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arXiv:1911.10619

Transitions between hyperfine structure states of antiprotonic $^4 \mathrm{He}$ at collisions with medium atoms: interaction \emph{ab initio}

Anton V. Bibikov, Grigory Ya. Korenman, S. N. Yudin

Published Nov 24, 2019• 0 citations
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Abstract

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 $(\mathrm{\bar{p} He} ^+)$ and $\mathrm{He}$, 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.

DOI
10.48550/arxiv.1911.10619

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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.
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.
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.
The rates of Auger transitions of antiprotonic helium 4{}^{4}4He+p‾{}^{+}\overline{p}+p​ and 3{}^{3}3He+p‾{}^{+}\overline{p}+p​ are calculated by using a variational scattering method with an elaborate three-body trial function. The shift of the energy levels of these systems due to the coupling with the Auger-decay channels is also obtained from this calculation. Thus an improvement is made over the previously calculated nonrelativistic energies. Together with the relativistic corrections calculated elsewhere, the theoretical transition wavelength between the states (n,l)=(37,34)(n,l)=(37,34)(n,l)=(37,34) and (38,33)(38,33)(38,33) of 4{}^{4}4He+p‾{}^{+}\overline{p}+p​, for example, is significantly improved to be 713.593 nm, which compares well with the experimental value 713.578$\ifmmode\pm\else\textpm\fi{}0.006nm.ThecalculatedAugerlifetimeofthelevel(38,33)is3.2ps,ascomparedwiththevalue4.10.006 nm. The calculated Auger lifetime of the level (38,33) is 3.2 ps, as compared with the value 4.10.006nm.ThecalculatedAugerlifetimeofthelevel(38,33)is3.2ps,ascomparedwiththevalue4.1\ifmmode\pm\else\textpm\fi{}$0.2 ps deduced from the measured line broadening. Auger rates are calculated also using Fermi's golden-rule formula with a regular Coulomb function with no phase shift for the Auger electron. The results agree fairly well with the accurate variational results.
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 $n\ensuremath{\geqslant}38$.
The long-range interaction between an antiprotonic helium atom p‾He+\overline{p}{\mathrm{He}}^{+}p​He+ and helium atom in its ground state is studied. We calculate the dispersion coefficients C6{C}_{6}C6​ using the complex coordinate rotation (CCR) formalism in order to comply with the resonant nature of metastable states of the antiprotonic helium. We present as well numerical data on static dipole polarizabilities of antiprotonic helium states. The obtained coefficients C6{C}_{6}C6​ may be used to estimate the collisional shift and broadening of transition lines in a low-density precision spectroscopy of the antiprotonic helium.