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Collisions of metastable antiprotonic helium with atoms of medium inducetransitions between hyperfine structure sublevels as well as shifts andbroadenings of the microwave M1 spectral lines. We consider these phenomena inthe framework of a model with scalar and tensor interactions betweenantiprotonic and ordinary helium atoms. S-matrix is obtained by solvingcoupled-channels equations involving 4 HFS sublevels (F=L\pm 1/2, J=F\pm 1/2)of the nL level and relative angular momenta up to l=5 at the kinetic energyE<25 K. The calculated spin-flip cross sections are less than elastic ones byfour orders of value in the case \Delta J=\pm 1, and by seven orders of valuein the case \Delta F=\pm 1, \Delta J=0 or \Delta J=\pm 2. The considered crosssections reveal a resonance behaviour at very low energy (E about 1 - 4 Kdepending on the model parameters). At the density N=3\times 10^{20} cm^{-3}and T=6 K we obtain the relaxation time =160 ns, the frequency shift \Delta\nu\= 80 kHz and the frequency broadening \gamma \lesssim 5.9 MHz for M1 spectrallines of the favored transitions (\Delta F=\pm 1, \Delta J=\pm 1). The resultsare compatible with the recent experimental data obtained by alaser-microwave-laser resonance method. With the temperature rising up to 25 Kthe rate of relaxation \lambda=1/\tau as well as shift and broadening of the M1microwave lines are lowered by a factor 1.5 - 2 reflecting the displacement ofa mean kinetic energy from the region of resonance scattering.

Coupled-channel analysis of collisional effects on HFS transitions in antiprotonic helium atoms