Amplitude of Electron Tunneling Transfer

The term tunneling transition may be applied to this case, if the acceptor is placed in the asymptotic underbarrier region of the wave function of the initial state on the donor, and vice versa, the donor is placed in the asymptotic region of the acceptor. It will be shown that the amplitude of such tunneling transition is denoted by the values of the donor and acceptor wave functions in the corresponding asymptotic regions near the acceptor and donor, out of the main region of electron localization (MREL) [2-4]. 

In the beginning, let us examine for simplicity the one electron center-donor. The interaction of the donor with tunneling electron can be described by the sum of the short-range potential t/ (r) and Coulomb attractive potential Vo(r) — — jr where r is the distance from the donor center (here and below in this chapter it is used the atomic units). It means that far from the donor, the donor-positive ion interacts with the electron, so the donor is neutral in the initial state. The total donor potential is 

Coulomb s interaction of the electron with the donor ion residue may be picked out at r r0 only where rQ is the radius of the ion residue, but such division of the total potential proves convenient at all values of the radius r. 

Hamiltonian H of the system which contains the electron + the donor ion residue is written down in the form  

Schrodinger equation corresponding to Hamiltonian II for the wave function /D(r E) of the initial state of electron on the donor 

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The amplitude of electron tunneling transfer with simultaneous change of the vibrations in the case of the non-adiabatic asymptotics (56) may be found, if to substitute the expression (56) instead of F ) to the definition (9) and the acceptor wave function in the matrix element (9) should be its total expression... 

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