Numerical accuracy of the energy levels of antiprotonic helium atoms

We evaluate the numerical accuracy of our Coulomb three-body calculation by the complex coordinate rotation method. We examine convergence of eigenenergies of antiprotonic helium atoms. The exotic atom having both atomic and molecular characters is effectively described with the coupled rearrangement channel method. The relative numerical accuracy for the transition frequencies which are to be compared with the observed values by ASACUSA collaboration is estimated to be 9 ppb on average