Search for the 2S-2Penergy difference in muonicHe4ions

We searched for laser-induced 2${\mathit{S}}_{1/2}$-2${\mathit{P}}_{3/2}$ transitions in (${\mathrm{\mu }}^{\mathrm{-}}$ ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ${)}^{+}$ ions at low pressure (4.1 kPa), where we determined a 2S lifetime of 1.014±0.121 μs from the simultaneously measured 2S→1S two-photon transitions. In contrast to a similar experiment in He gas of 40 bar (4×${10}^6$ Pa) reported by Carboni et al. [Nucl. Phys. A278, 381 (1977)], which was based on the questionable metastability of the 2S state at that pressure, we found no resonance effect at the wavelength λ=811.7 nm. We can reject this wavelength with a confidence level of less than 2×${10}^{\mathrm{-}3}$, and the interval 811.4≤λ≤812.0 nm with a greater than 95% probability.