Wigner function generalized model

From the point of view of principles, it is interesting to note that the method based on the generalized form of Eq. III. 129 seems to be very closely connected both with Wigner s classical theory described in Section III.B and with Bohm and Pines plasma model (Krisement 1957). Following Krisement, we will replace the various trial functions flt /2,. . ., fn in Eq. III.9 by a single average function /, and Wigner s basic wave function (Eq. II1.7) takes then the simple form... 

Putting Wigner s theory in the simplified form (Eq. III. 130), Krisement was able to compare it with the results of the plasma model where, in a first approximation, Pines wave function may be written in the generalized form (Eq. III. 129) with... 

Davis and Oppenheim examined the validity of the IBC model from the point of view of quantum statistical mechanics using a generalized Wigner distribution function. They thus avoided the weak coupling approximation used by both Fixman and Zwanzig. They pointed out an inconsistency in Herzfeld s argument, since if a molecule undergoes a... 

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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