Anisotropic positronium in crystalline quartz

Abstract

Positronium (Ps = (e⁺ e⁻)) in synthetic crystalline quartz is investigated by means of the positron spin relaxation (e⁺SR) technique. The set-up employed measures the change in the Doppler broadening of the 511 keV annihilation photon line caused by the reversal of large magnetic fields applied along the spin polarization axis of positrons (e⁺) emitted from a ⁶⁸Ge/⁶⁸Ga source. In contrast with other methods, the technique allows the detection of Ps in condensed matter even if the Ps-forming e+ fraction r is quite small. Moreover, because in single crystals the magnetic field defines a preferred crystallographic direction, the e⁺SR technique permits the study of the anisotropy of the hyperfine interaction of Ps in matter. The theory necessary to deduce the Ps hyperfine tensor from the e⁺SR measurements is developed. Room-temperature measurements show that in synthetic quartz crystals (i) the Ps-forming e⁺ fraction is r = 0.15, (ii) the electron density at the e⁺ in Ps is about 0.3 of the vacuum value and, (iii) the Ps hyperfine interaction is strongly anisotropic. The relationship of the last-mentioned result to the much smaller anisotropy of the muonium hyperfine interaction is discussed.