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Physical Review A

Formation of metastable dtμ molecules in tμ(2s)−D2 collisions

Janne Wallenius, P. Froelich

Published Aug 1, 1996• 21 citations
Publisher

Abstract

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 ${D}_{2}$ molecules, whereby the excess of binding energy is absorbed by the rovibrational degrees of freedom of ${D}_{2}$. 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.

DOI
10.1103/physreva.54.1171

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The formation process of metastable dt\ensuremathμ\mathrm{dt}\ensuremath{\mu}dt\ensuremathμ molecules in D2\ensuremath−T2{D}_{2}\ensuremath{-}{T}_{2}D2​\ensuremath−T2​ mixtures in investigated. The dt\ensuremathμ\mathrm{dt}\ensuremath{\mu}dt\ensuremathμ molecule exhibits a series of three-body resonances embedded in the t\ensuremathμ+dt\ensuremath{\mu}+dt\ensuremathμ+d scattering continuum just below the t\ensuremathμ(2s)+dt\ensuremath{\mu}(2s)+dt\ensuremathμ(2s)+d threshold. These states can be formed in collisions of excited t\ensuremathμ(2s)t\ensuremath{\mu}(2s)t\ensuremathμ(2s) atoms with D2{D}_{2}D2​ molecules, whereby the excess of binding energy is absorbed by the rovibrational degrees of freedom of D2{D}_{2}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 dt\ensuremathμ\mathrm{dt}\ensuremath{\mu}dt\ensuremathμ 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\ensuremathμ(n=2)t\ensuremath{\mu}(n=2)t\ensuremathμ(n=2) atoms via radiative and collisional processes. The formation of metastable dt\ensuremathμ\mathrm{dt}\ensuremath{\mu}dt\ensuremathμ can therefore be one of the fastest processes depleting the n=2n=2n=2 levels of the t\ensuremathμt\ensuremath{\mu}t\ensuremathμ atom in hydrogen mixtures, of importance for low-energy muon science, electroweak physics, and muon catalyzed fusion.
Muon transfer and elastic scattering in low-energy collisions of t+d\ensuremath{\mu}(1s) are studied by the hyperspherical coupled-channel method in which many closed channels are explicitly coupled to obtain converged cross sections. A hybrid procedure of the diabatic-by-sector and the traditional adiabatic-basis-expansion methods is developed for solving a larget set of coupled equations influenced by the nearly singular nature of couplings induced by numerous avoided crossings. It is shown that the adiabatic states belonging to the n=2 excited states in the separated-atom limit contribute significantly to the muon transfer. The discrepancy between the previous hyperspherical calculation of Fukuda et al. [Phys. Rev. A 41, 145 (1990)] and other existing theoretical calculations has been resolved by taking into account the couplings with these excited states.
We have studied hydrogen-hydrogen-alkali three-body systems in the adiabatic hyperspherical representation. For the spin-stretched case, there exists a single XXXH molecular state when XXX is one of the bosonic alkali atoms: 7Li^{7}\mathrm{Li}7Li, 23Na^{23}\mathrm{Na}23Na, 39K^{39}\mathrm{K}39K, 87Rb^{87}\mathrm{Rb}87Rb, or 133Cs^{133}\mathrm{Cs}133Cs. As a result, the only recombination process is the one that leads to formation of XXXH molecules, $\text{H}+\text{H}+X\ensuremath{\rightarrow}X\text{H}+\text{H}$, and such molecules will be stable against vibrational relaxation. We have calculated the collision rates for recombination and collision-induced dissociation as well as the elastic cross sections for H+XH\text{H}+X\text{H}H+XH collisions up to a temperature of 0.5 K, including the partial wave contributions from ${J}^{\ensuremath{\Pi}}={0}^{+}$ to ${5}^{\ensuremath{-}}$. We have also found that there is just one three-body bound state for such systems for ${J}^{\ensuremath{\Pi}}={0}^{+}$ and no bound states for higher angular momenta.
A series of metastable states below the $t\ensuremath{\mu}(2s)+d$ threshold have been discovered. The structure of the metastable $dt{\ensuremath{\mu}}_{J\ensuremath{\nu}}$ ion is studied here by the related suitable wave function and using the variational method. Few resonance energies and the related widths for $dt{\ensuremath{\mu}}_{J\ensuremath{\nu}}$ molecular states located below the 2s2s2s threshold are determined. For precise assessment of the reliability of the given wave function, the resonance formation rate is also calculated for the states which take place in the Vesman region. The obtained results are close to those previously reported and give strong indications that the related wave function is good enough to be useful for further calculations.
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Cross sections and rate coefficients for collisions of two spin-polarized metastable hydrogen atoms are calculated at low energies and temperatures using complex scaling and Feshbach projection methods for the determination of the molecular potential-energy curves. The inclusion of the Lamb shift and fine-structure splitting of the excited n=2n=2n=2 atoms leads to an attractive van der Waals potential for two 2s1/2{2s}_{1/2}2s1/2​ atoms with an exceptionally large coefficient. The quenching of the metastable atoms is dominated at temperatures below 20 mK by ionization. The calculated values for the total loss rate coefficient at 87 \ensuremath{\mu}K and 230 \ensuremath{\mu}K are within a factor of 2 or 3 of the error bars of recent measurements of metastable loss rate coefficients.
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