Positronium emission spectra from self-assembled metal-organic frameworks

Results of positronium (Ps) emission into vacuum from self-assembled metal-organic frameworks (MOFs) are presented and discussed in detail. Four different MOF crystals are considered, namely, MOF-5, IRMOF-8, ZnO4(FMA)(3), and IRMOF-20. The measurements reveal that a fraction of the Ps is emitted into vacuum with a distinctly smaller energy than what one would expect for Ps localized in the MOFs' cells. Only calculations considering the Ps delocalized in a Bloch state can reproduce the measured Ps emission energy providing a robust demonstration of wave function delocalization in quantum mechanics. We show how the Bloch state population can be controlled by tuning the initial positron beam energy. Therefore, Ps in MOFs can be used both to simulate the dynamics of delocalized excitations in materials and to probe the MOFs for their advanced characterization.