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Physical Review A

Coupled rearrangement channel calculation of the fine and hyperfine structures of the antiprotonic helium atom

Nobuhiro Yamanaka, Yasushi Kino, Hiroshi Kudo, M. Kamimura

Published Dec 13, 2000• 34 citations
Publisher

Abstract

We precisely calculate the fine and hyperfine structure splittings of the $(v,J)=(1,35)$ state in the antiprotonic helium atom, where $v$ is the vibrational quantum number and $J$ is the total orbital angular momentum. The coupled rearrangement channel method is employed to efficiently describe correlation effects in the three-body system with atomic and molecular characters. An accuracy of better than ${\ensuremath{\alpha}}^{2}\ensuremath{\approx}50\mathrm{ppm}$ has been achieved. The result obtained is in good agreement with the previous calculation within $\ensuremath{\sim}200 \mathrm{ppm}.$ We also examine the correlation effects, in particular orbital polarization effects.

DOI
10.1103/physreva.63.012518

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We precisely calculate the fine and hyperfine structure splittings of the (v,J)=(1,35)(v,J)=(1,35)(v,J)=(1,35) state in the antiprotonic helium atom, where vvv is the vibrational quantum number and JJJ is the total orbital angular momentum. The coupled rearrangement channel method is employed to efficiently describe correlation effects in the three-body system with atomic and molecular characters. An accuracy of better than \ensuremathα2\ensuremath≈50ppm{\ensuremath{\alpha}}^{2}\ensuremath{\approx}50\mathrm{ppm}\ensuremathα2\ensuremath≈50ppm has been achieved. The result obtained is in good agreement with the previous calculation within \ensuremath∼200ppm.\ensuremath{\sim}200 \mathrm{ppm}.\ensuremath∼200ppm. We also examine the correlation effects, in particular orbital polarization effects.
Precise numerical calculation of radiofrequency intervals between hyperfine sublevels of the (37,35) state of the antiprotonic helium-4 atom is presented. Theoretical consideration includes the QED corrections of order $m{\ensuremath{\alpha}}^{6}$ to the electron spin-orbit interaction. Only the leading order contribution in the electron-to-antiproton and electron-to-$\ensuremath{\alpha}$ particle mass ratios is considered, so the $\ensuremath{\alpha}$ particle and antiproton are treated nonrelativistically. The effective Hamiltonian is derived using the formalism of the nonrelativistic quantum electrodynamics.
Using a newly developed laser-microwave-laser resonance method, we observed a pair of microwave transitions between hyperfine levels of the (n,L)=(37,35)(n,L)=(37,35)(n,L)=(37,35) state of antiprotonic helium. This experiment confirms the quadruplet hyperfine structure arising from the interaction of the antiproton orbital angular momentum, the electron spin and the antiproton spin as predicted by Bakalov and Korobov. The measured frequencies of ${\ensuremath{\nu}}_{\mathrm{H}\mathrm{F}}^{+}=12.895\text{ }96\ifmmode\pm\else\textpm\fi{}0.000\text{ }34\text{ }\mathrm{G}\mathrm{H}\mathrm{z}$ and ${\ensuremath{\nu}}_{\mathrm{H}\mathrm{F}}^{\ensuremath{-}}=12.924\text{ }67\ifmmode\pm\else\textpm\fi{}0.000\text{ }29\text{ }\mathrm{G}\mathrm{H}\mathrm{z}$ agree with recent theoretical calculations on a level of $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$.
Collisions of metastable antiprotonic helium with atoms of a 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 model with scalar and tensor interactions between 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 inelastic cross sections are less than elastic ones by four orders of value for the single electron or antiproton spin-flip transitions (Δ J = ±1, Δ F = 0, ± 1) and by seven orders of value for the double spin-flip transitions (Δ J = 0, ± 2, Δ F = ±1). The cross sections show a resonance behaviour at very low energy ( E ∼ 1–4 K). The results for the relaxation rate λ( F − → F + ), the frequency shift and broadening of the M1 spectral lines for the favoured transitions (Δ F = ±1, Δ J = ±1) are compatible with the recent experimental data obtained by a triple (laser–microwave–laser) resonance method at T = 6 K. The calculated values are lowered by a factor of 1.5–2 with the temperature rising up to 25 K.
We consider two types of collisional processes with excited antiprotonic helium systems. (i) Transitions between hyperfine structure sublevels in ( He + ) n LFJ are considered at T ≤ 25 K using the coupled-channels method and a model of scalar and tensor interactions between antiprotonic and ordinary He atoms. Inelastic cross sections for the single and double spin-flip transitions are less than elastic ones by four and seven orders of magnitude, respectively. The cross sections show a resonance behaviour at E ∼ 1–4 K, and therefore the relaxation rates, density shift and broadening of the M1 spectral lines decrease with increasing temperature from 3 to 25 K. (ii) Stark transitions and induced annihilation during collisions of the ( He 2+ ) nl ion with He atoms at E ∼ 10 K are considered for all l -states at n ∼ 30 in the framework of the coupled-channels method. In order to take into account complex energy shifts of the ns and np -states, we introduce modified boundary conditions in these channels. The main contribution to elastic scattering, Stark transitions and induced annihilations during collisions comes from the long-range polarization interaction. Admixtures of ns and np -states to nl -states ( l ≥ 2) during collisions induce the effective annihilation cross sections for the initial l up to 15, but don't affect the Stark cross sections for states with nearly-circular orbits. The calculated values for both types of processes are compatible with recent experimental data.
Potential energy curves for excited leptonic states of the helium-antihydrogen system are calculated within the Ritz variational approach. An explicitly correlated ansatz for the leptonic wave function is employed describing accurately the motion of the leptons (two electrons and positron) in the field of the helium nucleus and of the antiproton with an arbitrary orbital angular momentum projection Lambda onto the internuclear axis. Results for Lambda=0, 1, and 30 are presented. For quasibound states with large values of Lambda and rotational quantum numbers J>Lambda no annihilation and rearrangement decay channels occur; i.e., they are metastable.