Coupled rearrangement channel calculation of the fine and hyperfine structures of the antiprotonic helium atom

Abstract

We precisely calculate the fine and hyperfine structure splittings of the $(v,J)=(1,35)$ state in the antiprotonic helium atom, where $v$ is the vibrational quantum number and $J$ is the total orbital angular momentum. The coupled rearrangement channel method is employed to efficiently describe correlation effects in the three-body system with atomic and molecular characters. An accuracy of better than ${\ensuremath{\alpha}}^{2}\ensuremath{\approx}50\mathrm{ppm}$ has been achieved. The result obtained is in good agreement with the previous calculation within $\ensuremath{\sim}200 \mathrm{ppm}.$ We also examine the correlation effects, in particular orbital polarization effects.