  Collisions of metastable antiprotonic helium atoms with atoms of the medium
induce, among other processes, transitions between hyperfine structure (HFS)
states, as well as shifts and broadening of microwave M1 spectral lines. In
order to obtain matrix potential of interaction between $(\mathrm{\bar{p} He}
^+)$ and $\mathrm{He}$, we have calculated the potential energy surface (PES)
in the framework of unrestricted Hartree-Fock method taking into account
electron correlations in the second-order perturbation theory (MP2). With this
potential, the system of close-coupling equations for HFS channels is solved
numerically. Cross sections and transition rates, shifts and broadening of M1
spectral lines are calculated. They are used to obtain a numerical solution of
the master equation that determines the time evolution of the HFS-states
density matrix. The results are compared with the experimental data and with
the results of model calculation.
