Fine and hyperfine structures of pionic helium atoms

The fine and hyperfine structures of pionic helium metastable states is calculated within the formalism of the Breit–Pauli Hamiltonian by using the variationally generated wave functions in Hylleraas coordinates. Our results not only verify the existing values of Hori et al. Phys. Rev. A 89, 042515 (2014) for the fine structure of π ⁴He ⁺, but also determine the hyperfine structure of π ³He ⁺.