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Physical Review A

Muonium-muonium interactions: Binding and scattering

M.-S. Wu, Y. Zhang, Jun-Yi Zhang, Kálmán Varga, Z.-C. Yan

Published Oct 21, 2024• 5 citations
Publisher

Abstract

The study of muonium-muonium binding and scattering is crucial for precision experiments involving muonium. In this paper, we investigate the bound-state energies and structures of the ${(\mathrm{muonium})}_{2}$ molecule for total orbital angular momentum $L=0$ using the non-Born-Oppenheimer variational method combined with explicitly correlated Gaussian basis functions. Additionally, we employ the confined variational method to explore muonium-muonium scattering at scattering momenta below $0.11{a}_{0}^{\ensuremath{-}1}$, where ${a}_{0}$ is the Bohr radius. Our approach provides accurate $S$-wave phase shifts, as well as the $S$-wave scattering length of $3.71{a}_{0}$ using the effective range formula. In this study, the two positive muons and two electrons are considered in a spin singlet state.

DOI
10.1103/physreva.110.042822

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In this paper, we investigate spin-polarized muonium-muonium and spin-polarized hydrogen-hydrogen scattering for total orbital angular momentum L=0L=0L=0 using the non-Born-Oppenheimer confined variational method combined with explicitly correlated Gaussian basis functions. Our approach yielded accurate SSS-wave phase shifts and elastic cross sections at scattering momenta below $0.6{a}_{0}^{\ensuremath{-}1}$, where a0{a}_{0}a0​ is the Bohr radius. By utilizing the effective range formula, we determined the SSS-wave scattering lengths to be 3.70a03.70{a}_{0}3.70a0​ and 1.35a01.35{a}_{0}1.35a0​ for spin-polarized muonium-muonium and spin-polarized hydrogen-hydrogen scattering, respectively.
In this study, we investigate the structural properties of the three-body system $\textmu{}{\text{He}}^{+}$ and the four-body system $\textmu{}\text{He}$ using explicitly correlated Gaussian basis functions with global vectors. Our results quantitatively demonstrate the pronounced shielding effect of the muon on the nucleus and reveal structural characteristics of $\textmu{}{\text{He}}^{+}$ and $\textmu{}\text{He}$, analogous to those of H and ${\mathrm{H}}^{\ensuremath{-}}$, respectively. Using the confined variational method, we examine sss-wave electron scattering from $\textmu{}{\text{He}}^{+}$ at incident energies below 8.7 eV, considering both 1S^{1}S1S and 3S^{3}S3S symmetries of the two electrons. By fitting near-threshold phase shifts to the modified effective range theory, we determine the scattering lengths to be 5.95 a0{a}_{0}a0​ for 1S^{1}S1S symmetry and 1.76 a0{a}_{0}a0​ for 3S^{3}S3S symmetry. Finally, we explore the distortion effects on $\textmu{}{\text{He}}^{+}$ induced by electron impact.
The confined variational method is employed to study low-energy electron collisions with a lithium atom, for energies below the 2p2p2p excitation threshold. The accuracy of the phase shifts has been markedly improved in our calculations. From these calculations, we obtain an electron affinity of 4985.6124 ${\mathrm{cm}}^{\ensuremath{-}1}$, in excellent agreement with experiment, validating the accuracy of the approach. A least-squares fit of the phase shifts to effective-range theory yields an SSS-wave scattering length of A=3.02a0A=3.02{a}_{0}A=3.02a0​, where a0{a}_{0}a0​ is the Bohr radius. These results provide a stringent benchmark for future theoretical and experimental investigations. In this study, the sum of all electron spins is considered to be zero.
Low-energy properties of spin-polarized electron-helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) and spin-polarized positronium-helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) scattering are calculated using the modified confined variational method. To take the van der Waals interaction into consideration, the van der Waals coefficient between positronium and helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) is calculated using the explicitly correlated Gaussian basis. Compared with the ground state noble gases, the larger scattering length and zero pickoff annihilation rate indicates that He(23S)\mathrm{He}(2\phantom{\rule{0.16em}{0ex}}^{3}S)He(23S) may be a more suitable cooling gas. In the energy range we considered, no similarity is found for the SSS-wave cross sections between these two scatterings. A Ramsauer-Townsend minimum is observed in spin-polarized electron-helium(23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) scattering due to the large polarization of metastable helium. This may open a new way to find and study the Ramsauer-Townsend effect.
Positronium-hydrogen (Ps-H) scattering is of interest, as it is a fundamental four-body Coulomb problem. We have investigated low-energy Ps-H scattering below the Ps(n=2) excitation threshold using the Kohn variational method and variants of the method with a trial wavefunction that includes highly correlated Hylleraas-type short-range terms. We give an elegant formalism that combines all Kohn-type variational methods into a single form. Along with this, we have also developed a general formalism for Kohn-type matrix elements that allows us to evaluate arbitrary partial waves with a single codebase. Computational strategies we have developed and use in this work will also be discussed.With these methods, we have computed phase shifts for the first six partial waves for both the singlet and triplet states. The 1S and 1P phase shifts are highly accurate results and could potentially be viewed as benchmark results. Resonance positions and widths for the 1S-, 1P-, 1D-, and 1F-waves have been calculated.We present elastic integrated, elastic differential, and momentum transfer cross sections using all six partial waves and note interesting features of each. We use multiple effective range theories, including several that explicitly take into account the long-range van der Waals interaction, to investigate scattering lengths for the 1,3S and 1,3P partial waves and effective ranges for the 1,3S-wave.
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