According to our current theoretical understanding, two muonium atoms cannot undergo nuclear fusion to form a helium-like atom. Muonium is a short-lived exotic atom consisting of a positive muon (μ+) and an electron (e-) bound together. It is similar to a hydrogen atom but with a muon replacing the proton.
Muons are elementary particles with a mass 207 times greater than that of an electron. They are unstable and have a relatively short lifetime of around 2.2 microseconds. As a result, muonium atoms are also short-lived and quickly decay into other particles.
Nuclear fusion, on the other hand, involves the combination of atomic nuclei to form a heavier nucleus. In the case of helium-like atoms, fusion occurs between two hydrogen nuclei (protons) to produce a helium nucleus. This process releases a significant amount of energy.
In the case of muonium atoms, fusion is not possible because muons are not stable enough to participate in a nuclear fusion reaction. Muons decay into an electron and two neutrinos through the weak interaction, with a lifetime too short to enable fusion reactions to take place.
Therefore, muonium atoms cannot fuse to form a helium-like atom, and there would be no positive energy gain associated with such a hypothetical fusion process.