The exotic helium atom, consisting of a helium nucleus
He2+, an electron ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$, and a massive, negatively charged particle ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$, such as an antiproton (p\ifmmode\bar\else\textasciimacron\fi{}) or a kaon (${\mathit{K}}^{\mathrm{\ensuremath{-}}}$), is studied theoretically. This exotic atom is more like a polar molecule with two nuclei
He2+ and ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$, if ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ is in a low-lying orbital and ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ is in a highly excited orbital. Such states are generally formed in the capture of ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ by helium. The Born-Oppenheimer (BO) separation of the ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ motion and the
He2+-${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ motion is a good approximation for these states, and affords a transparent, unified perspective of exotic helium with different ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ and different isotopes of
He2+. A propensity rule that favors small transition energies (except for the smallest one) is found for radiative emission by low vibrational and high rotational levels. This rule resembles the selection rule for infrared emission by the usual diatomic polar molecules, and contradicts the conventional expectation that radiative transitions in exotic atoms favor larger transition energies. The radiative lifetimes \ensuremath{\tau} of highly excited states formed immediately after the capture of ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ are of the order of \ensuremath{\mu}sec for
4He2+-p\ifmmode\bar\else\textasciimacron\fi{}-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ and
3He2+-p\ifmmode\bar\else\textasciimacron\fi{}-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$, and those for
4He2+-${\mathit{K}}^{\mathrm{\ensuremath{-}}}$-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ are about half the values for the antiprotonic helium.The effect of the electronic charge polarization by ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ on \ensuremath{\tau} is explained quantitatively in a simple picture in terms of the molecular dipole moment. Low vibrational, high rotational states are described as circular or near-circular states in the atomic picture. They are stable against Auger decay, which the nonadiabatic perturbation on the BO states induces. An infinite series of bound \ensuremath{\Sigma} electronic states of exotic helium negative ions (
He2+-${\mathit{X}}^{\mathrm{\ensuremath{-}}}$-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$)-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ exists for any
He2+-${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ distances R beyond 0.819 a.u. in the BO approximation. An infinite \ensuremath{\Pi} series exists for R>3.811 a.u., and an infinite \ensuremath{\Delta} series for R>9.532 a.u.
The formation process of metastable $\mathrm{dt}\ensuremath{\mu}$ molecules in ${D}_{2}\ensuremath{-}{T}_{2}$ mixtures in investigated. The $\mathrm{dt}\ensuremath{\mu}$ molecule exhibits a series of three-body resonances embedded in the $t\ensuremath{\mu}+d$ scattering continuum just below the $t\ensuremath{\mu}(2s)+d$ threshold. These states can be formed in collisions of excited $t\ensuremath{\mu}(2s)$ atoms with
D2 molecules, whereby the excess of binding energy is absorbed by the rovibrational degrees of freedom of
D2. We present a scattering-theoretic model for this process, and perform a numerical calculation of its cross section. The essential transition amplitudes are obtained from three-body wave functions for the $\mathrm{dt}\ensuremath{\mu}$ subcluster, and adiabatic wave functions for the entire hybrid system in the final channel. It is found that the effective formation rate is limited by the Auger-transition rates of the molecular complex formed. The calculated cross sections exhibit broad "peaks," with magnitudes large enough for the formation process to favorably compete with deexcitation of $t\ensuremath{\mu}(n=2)$ atoms via radiative and collisional processes. The formation of metastable $\mathrm{dt}\ensuremath{\mu}$ can therefore be one of the fastest processes depleting the
n=2 levels of the $t\ensuremath{\mu}$ atom in hydrogen mixtures, of importance for low-energy muon science, electroweak physics, and muon catalyzed fusion.
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=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) state of antiprotonic helium and a large disagreement for the
(37,34) state. As a byproduct of this work, the existence of a series of bound states of the
He−−p4He+ dimer is demonstrated numerically for $n\ensuremath{\geqslant}38$.
A theoretical study is performed for the photoassociation of metastable helium. Combining short-range, high-level, ab initio calculations for 5 Σ g / u + and 5 Π g / u symmetries and long-range behaviour, better described in Hund's case (c), potential-energy curves for attractive, 5 Σ u + and 5 Π g , as well as repulsive, 5 Π u and 5 Σ g + , states of quintet metastable helium molecules dissociating to 2 3 S + 2 3 P are obtained. Taking into account the atomic spin-orbit couplings, vibrational levels are derived for near-dissociation levels at the 3 P 2 asymptote. Comparison with results from three recent photoassociation experiments obtained under different conditions (μK temperatures with spin alignment and mK temperatures without) allowed for an assignation of about three quarters of the observed levels. The robustness of the vibrational numbering is confirmed by testing a modification of the short-range potentials.
Total cross sections for quenching of low-n Rydberg states of Li
(n<10, l=0) in collision with the ground state He have been calculated in the low-energy region
(v< 0.1a.u.) by employing the molecular orbital approximation. Results for the total depopulation of the parent states, along with those for excitation and de-excitation mechanisms have been presented. Present cross sections exhibit the low-energy Stueckelberg oscillations. Using a model two-state calculation we present a detailed comparative study between the quantum-mechanical and semiclassical findings. Except at very low energies, the semiclassical cross sections agree nicely with their quantum counterparts. The reaction rates at thermal energies are also reported.