The affinity A_{Ps} of positronium (Ps) atoms for a metal is the negative of the maximum kinetic energy with which Ps is emitted into vacuum when thermalized positrons in a metal encounter the surface. When this quantity is measured by ground state Ps time of flight (TOF), the precision is severely limited by the short triplet state lifetime of 142 ns. By quickly converting the emitted Ps atoms into long-lived Rydberg states, we are able to dramatically increase the TOF to allow precision measurements of A_{Ps}. From our measurements made on a Cu(110) sample at T=128 K, we find A_{Ps}(128 K)=(-2.476±0.010_{stat}±0.013_{syst}) eV, compared with the result A_{Ps}(128 K)=(-2.545±0.010_{num}±0.010_{syst}) eV found using highly accurate generalized gradient approximations for both electrons and positrons within density functional theory. Such precision opens up opportunities in the quest for an improved density functional.
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