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Physical Review A

Coupled rearrangement channel calculation of the fine and hyperfine structures of the antiprotonic helium atom - art. no. 012518

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

Published Jan 1, 2001• 6 citations
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Abstract

We precisely calculate the fine and hyperfine structure splittings of the (v,J) = (1,35) state in the antiprotonic helium atom, when v is the vibrational quantum number and J is the total orbital angular momentum. The coupled rearrangement channel method

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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 ${\ensuremath{\alpha}}^{2}\ensuremath{\approx}50\mathrm{ppm}$ 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.
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.
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.
The cross sections and rates for quenching of thermalized antiprotonic helium atoms in binary collisions with ordinary helium atoms are calculated in perturbation theory and in the coupled-channel formalism at the temperature and the number density of the helium gas, T=6KT=6\phantom{\rule{0.3em}{0ex}}\mathrm{K}T=6K and $N={10}^{21}\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}3}$, respectively. It is shown that quenching is unlikely to be relevant for the metastable states of the antiprotonic helium atom with $32\ensuremath{\leqslant}n\ensuremath{\leqslant}40$. Comparison with experiment shows a good quantitative agreement for the (n,l)=(39,35)(n,l)=(39,35)(n,l)=(39,35) state of antiprotonic helium and a large disagreement for the (37,34)(37,34)(37,34) state. As a byproduct of this work, the existence of a series of bound states of the He−−p‾4He+\mathrm{He}--\overline{p}\phantom{\rule{0.2em}{0ex}}^{4}\mathrm{He}^{+}He−−p​4He+ dimer is demonstrated numerically for $n\ensuremath{\geqslant}38$.
A comprehensive set of lecture and study notes covering fundamental atomic and molecular physics. The text systematically works through the breakdown of the classical Rutherford atom and the Bohr-Sommerfeld model, followed by a full 3D Schrödinger treatment of the hydrogen atom using spherical harmonics and Laguerre polynomials. It details relativistic corrections, spin-orbit coupling, and fine structure via Clebsch-Gordan addition and Kramers' recursion relations. The notes further explore magnetic field interactions (normal and anomalous Zeeman effect, Paschen-Back effect), time-dependent perturbation theory for light-matter transitions, electric dipole selection rules, the 21-cm hyperfine splitting of hydrogen, and two-electron systems (Helium, exchange integrals, and Slater determinants). Includes extensive reference tables and angular momentum formulas.