Positronium (Ps = (e(+) e(-))) in synthetic crystalline quartz is investiga
ted 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 anni
hilation photon line caused by the reversal of large magnetic fields applie
d along the spin polarization axis of positrons (e(+)) emitted from a Ge-68
/Ga-68 source. In contrast with other methods. the technique allows the det
ection of Ps in condensed matter even if the Ps-forming e(+) fraction r is
quite small. Moreover, because in single crystals the magnetic field define
s a preferred crystallographic direction, thee-SR technique permits the stu
dy of the anisotropy of the hyperfine interaction of Ps in matter. The theo
ry necessary to deduce the Ps hyperfine tensor from the e(+) SR measurement
s is developed. Room-temperature measurements show that in synthetic quartz
crystals (i) the Ps-forming e(+) fraction is r = 0.15, (ii) the electron d
ensity 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 las
t-mentioned result to the much smaller anisotropy of the muonium hyperfine
interaction is discussed.