We have performed laser spectroscopy of metastable antiprotonic helium atoms (p He ϩ ) 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 (n,l)ϭ(39,35)→(38,34) and (37,34)→(36,33). They showed linear redshifts of 0.61Ϯ0.01 GHz and 0.22Ϯ0.02 GHz per 1 g/l, respectively. With the shift parameters above, the transition vacuum wavelengths were extrapolated to zero-density limits, yielding 0 ϭ597.2570Ϯ0.0003 nm and 0 ϭ470.7220Ϯ0.0006 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 2ϫ10 Ϫ6 . 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 (ϪQ p ) and the mass (M p ) that both ͉Q p ϪQ p ͉/e and ͉M p ϪM p ͉/M p be less than 5ϫ10 Ϫ7 , 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.

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The time evolution of the state populations in the v ϵ n − ᐉ −1=2 and 3 metastable cascades of antiprotonic helium (p 4 He + ) atoms were studied using laser spectroscopy. The antiprotonic states ͑n , ᐉ͒ = ͑39, 35͒, (40,36), and (41,37) in the v = 3 cascade were estimated to initially contain, respectively, ͑0.28± 0.04͒%, ͑0.06± 0.02͒%, and ͑0.02± 0.01͒% of the antiprotons stopped in the helium target, while the corresponding values for states ͑37, 34͒, ͑38, 35͒, and ͑39, 36͒ in the v = 2 cascade were ͑0.21± 0.04͒%, ͑0.49± 0.07͒%, and ͑0.19± 0.07͒%. The shortening of the state lifetimes due to collisions between pHe + and helium atoms was studied. As the atomic density of the target was increased from =2ϫ 10 20 to 2 ϫ 10 21 cm −3 , the lifetime of state ͑37, 34͒ decreased by an order of magnitude, whereas the higher states ͑38, 35͒ and ͑39, 35͒ were relatively unaffected. Between densities =6ϫ 10 20 and 2 ϫ 10 22 cm −3 , a short-lived component with a time constant ϳ 0.2 s appeared at early times in the delayed annihilation time spectrum of pHe + , while the total fraction of long-lived antiprotons decreased from 3.0 to 2.5%. These effects were caused by the lifetime-shortening of specific pHe + states such as ͑37, 34͒.

A laser spectroscopic method was developed to directly observe the lifetimes of individual states in metastable antiprotonic helium atoms ( p 4 He ϩ ). Collisional effects with surrounding helium atoms were studied in cryogenic gas targets at pressures between 0.1 and 9.0 bars and at temperatures between 5.5 and 7.0 K. The metastable state (n,l )ϭ(39,35) showed a lifetime of 1.5 s, regardless of density, whereas the lifetime of the energetically lower-lying state (37,34) was found to shorten from 1.3 to 0.1 s with increasing density. The lifetimes of the states (38,34) and (36,33) were determined to be 10 ns and 5 ns, respectively, showing the effects of the internal Auger process. When extrapolated to zero density, the measured lifetimes agreed with the results of calculations for the radiative and Auger widths. Using the fact that the state (37,34) becomes short lived at high density, the resonance (38,35)→(37,34) at 529.62 nm was detected.