Laser measurements of the density shifts of resonance lines in antiprotonic helium atoms and stringent constraint on the antiproton charge and mass

We have performed laser spectroscopy of metastable antiprotonic helium atoms [Formula Presented] formed in helium media of 0.2–8.0 bars at 5.8–6.3 K and have observed a density dependence of the resonance vacuum wavelengths for the known transitions [Formula Presented] and [Formula Presented] They showed linear redshifts of [Formula Presented] GHz and [Formula Presented] GHz per 1 g/l, respectively. With the shift parameters above, the transition vacuum wavelengths were extrapolated to zero-density limits, yielding [Formula Presented] nm and [Formula Presented] nm, respectively. These values, with a 0.5-ppm precision, were compared with the result of recent theoretical calculations on the energy of the Coulombic three-body system, including relativistic corrections and the Lamb shift. The agreement between our experimental values and the calculations has become as good as [Formula Presented] This excellent agreement in turn provides a precise value of the antiproton Rydberg constant that surpasses the currently known precision and sets a severe constraint on the antiproton charge [Formula Presented] and the mass [Formula Presented] that both [Formula Presented] and [Formula Presented] be less than [Formula Presented] when a more precisely known constraint on the charge-to-mass ratio is combined. Thus we have opened a possibility of determining fundamental constants of the antiproton.