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Theor. Phys. 56 (1969) 1278. 25. R. R. Dogonadze, A. A. Kornyshev, Phys. Status Solidi B53 (1972) 439. 26. A. A. Kornyshev, M. A. Vorotyntsev, H. Nielsen, J. Ulstrup, J. Chem. , Faraday Trans. 78 (1982) 217. 27. P. Ha¨nggi, P. Talkner, M. Borkovec, Reaction-Rate Theory: Fifty Years After Kramers, Rev. Mod. Phys. 62 (1990) 251. 28. V. I. Gol’danskii, L. I. Trakhtenberg, V. N. Flerov, Tunneling Phenomena in Chemical Physics, Gordon and Breach, NY, 1989. 29. I. M. Bystriak, G. I. Likhtenshtein, A.

It is assumed the temperature is so low that: & ' _o Er _o ¯ ¯ 441; 44 exp . (31) kT kT _o ¯ As it follows from these inequalities, the argument of Bessel’s function in the expression (21) is very small, and cothð_o=2kTÞ % 1. The resulting formula ¯ ~ can be deduced, if we take into account that DE=_ o ¯ ¼ p, where p is integer and I p ðxÞ ¼ I Àp ðxÞ [14], 8 ÀEr =_o À Áp 9 Er e < = ; p40 2 ¯ p! _ o ~ ~ TÞ ¼ 2pjV if j eÀB=4 À Á . (32) Â W ðDE; ~ : eÀEr =_o E¯r p eDE=kT ; po0 ; _2 o ¯ p! _o The ground states of the vibration modes are only populated at low temperatures.

37 38 44 48 54 63 64 In this chapter, a description is provided on how to determine the electron component of the transition amplitude (electron tunneling amplitude) for multielectron systems. The electron Green’s function determines the distance dependence of the electron matrix element. The influence of crystal media on Green’s function is examined. The effect of the intermediate particles on electron tunneling will be considered within the framework of electron sub-barrier scattering to adequately describe the bridge effect.

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