Free Volume Model and Positronium Lifetime Connection

Free Volume Model and Positronium Lifetime Connection 

A simplified theory was proposed by Brandt, Berko and Walker [104] in which the positron of Ps wave function in the field of the electron was replaced by the wave function of the Ps atom. The Ps wave function was then calculated for different lattice structures in the Wigner-Seitz approximation. This approximation is generally referred to as the free volume model, since the free volume is used as one of the parameters in the calculation. This model relates o-Ps lifetime to the average free volume hole size of the medium, and results construed that the o-Ps lifetime would measure the lattice-Ps interaction. Later, Tabata et al. [105] and Ogata and Tao [106] each adopted similar - but different - approaches by considering a unit cell and Ps located at the center instead of the center of the molecule, as used by Brandt et al. [104]. 

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