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arXiv:nucl-th/0411077 · Journal of Physics B Atomic Molecular and Optical Physics

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

Grigory Ya. Korenman, S. N. Yudin

Published Mar 6, 2006• 21 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/0953-4075/39/6/016

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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.
Transitions between hyperfine structure states of antiprotonic 4He^4 \mathrm{He}4He at collisions with medium atoms: interaction \emph{ab initio}
Collisions of metastable antiprotonic helium atoms with atoms of the medium induce, among other processes, transitions between hyperfine structure (HFS) states, as well as shifts and broadening of microwave M1 spectral lines. In order to obtain matrix potential of interaction between (pˉHe+)(\mathrm{\bar{p} He} ^+)(pˉ​He+) and He\mathrm{He}He, we have calculated the potential energy surface (PES) in the framework of unrestricted Hartree-Fock method taking into account electron correlations in the second-order perturbation theory (MP2). With this potential, the system of close-coupling equations for HFS channels is solved numerically. Cross sections and transition rates, shifts and broadening of M1 spectral lines are calculated. They are used to obtain a numerical solution of the master equation that determines the time evolution of the HFS-states density matrix. The results are compared with the experimental data and with the results of model calculation.
Stark transitions and induced annihilation of antiproton in the collisions of antiprotonic helium ions (\bar{p}He^{+2})_{nl} with He atoms at very low energy (~ 10 K) are considered in the framework of quantum coupled-channels method taking into account all the states with different l at given n~30, including the annihilating ns and np-states. Elastic scattering, Stark transitions and induced annihilation during collisions are produced by scalar and dipole terms in the interaction. It is shown that the most important contribution to the processes comes from the long-range polarization interaction. Admixtures of the ns and np-states to the states with higher l during collisions induce the effective annihilation cross sections for the initial l up to 15, but don't affect the Stark cross sections for the initial states nearly to circular orbits. Total rates of the Stark transitions from the circular orbits with n=28 - 32, averaged over the thermal motion, are compatible with the recent ASACUSA data. Isotope effect as well as the dependence on n are also qualitatively agree with the experiment.
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 $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$.
Laser resonance transitions between normally metastable states of antiprotonic helium atoms were induced making use of state dependent quenching effects caused by trace admixtures of H2 to the target helium gas. With this method of “H2-assisted inverse resonances” the decay rates of the states (n,l)=(39,l),l=36,37,38, and (38,l),l=35,36,37 of p̄He+ were determined as a function of the H2 admixture. The quenching cross sections at 30 K deduced therefrom for the states with n=39 were found to be of the order of the geometrical cross section for p̄He+–H2 collisons (2⋅10−15 cm2), with a moderate decrease with increasing l. Within a given cascade with constant v=n−l−1, the quenching cross sections for states with n=38 are smaller by a factor of 4–6 than those for states with n=39.
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 $n\ensuremath{\geqslant}38$.