Logarithmic barrier function

The dependence of the logarithm of the tunneling current with respect to distance is a measure of the work function, or the tunneling barrier height (Garcia, 1986 Coombs and Pcthica, 1986). In fact, from Eq. (1.12),... 

Figure 14.11. Logarithm of the ratio of the cross sections (Tn,f and for various nuclides of the actinides as a function of the difference between the neutron binding energy B(n) and the energy barrier of fission E. (According to G. T. Seaborg The Transuranium Elements. Yale University Press 1958 Addison-Wesley Publ. Comp, Reading, Mass., S, 166/167 S. 240/241.)...

Another way of examining the mechanism of proton transfer is by comparing its temperature dependence with that of other monoatomic cations. Plots of the molar conductance of three cations, namely, H, Li, and K, on a logarithmic scale are shown as a function of reciprocal temperature in the range 5-55°C in fig. 6.14. Excellent linear plots are found from which an energy barrier associated with the process may be calculated. Using a simple Arrhenius expression, the temperature dependence of X,- for a small temperature interval is given by... 

Fig. 2. Cross-section and astrophysical S-factor for charged particle reactions as a function of beam energy. The effective range of energy in stellar interiors is usually far less than the Coulomb barrier energy Ec or the lower limit El of laboratory measurements. The y-scale is logarithmic for cross-section but linear for S-factor thus the cross section drops sharply in regions of astrophysical interest, while the change is much less severe for the S-factor. The extrapolation of laboratory data to lower energies relevant for astrophysical situations is more reliable for S-factor...

The orbiting effect which arises from collisions where the particle is kept spiralling around the other particle due to the potential barrier from the centrifugal part of the potential. This is a resonance behaviour and the deflection function displays a logarithmic singularity. 

A further barrier to corrosion reactions is provided by electrical resistance. When the anodic and cathodic reactions at the metal surface take place with locally different current densities, resistance in the current circuits can cause a measurable drop in potential (resistance polarization). This resistance polarization is a linear function of the current. Resistance polarization frequently arises through the formation of passive films. The resulting relationship between the change in potential and the current usually no longer follows Ohm s law, but instead is subject to a logarithmic relationship. 

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