Accurate Determination of the Scattering Length of Metastable Helium Atoms Using Dark Resonances between Atoms and Exotic Molecules

We present a new measurement of the s-wave scattering length a of spin-polarized helium atoms in the 2 ³S₁ metastable state. Using two-photon photoassociation spectroscopy and dark resonances, we measure the energy Eᵥ₌₁₄=-91.35±0.06 MHz of the least-bound state $v=14$ in the interaction potential of the two atoms. We deduce a value of a=7.512±0.005 nm, which is at least 100 times more precise than the best previous determinations and is in disagreement with some of them. This experiment also demonstrates the possibility to create exotic molecules binding two metastable atoms with a lifetime of the order of 1 μs.