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AbstractThe electric field surrounding a single positron in a metal is screened by an increase in the local electron density which, in the case of nearly free-electron metals (like Al, Na, etc.), has a radial distribution similar to that of the electron in positronium (Ps). In such metals, a singlet pair of positrons would experience an attractive interaction and at low enough electron densities could possibly form a bound state that is held together by exchange and correlation energies, thus forming structures analogous to that of the positronium molecule (Ps$$_2$$ ${}_2$), with binding energies of a few tenths of an eV. Such di-positrons could be prevalent at positron densities of around 10$$^{18}$$ ${}^{18}$cm$$^{-3}$$ ${}^{-3}$and, if so, would be evident from an apparent broadening of the sharp step at the Fermi surface in measurements of the electron momentum distribution by the angular correlation of the 2$$\gamma $$ $\gamma$annihilation radiation. Even if di-positrons are not directly formed in a metal, optical spectroscopy of Ps$$_2$$ ${}_2$formed in vacuum via pairs of positrons simultaneously being emitted from the surface could be applied to the direct measurement of the momentum distribution of Cooper pairs. If they exist, di-positrons in metals would yield interesting information about electron and positron interactions and at very high densities might allow the study of a di-positron Bose–Einstein condensate immersed in an electron gas. Graphic Abstract 

AbstractThe quest for making a triplet positronium (Ps) Bose–Einstein condensate confined in a micron-sized cavity in a material such as porous silica faces at least three interrelated problems: (1) About$$10^7$$ ${10}^7$spin polarized Ps atoms must be injected into a small cavity within a porous solid material without vaporizing it. (2) It is known that Ps atoms confined in 30–100 nm diameter cavities in porous silica do not remain in the gas phase, but become stuck to the cavity walls at room temperature (Cooper et al., Phys. Rev. B 97:205302, 2018). (3) Cooling a gas of Ps atoms to cryogenic temperatures by energy exchange with the walls would be a very slow process (Saito and Hyodo, in: Surko, Gianturco (eds) New Directions in Antimatter Chemistry and Physics, Springer Dordrecht, Netherlands, 2001) because of the relatively low collision rate with the walls and the large mismatch between the masses of the Ps and the wall atoms. A possible solution of these difficulties is presented, based on cooling the implanted positrons in an isotopically pure diamond single crystal target, subsequent saturating of the wall Ps coverage so that a substantial portion of the Ps will be in the gaseous state, and thermalizing the gas-phase Ps via collisions with the low effective mass wall Ps. A design process for the target material is outlined as well, including preliminary results in porous cavity fabrication using focused ion beam milling. Graphical abstract