Collisional Effects on HFS Transitions of Antiprotonic Helium

Collisions of metastable antiprotonic helium with medium atoms induce transitions between hyperfine structure sublevels as well as shift and broadening of the microwave M1 spectral lines. We consider these effects in the framework of a simple model with scalar and tensor interactions between $(\bar{p}\mathrm{He}^+)_{nL}$ and $\mathrm{He}$ atoms. $S$-matrix is obtained by solving coupled-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 energy $E\lesssim 10$ K. The calculated spin-flip cross sections are less than elastic ones by 4 orders of value. At the density $N=3\times 10^{20}$ cm$^{-3}$ and T=6 K we obtain the relaxation times $\tau(FJ\to F'J')\gtrsim 160$ ns, the frequency shifts of M1 spectral lines $\Delta\nu\lesssim 66$ KHz for the favored transitions ($\Delta F=\pm 1, \Delta J=\pm 1$) and frequency broadening of the M1 spectral lines $\gamma/2\lesssim 5.8$ MHz. The results are compatible with the recent experimental data obtained by a laser-microwave-laser resonance method.