Steps towards the hyperfine splitting measurement of the muonic hydrogen ground state: pulsed muon beam and detection system characterization

Abstract

The high precision measurement of the hyperfine splitting of the muonic-hydrogen atom ground state with pulsed and intense muon beam requires careful technological choices both in the construction of a gas target and of the detectors. In June 2014, the pressurized gas target of the FAMU experiment was exposed to the low energy pulsed muon beam at the RIKEN RAL muon facility. The objectives of the test were the characterization of the target, the hodoscope and the X-ray detectors.The apparatus consisted of a beam hodoscope and X-rays detectors made with high purity Germanium and Lanthanum Bromide crystals. In this paper the experimental setup is described and the results of the detector characterization are presented. * Andrea.Vacchi@ts.infn.it

Two-photon exchange correction to the Lamb shift and hyperfine splitting of S levels

“…1, is a limiting factor extracting radii from the muonic hydrogen spectroscopy [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Moreover, an accurate evaluation of two-photon corrections to hyperfine splitting (HFS) of ground state in electronic hydrogen in combination with an excellent experimental knowledge [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] (known with mHz accuracy) could help to analyse future precise measurements of 1S HFS in muonic hydrogen [41][42][43][44], which aim to decrease an uncertainty of 1S-level HFS from the level of 40 µeV [2] up to the level of 0.2 µeV. Though the two-photon correction is smaller than the modern accuracy of Lamb shift measurements in usual hydrogen, it can affect the precisely measurable 1S-2S transition [45,46] (with the experimental uncertainty 10-11 Hz), as well as the isotope shift [47,48] (with the experimental uncertainty 15 Hz), above the accuracy level of the difference between proton and deuteron charge radii [25,…”

“…We presented the current knowledge of the TPE correction to S energy levels. The Lamb shift results can be useful in future extractions of the isotope shift, while the contributions to the hyperfine splitting can help to tune and analyze forthcoming 1S HFS measurements in µH [41][42][43][44].…”

Hyperfine structure of P states in muonic ions of lithium, beryllium, and boron

“…In the practical use of (31) - (32) , it is convenient to single out the contributions of the symmetric and antisymmetric parts of the projection operators. The general structure of the amplitudes and interaction potentials of particles in these states has the same form as (13), (17), (21), (22), and the intervals of the hyperfine structure themselves are determined by formulas similar to (23):…”

“…Only in the case of simple two particle bound states the theoretical methods are well developed to calculate the energy levels including nuclear effects from first principles. In general, it can be noted that the program for studying muon systems is gaining momentum: a precision study of the ground state hyperfine structure of muonic hydrogen, the energy interval (1S − 2S), and the processes of production of dimuonium are planned [10][11][12][13].…”

Model-independent determination of the two-photon exchange contribution to hyperfine splitting in muonic hydrogen

“…4,TPE from hyperfine splitting in muonic hydrogen The possibility of measuring the hyperfine splitting in muonic hydrogen has be come a reality in recent years: [31][32][33][34]. Actually an experimental number has been given for the 2S hyperfine splitting in ref.…”