Ps trapping in liquids the bubble model

Due to its high zero-point kinetic energy, Ps is supposed to dig a cavity, or bubble in liquids [56, 57]. Various levels of approximation are possible for a quantum mechanical approach to the problem the potential well (of depth U) constituting the bubble may be considered or not as infinite and/or rigid [58-60]. Some typical values of (rigid) well depth and radius are given in Table 4.2 [61] the bubble radius, Rb, remains in a rather narrow range, about 0.3—0.45 nm, independently of the solvent or temperature. 

From the bubble model, it is expected that the o-Ps pick-off decay rate constant should increase with the surface tension. Thus, the following empirical equation [62], later theoretically explicited [63], has been proposed, with (3 = 0.5 for liquid hydrocarbons  

(8) has been quantitatively verified for a large number of solvents [61]. However, at least 3 classes of solvents should be considered [61] more systematic examination of experimental data is required to better understand the reasons for this and settle the applicability of the model. 

For a rigid bubble, the zero-point kinetic energy of Ps is correlated to Rb 2 which is proportional to y l/4. From the expression of the Ps energy level in the bubble, a constant ratio of 0.329 eVl/2 cm1/4 dyn ,/4 is effectively found between the Ps average momentum and y l/4 for a variety of liquids [61], 

Further support to the model should be found by examining the values of F], as deduced from AC or DB measurements since p-Ps annihilates in an intrinsic mode, this parameter should reflect directly the average Ps kinetic momentum. However, the data on F, are usually poorly defined [61, 64], so that the correlation with y is more conveniently sought using experimental values of r3, provided that the momentum distribution of the valence electrons participating in the o-Ps pick-off annihilation is reasonably solvent independent. Such a correlation has been effectively found for a variety of solvents at various temperatures [61], leading to  

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