Antiproton – to – electron mass ratio determined by two-photon laser spectroscopy of antiprotonic helium atoms

The ASACUSA collaboration of CERN has recently carried out two-photon laser spectroscopy of antiprotonic helium atoms. Three transition frequencies were determined with fractional precisions of 2.3–5 parts in 109. By comparing the results with three-body QED calculations, the antiproton-to-electron mass ratio was determined as 1836.1526736(23).


Introduction
Antiprotonic helium (pHe + ) is a three-body atom [1][2][3][4] consisting of a helium nucleus, an electron in the 1s state, and an antiproton occupying a Rydberg state with high principal and angular momentum quantum numbers n ∼ + 1 ∼ 38.The transition frequencies of pHe + have been calculated by QED calculations to fractional precisions of 1 × 10 −9 [5].The calculations included relativistic and radiative recoil corrections up to order m e c 2 α 6 /h, and nuclear size effects.By comparing the measured and calculated transition frequencies, the antiproton-to-electron mass ratio was determined [4] as 1836.1526736(23).

Experiment and results
The two-photon transitions were induced between pHe + states with microsecond and nanosecondscale lifetimes against Auger emission of the electron.After Auger decay, the remaining two-body a e-mail: Anna.Soter@mpq.mpg.depHe 2+ ion [11] was destroyed by Stark collisions with other helium atoms in the experimental target.
The charged pions emerging from the resulting antiproton annihilations were by Cherenkov detectors [12] placed around the target.The two-photon resonance condition between the laser and pHe + was revealed as a sharp spike in the rate of annihilations [Fig. 1 (b)].Two sets of Ti:Sapphire lasers [13] of pulse length 30-100 ns with a spectral linewidth of ∼ 6 MHz and a pulse energy of 50-100 mJ were used to excite the antiprotonic transitions.The system included continuous-wave (cw) lasers whose frequencies were measured to a precision of < 1 × 10 −10 against a femtosecond optical frequency comb [14].
The experiments were carried out at the Antiproton Decelerator (AD) facility of CERN as part of its atomic physics [15] program.The AD provided 200-ns-long pulsed beams, which contained ∼ 10 7 antiprotons of kinetic energy 5.3 MeV.The antiprotons were decelerated to ∼ 70 keV using a radiofrequency quadrupole decelerator [7].Secondary electron emission detectors measured the spatial profiles of the beam [16].The pHe + atoms were produced by stopping the antiprotons in a target filled with 4 He or 3 He gas at temperature T ∼ 15 K and pressure p = 0.8 − 3 mbar.Two horizontally-polarized laser beams of energy density ∼ 1 mJ/cm 2 fired through the target excited the two-photon transitions.
The Cherenkov signal corresponding to some 10 7 pHe + atoms is shown in Fig. 1(b), as a function of time elapsed since the arrival of antiproton pulses at the experimental target.Lasers of wavelengths c/ν 1 = 417 and c/ν 2 = 372 nm were tuned to the two-photon transition (n, ) = (36, 34) → (34, 32), so that the virtual intermediate state lay ∆ν d ∼ 6 GHz away from the real state (35, 33).This arrangement strongly enhanced the transition probability.The annihilation spike which corresponds to the twophoton transition can be seen at t = 2.4µs.The intensity of the spike reflects the number of antiprotons populating state (36, 34) [17,18].When the 417-nm laser was tuned some ∼ 0.5 GHz off the twophoton resonance condition, the signal disappeared as indicated in the same figure.The linewidth (∼ 200 MHz) of this two-photon resonance is more than an order of magnitude smaller than the Doppler-and power-broadened profile of the single-photon resonance (36, 34) → (35, 33) [Fig.2(a)].The two-peak fine structure arises due to the interaction between the electron spin and the orbital angular momentum of the antiproton.We also detected the (33, 32) → (31, 30) and (35, 33) → (33, 31) resonances of p 4 He + and p 3 He + , respectively [Fig.2(c)-(d)].The latter resonance profile contains eight partially-overlapping hyperfine lines, which arose from the spin-spin interactions of the three constituent particles.The spin-independent transition frequencies ν exp were obtained by fitting these measured profiles with a theoretical lineshape (solid lines in Fig. 2) which was determined by numerically solving the rate equations of the two-photon process [10].The positions of the hyperfine lines were fixed to the theoretical values [19], which have a precision of < 0.5 MHz.The experimental transition frequencies ν exp (filled circles with error bars in Fig. 3) agree with the theoretical frequencies ν th (squares) within a fractional precision of (2.3 − 5) × 10 −9 .The calculation uses the fundamental constants compiled in CODATA2002 [20], such as the 3 He-and 4 He-to-electron mass ratios, the Bohr radius, and Rydberg constant.The charge radii of the 3 He and 4 He nuclei give relatively small corrections to ν th of 4 − 7 MHz [5].The correction from the antiproton radius is less than 1 MHz.The theoretical precision of ν th is now mainly limited by the uncalculated radiative corrections of order m e c 2 α 8 /h [5].When the antiproton-to-electron mass ratio M p /m e in these calculations was increased by a relative amount of 10 −9 , the ν th -value changed by 2.3-2.8MHz.By minimizing the difference between ν th and ν exp and considering the systematic errors, we obtained the above antiproton-to-electron mass ratio which yielded the best agreement between theoretical and experimental frequencies.The uncertainty includes the statistical and systematic experimental, and theoretical contributions of 18 × 10 −7 , 12 × 10 −7 , and 10 × 10 −7 .This is in good agreement with previous measurements [21][22][23][24] of the proton-to-electron mass ratio (Fig. 4).Under the assumption that CPT invariance is valid (i.e, M p = M p = 1.00727646677(10) u), we derived a value for the electron mass, m e = 0.0005485799091 (7) u [4].

Figure 4 .
Figure 4. Mass ratio M p /m e determined in this work, compared with M p /m e measured previously [21-24] and the CODATA 2002 value obtained by averaging them.From Ref. [4].