Theoretical transition frequencies beyond 0.1 ppb accuracy inH2+,HD+, and antiprotonic helium

Abstract

We present improved theoretical calculations of transition frequencies for the fundamental transitions (L = 0, v = 1) → (L = 0, v = 0) in the hydrogen molecular ions H + 2 and HD + with a relative uncertainty 4 · 10 −11 and for the two-photon transitions in the antiprotonic helium atom with a relative uncertainty 10 −10 . To do that, the one-loop self-energy correction of order α(Zα) 6 is derived in the two Coulomb center approximation, and numerically evaluated in the case of the aforementioned transitions. The final results also include a complete set of other spin-independent corrections of order mα 7 . The leading order corrections of α 2 ln 3 (Zα) −2 (Zα) 6 are also considered that allows to estimate a magnitude of yet uncalculated contributions.

High-precision spectroscopy of the HD+ molecule at the 1-p.p.b. level

“…For example, the theoretically determined value of the HD + (v, L):(0, 2)→(8, 3) transition frequency, ν th , is 383,407,177.150 (15) MHz and has a relative uncertainty of 4 × 10 −11 [1,2]. Note that the specified error (within parentheses) does not include the uncertainty of the fundamental constants used.…”

“…Here Q (0) and Q (2) are the irreducible scalar and tensor components that belong to the two-photon operator (in atomic units):…”

“…Because of their relative simplicity, molecular hydrogen ions such as H + 2 and HD + are benchmark systems for molecular theory [1,2], and suitable probes of fundamental physical models [3,4]. Already four decades ago, Wing et al [5] performed measurements of ro-vibrational transitions in HD + and conjectured that such measurements could be used to test quantum electrodynamics (QED) theory in molecules and lead to an improved value of the proton-to-electron mass ratio, μ.…”

“…Already four decades ago, Wing et al [5] performed measurements of ro-vibrational transitions in HD + and conjectured that such measurements could be used to test quantum electrodynamics (QED) theory in molecules and lead to an improved value of the proton-to-electron mass ratio, μ. Today, QED corrections to ro-vibrational transition frequencies in H + 2 and HD + have been calculated up to the order m e α 8 , with m e the electron mass and α the fine-structure constant, leading to relative uncertainties of the order of 3-4 × 10 −11 [1,2]. The frequencies of these transitions are typically in the (near-) infrared with linewidths below 10 Hz, which makes them amenable to high-resolution laser spectroscopy.…”

Precision measurements and test of molecular theory in highly excited vibrational states of H2 (v = 11)

“…For the H + 2 and HD + ions, extensive efforts by Korobov and co-workers over the years, have recently led to the theoretical determination of ground electronic state level energies at 0.1 ppb accuracies [12]. The latter accuracy enables the extraction of the proton/electron mass ratio, m p /m e , when combined with the recent HD + spectroscopy using a laser-cooled ion trap [13].…”