Eur. Phys. J. D (2012) 66: 212
https://doi.org/10.1140/epjd/e2012-30272-4

Regular Article

On the bound states in the muonic molecular ions

Department of Chemistry University of Western Ontario, London, Ontario N6H 5B7, Canada

^a e-mail: afrolov@uwo.ca

Received: 25 April 2012
Received in final form: 30 May 2012
Published online: 16 August 2012

Abstract

The mass corrections to the bound state energies of the three-body muonic molecular ions ppμ, pdμ, ptμ, ddμ, dtμ and ttμ are determined numerically from the results of highly accurate computations. The total energies and some other bound state properties of these ions are evaluated to very high accuracy for the bound S(L = 0) − , P(L = 1) − and D(L = 2)-states. In these highly accurate calculations we used the most recent and accurate masses of particles m_p, m_d, m_t and m_μ known from high energy experiments. We also investigate some bound state properties of the muonic molecular ions. In particular, we determine the hyperfine structure splittings of the ground states of the pdμ,ptμ and dtμ ions. In these calculations we used our highly accurate expectation values of the interparticle delta-functions obtained in recent computations. The corresponding hyperfine structure splittings, e.g., Δ₁₂ = 1.3400149 × 10⁷ MHz and Δ₂₃ = 3.3518984 × 10⁷ MHz for the ptμ ion, can directly be measured in modern experiments. Analogous hyperfine structure splittings are evaluated to very high accuracy for all five bound S(L = 0)-states in the three symmetric muonic molecular ions: ppμ, ddμ and ttμ.