Leading term of the He-$\overline{p}{\mathrm{He}}^{+}$ long-range interaction

The long-range interaction between an antiprotonic helium atom $\overline{p}{\mathrm{He}}^{+}$ and helium atom in its ground state is studied. We calculate the dispersion coefficients $C_6$ using the complex coordinate rotation (CCR) formalism in order to comply with the resonant nature of metastable states of the antiprotonic helium. We present as well numerical data on static dipole polarizabilities of antiprotonic helium states. The obtained coefficients $C_6$ may be used to estimate the collisional shift and broadening of transition lines in a low-density precision spectroscopy of the antiprotonic helium.