturbed by atomic helium. To overcome critical limitations of previous studies, we construct a new highly accurate potential energy surface (PES) that spans a wide range of $\bar{p}$He$^{+}$-He geometries relevant to all metastable states of the exotic helium atom. Rigorous quantum scattering calculations performed using the new PES yield scattering $S$-matrices from which we extract pressure broadening and shift coefficients for 50 transitions in antiprotonic helium-4 ($\bar{p}^{4}$He$^{+}$). This dataset provides the first rigorous benchmark for earlier semiclassical calculations and establishes a robust theoretical reference for high-precision spectroscopy of antiprotonic helium, which is used to test the fundamental charge, parity, and time reversal (CPT) symmetry. The results extend to temperatures relevant to non-gaseous phases of helium, supporting a new class of precision measurements. This study introduces a methodological framework for future investigations of other exotic systems, such as pionic or kaonic helium atoms, enabling the development of reference data for high-precision spectroscopy of these species - an essential component for improving the determination of the pion and kaon masses.