For the metastable states of antiprotonic helium atoms, He-3(+)(p) over bar, the fine and hyperfine splittings of energy levels are calculated within the framework of the Breit-Pauli Hamiltonian. The latter represents the alpha(2) order relativistic corrections to the nonrelativistic energy. Results include as well the leading alpha(3) order contribution due to the anomalous magnetic moment of electron. The final relative accuracy of the hyperfine intervals is estimated to be about 5x10(-5).
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