Observation of Long-Lived Muonic Hydrogen in the2SState

Abstract

The kinetic energy distribution of ground state muonic hydrogen atoms µp(1S) is determined from time-of-flight spectra measured at 4, 16, and 64 hPa H2 room-temperature gas. A 0.9 keVcomponent is discovered and attributed to radiationless deexcitation of long-lived µp(2S) atoms in collisions with H2 molecules. The analysis reveals a relative population of about 1 %, and a pressuredependent lifetime (e.g. 30.4 +21.4 −9.7 ns at 64 hPa) of the long-lived µp(2S) population, equivalent to a 2S-quench rate in µp(2S)+H2 collisions of 4.4 +2.1 −1.8 × 10 11 s −1 at liquid hydrogen density.PACS numbers: 36.10. Dr, 34.20.Gj A measurement of the Lamb shift in muonic hydrogen, i.e. the energy difference of 0.2 eV between the 2P -and 2S-states of µ − p atoms [1,2,3], is in progress at the Paul Scherrer Institute (PSI), Switzerland [4]. Vacuum polarization shifts the 2S-levels by 0.2 eV below the 2P -levels; fine and hyperfine splittings of the n = 2 levels are much smaller. The finite size effect is 2 % of the Lamb shift.The µp Lamb shift experiment is expected to give a precise value for the root-mean-square charge radius of the proton [5]. Together with recent advances in H-atom spectroscopy [6,7], this leads to a better determination of the Rydberg constant, and to a test of bound-state quantum electrodynamics on a new level of precision [8].The most important prerequisite for such an experiment, the availability of sufficiently long-lived µp(2S) atoms, has so far not been experimentally established. When muons are stopped in H 2 gas, µp atoms are formed at high n-levels and then deexcite predominantly to the ground state ("muonic cascade"). A fraction ε 2S of a few percent reaches the metastable 2S state whose lifetime is, in absence of collisions, essentially given by the muon lifetime of 2.2 µs.In a gas, there is collisional 2S-quenching, with very different rates depending on the µp kinetic energy being above or below the 2S-2P threshold (≈ 0.3 eV in the lab frame) [9]. Most µp(2S) atoms are formed at energies above this threshold [10], where collisional 2S → 2P Stark transitions (followed by 2P → 1S radiative deexcitation) lead to rather fast 2S-depletion. This is the "short-lived" 2S-component with a predicted lifetime [11] τ short 2S∼ 100 ns/p H2 [hPa]. There is, however, a competition between such Stark transitions and deceleration [9]. A fraction of the µp(2S) atoms should therefore survive the process of slowing down below 0.3 eV, where transitions to the 2P state are energetically forbidden. These µp(2S) atoms form the "long-lived" 2S-component, with a lifetime τ long 2S and a population ε long 2S (per µp atom).The 2S-population ε 2S is well determined from the measured µp X-ray yields [12,13,14]. ε long 2S can be derived from the measured 1S kinetic energy distributions [15] by using calculated elastic and inelastic µp(2S) cross sections [9]. At 16 hPa, for example, ε 2S = (4.40 ± 0.17) % and ε long 2S = (1.16 ± 0.12) %. Calculations of the radiative quenching process during collisions [16,17,18] predicted v...

The size of the proton from the Lamb shift in muonic hydrogen

“…The first 2S-lifetime measurements in μp were proposed at Columbia University (USA) already in 1971, but the crucial existence of the so-called long-lived 2S component could only be verified by our group three decades later [14,15]. In the 1980s, the aim of the Lamb shift experiment changed from testing vacuum polarization terms towards the determination of the proton charge radius.…”

Is the proton radius a player in the redefinition of the International System of Units?

“…keV) has been designed and built at the Paul Scherrer Institute to efficiently stop muons at this ultra-low gas pressure within the small target volume required for efficient laser excitation. At 1 hPa, the lifetime of the 2S metastable state is around 1 ms [29,30]. Many details of this muon line can be found in [28,[33][34][35][36][37].…”

“…Radiative and collisionally induced de-excitation processes bring it down to the 2S or 1S state within a few nanoseconds (figure 1). This cascade has been carefully studied [28], especially the collisional quenching of the 2S state [29][30][31]. Ninety-nine per cent of atoms decay to the 1S state, producing a large 2 keV fluorescence early peak.…”

Laser Spectroscopy of Muonic Atoms and Ions

“…In a gaseous environment like H 2 , D 2 , He, etc., collisional effects may shorten the 2S lifetime [8]. Thus, our recent experiments in muonic hydrogen [9,10], muonic deuterium [11] and muonic helium ions [12,13] were performed at gas pressures around 1 hPa, where the 2S lifetimes are on the order of 1 µs [3,14]. Fig.…”