The triplet state of helium can bind a positron to form a quantum halo state with a nonrelativistic binding energy of only about 0.6 mhartree. Owing to its extremely weakly bound nature, evaluating relativistic corrections to the binding energy is essential for confirming its stability beyond the nonrelativistic limit. In this work we first examine the nonrelativistic structural properties of positronic metastable helium using a highly accurate variational expansion constructed from explicitly correlated Gaussian basis functions. Our results show that the system is remarkably diffuse and meets the established criteria for a quantum halo state. Using the resulting high-accuracy nonrelativistic wave function, we then compute the relativistic corrections within the framework of perturbation theory. The calculations indicate that the system remains bound even after including relativistic effects. Notably, the relativistic corrections to the bound and dissociated states largely cancel, yielding a net change in the binding energy of less than 4%. Finally, we evaluate the annihilation rates and lifetimes of both the quartet and doublet states. We find that the quartet state has a significantly longer lifetime because the positron and all electrons are aligned in a spin-triplet configuration, making three-photon annihilation the dominant decay channel.

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• Atomic & molecular structure
• Electron & positron scattering
• Electron correlation calculations for atoms & ions
• Exotic atoms & molecules
• Ab initio molecular dynamics