Collisions of the metastable antiprotonic helium atoms with the atoms of the medium cause, among other processes, transitions between hyperfine structure (HFS) states, as well as shifts and broadening of microwave M1 spectral lines. To obtain the interaction potential matrix ( $$\bar{p}$$ $$\bar{He}^{+}){-}\textrm{He}$$ , the potential energy surface (PES) is calculated by the unrestricted Hartree–Fock method with consideration of the electron correlations within the second-order of perturbation theory (MP2). With this potential, the system of equations of close coupling of the HFS channels is numerically solved; the cross sections and transition rates, shifts, and broadenings of M1 spectral lines are calculated; they are then used to solve the kinetic equation that determines the time evolution of the HFS state density matrix. The results of these calculations are compared with the experimental data and with the results of model calculations.
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