Other theories of tunnelling

The interference of Pjo and gives rise to adiabatic tunnelling motion, as is discussed in textbooks. Asymmetry leads to an increase in the frequency of interference by (AEo/h) and a reduction in the amplitude by (AEj-o/AEof. But the interpretation of this motion is uncertain, the uninterrupted interference cannot absorb the energy needed for it to be observed in experiments. Tunnelling interference in the excited states E is used in the old formula  

The textbook formulae for barrier penetration to a free wave on the other side, give wrong results for the two-well potential with left and right states in near resonance. 

The small polaron theories for hydrogen tunnelling in metals assume that the asymmetry A is mostly caused by the H self-trapping energy, which has to be thermally overcome by a dynamic tilting of the potential before instantaneous tunnelling can occur in the coincidence configuration 

But the magnitude of E x is uncertain, and there have been problems in fitting (6.9) to the experimental data . Even recent refined calculations with this approach predict diffusion rates of H in Nb that do not lit case (ii) in Fig. 6.3 too well We believe that the self-trapping energy does not have to be explicitly included in the formulae for tunnelling, since it is the same whether the particle is in the left or the right well. 

Some other theories of tunnelling assume that the two-level system is overdamped by the electrons, and that leads to the surprising predictions that the tunnelling transition rate and the diffusion of H in Nb should vary with T as = 7 - and be extremely fast at 

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