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Modification of Tao-Eldrup model

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Since 20 years the relation between ortho-positronium lifetime and free volume size has been determined using the Tao-Eldrup model [1,2]. It assumes that ortho-positronium trapped inside the spherical free volume(represented by rectangular potential well) may decay spontaneously by three quantum annihilation or by pick-off process.

The Tao-Eldrup model was elaborated for small free volumes, like vacancies in solids, voids in polymers, bubbles forced by Ps in liquids. In that case the spacings of energy levels in small voids are much larger than thermal energy kT and thus only the lowest level is populated. In order to simplify the calculations, the well of finite depth is substituted by infinitely deep one but broadened by Δ, which is needed to reproduce the value of the probability to find o-Ps outside the potential well in finite well depth and radius R [2,3].

The Tao-Eldrup model describes well the o-Ps annihilation in small voids at low temperatures. The limitations of this approach can be avoided including in the calculations the contribution of excited states in the well [4,5]. Retaining the spherical free volume geometry is the simplest extension of the Tao-Eldrup model. The pores are usually described as capillaries (infinitely long cylinders). For such a geometry some modifications in the model are also needed. Some results of calculations made using described above models are presented in

'Positronium lifetime vs. temperature and free volume size tables. Pick-off model calculations.' [R. Zaleski, 'EL-Press', Lublin (2002)]

[1] S.J. Tao, J. Chem. Phys. 56, 5499 (1971)
[2] M. Eldrup, D. Lightbody, J.N. Sherwood, Chem. Phys. 63 (1981) 51
[3] H. Nakanishi, Y.C. Jean in D.M. Schrader, Y.C. Jean, Positron and Positronium Chemistry, Elsevier, Amsterdam, 1998
[4] T. Goworek, K. Ciesielski, B. Jasińska, J. Wawryszczuk, Chem. Phys. 230 (1998) 305-315
[5] K. Ciesielski, A.L Dawidowicz, T. Goworek, B. Jasińska, J. Wawryszczuk, Chem. Phys. Lett. 289 (1998) 41-45