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Collisions of metastable antiprotonic helium with atoms of medium induce transitions between hyperfine structure sublevels as well as shifts and broadenings of the microwave M1 spectral lines. We consider these phenomena in the framework of a simple model with scalar and tensor interactions between (pHe + ) nL and He atoms. S-matrix is obtained by solving coupled-channels equations involving 4 HFS sublevels (F = L ± 1/2, J = F ± 1/2) of the nL level and relative angular momenta up to l = 5 at the kinetic energy E 25 K. The calculated spin-flip cross sections are less than elastic ones by four orders of value in the cases ∆F = ∆J = ±1 and ∆F = 0, ∆J = ±1, and by seven orders of value in the case ∆F = ±1, ∆J = 0 or ∆J = ±2. The considered cross sections reveal a resonance behaviour at very low energy (E ∼ 1 ÷ 4 K depending on the model parameters). At the density N = 3× 10 20 cm −3 and T = 6 K we obtain the relaxation time τ (F J → F ′ J ′ ) ≥ 160 ns, the frequency shift ∆ν ≃ 80 kHz and the frequency broadening γ 5.9 MHz for M1 spectral lines of the favored transitions (∆F = ±1, ∆J = ±1). The results are compatible with the recent experimental data obtained by a laser-microwave-laser resonance method. With the temperature rising up to 25 K the rate of relaxation λ = 1/τ as well as shift and broadening of the M1 microwave lines are lowered by a factor 1.5 ÷ 2 reflecting the displacement of a mean kinetic energy from the region of resonance scattering.

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 (pHe + ) nL and He atoms. Smatrix is obtained by solving coupled-channels equations involving 4 HFS sublevels (F = L ± 1/2, J = F ± 1/2) of the nL level and relative angular momenta up to l = 5 at the kinetic energy E 10 K. The calculated spin-flip cross sections are less than elastic ones by 4 orders of value. At the density N = 3 × 10 20 cm −3 and T = 6 K we obtain the relaxation times τ (F J → F ′ J ′ ) 160 ns, the frequency shifts of M1 spectral lines ∆ν 66 KHz for the favored transitions (∆F = ±1, ∆J = ±1) and frequency broadening of the M1 spectral lines γ/2 5.8 MHz. The results are compatible with the recent experimental data obtained by a laser-microwave-laser resonance method.Key words: antiproton, antiprotonic helium, hyperfine structure, collisional relaxation, collisional shift and broadening 34.60.+z, 32.70.Jz The discovery of antiproton longevity in helium and investigations of antiprotonic helium (pHe + ) metastable states by the method of laser resonance spectroscopy have opened a new layer of very interesting physics (see [1] and the references therein). One of the actual problems in the topics is an influence of ambient atoms on the antiprotonic states. In particular, the density shifts and broadenings of E1 spectral lines (nL → n ′ L ′ = L ± 1) were observed for laserinduced transitions. The model theoretical analysis [2] shows that qualitative

We consider collisional effects on the transitions between HFS states of (p 3 He + ) in the presence of microwave radiation. Cross sections and rates of collisional HFS transition, density shifts and broadening of M1 spectral lines are calculated within the approach developed previously for (p 4 He + ). The values averaged over thermal motion are used in the quantum master equation for the density matrix of HFS states in the microwave field. At the target density 3 × 10 20 cm −3 and T = 6 K, partial rates of the single spin-flip transition in (p 3 He + ) are ∼ 1 · 10 6 s −1 . Effective relaxation rates by considering the kinetics are approximately twice more. At the same conditions collisional shifts of the M1 spectral lines are ≤ 4 kHz, collisional broadening of the lines is 0.5 MHz. The total width of the line J −−+ → J +−+ at t d = 350 ns is 2.4 MHz allowing for collisional and Fourier broadenings. Maximum MW resonance signal in 3 He is about 0.5 of that one in 4 He.

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