Laser excitation of the 1s-hyperfine transition in muonic hydrogen

Abstract

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen (\muμp) with 1 ppm accuracy by means of pulsed laser spectroscopy to determine the two-photon-exchange contribution with 2\times10^{-4}2×10−4 relative accuracy. In the proposed experiment, the \muμp atom undergoes a laser excitation from the singlet hyperfine state to the triplet hyperfine state, {then} is quenched back to the singlet state by an inelastic collision with a H_22 molecule. The resulting increase of kinetic energy after the collisional deexcitation is used as a signature of a successful laser transition between hyperfine states. In this paper, we calculate the combined probability that a \muμp atom initially in the singlet hyperfine state undergoes a laser excitation to the triplet state followed by a collisional-induced deexcitation back to the singlet state. This combined probability has been computed using the optical Bloch equations including the inelastic and elastic collisions. Omitting the decoherence effects caused by {the laser bandwidth and }collisions would overestimate the transition probability by more than a factor of {two in the experimental conditions. Moreover,} we also account for Doppler effects and provide the matrix element, the saturation fluence, the elastic and inelastic collision rates for the singlet and triplet states, and the resonance linewidth. This calculation thus quantifies one of the key unknowns of the HFS experiment, leading to a precise definition of the requirements for the laser system and to an optimization of the hydrogen gas target where \muμp is formed and the laser spectroscopy will occur.

Experimental determination of the energy dependence of the rate of the muon transfer reaction from muonic hydrogen to oxygen for collision energies up to 0.1 eV

“…The ground-state hyperfine splitting of pμ, E hfs ∼ 0.182 eV, turns out to be in the infrared optical range, thus enabling the application of laser spectroscopy techniques. A number of experimental proposals for the measurement of E hfs have been put forward in recent years [42][43][44][45][46][58][59][60]. This was stimulated the need for new data on proton electromagnetic that had become an issue with the proton charge determination from the Lamb shift in muonic hydrogen [61].…”

“…The experimental investigations of (3) in the 1990s led to the two-step model [39] for the rate of the process, which was consistent with the then available data from measurements at room temperature. The interest in the subject was revived a few years later in relation to the projects to measure the hyperfine splitting in the ground state of muonic hydrogen [42][43][44][45][46] and extract out of it the value of the electromagnetic Zemach radius of the proton [47,48]. In a series of advanced theoretical calculations [24,25,29] significant progress was achieved in the quantitative description of the process (3) for energies up to 10 eV, but these theoretical results necessitate experimental verification.…”

Proton and neutron electromagnetic radii and magnetic moments from $N_f = 2 + 1$ lattice QCD

“…which determines the leading-order proton-structure contribution to the 𝑆-state hyperfine splitting (HFS) of hydrogen [24]. A firm theoretical prediction of the Zemach radius is of crucial importance for the next generation of atomic spectroscopy experiments on muonic hydrogen [25][26][27].…”

Muonic-Atom Spectroscopy and Impact on Nuclear Structure and Precision QED Theory

“…There are three collaborations aiming at the measurement of the ground-state HFS in µH: one collaboration at J-PARC (Japan) [67], one at RIKEN-RAL (UK) [68,69], and one at PSI (Switzerland) [70]. Their goal is to measure with 1 ppm accuracy by means of pulsed laser spectroscopy from which precise information about the magnetic structure of the proton can be extracted.…”