Positronium Bloch Function, and Trapping of Positronium in Vacancies, in Ice

Positron annihilation techniques (PAT) were used to study the behaviour of positronium (Ps) in pure H,0 and D-0 ice in the temperature interval -185 < t < 2°C. At temperatures below roughly -100°C, the linear-slit angular correlation curves consisted of a broad component (fwhm = 10.5 mrad), resulting from free positron and Ps pick-off annihilation, and narrow central and side peaks (fwhm = 1 mrad), resulting from intrinsic paraPs annihilation from a center-of-mass Bloch-function state.

At higher temperatures there also occurred a middle-broad component (fwhm - 3.9 mrad) resulting from intrinsic para-Ps annihilation from a localized Ps state. Positron lifetime measurements on pure ice gave an ortho-Ps pick-off lifetime of 0.66 nsec at low temperatures, which above -100°C increased to about 1.0 nsec at the melting point, in agreement with previous measurements.

This increase in ortho-Ps lifetime and the middle-broad angular correlation component are believed to be caused by Ps trapping by temperature created vacancies. A weak long-lifetime component ( t»2 nsec) present at higher temperatures is ascribed to Ps trapping in divacancies. The theory of the 2-Y annihilation of a Ps many-electron system is discussed.

Two new "exchange" terms in the annihilation probability were derived, and it was shown that the para-Ps pick-off annihilation rate is smaller than that of ortho-Ps. The square of the numerical value of the Fourier transform at various reciprocal lattice points of the Ps Bloch function, |a_| , was extracted by very detailed computer analyses.

A nearfy-free-Ps theory, taking into account the influence of phonons, could not explain the temperature dependence of |a_| . The Ps trapping in vacancies could not be explained9in detail in terms of several models, including the simple "trapping model". The main difficulty was the fact that para-Ps and ortho-Ps are trapped at roughly the same amount at a certain vacancy concentration.

Our results imply a high (several ppm) vacancy concentration at the melting point in ice in agreement with other independent estimates. This fact might introduce pronounced changes in currently accepted theories of the electrical properties of ice.