Coulombic potential barrier

In this case, the photoionization cross section possesses no Coulomb confinement resonances. This is because the fullerene cation s potential Vcti(r) seen by an outgoing photoelectron does not exhibit a Coulomb potential barrier (see Figure 10 for z = +5 for illustration purposes). 

In the presence of an electric field, E, the Coulomb potential barrier in the downfield direction is lowered and escape from geminate recombination becomes easier. The quantum efficiency for charge generation is then given, to first order in the field, by ... 

Mn +-Mn + state, which demonstrates a small polaron-type conductivity. One very likely reason for such behavior is an ordering of the K ions inside the tunnel structure. Notably, due to the electrostatic interactions, it is expected that K ions will accumulate around less electronegative Mn ions. Such K ion ordering would create a Coulombic potential barrier for hopping, even in the mixed Mn -Mn valence state. It is therefore not surprising that an activated type of behavior would dominate both the conductivity as well as the EPR linewidths. It should also be mentioned that anomalies between 250 and 300 K may be seen in the conductivity, susceptibility and EPR data, but this might be associated with a freezing out of the K+ ion motion in the tunnel. 

The excited n-electron may tunnel through a potential barrier in the free state of the neighbouring molecule preserving the energy. The probability for tunnel transition is as a rule, more than the probability of the returning to the initial state. Apparently the energy of the potential barrier may be considered equal to the molecule ionization potential. The barrier form depends on the coulomb potential between the electron and positive ion and affinity of the neutral molecule. 

To belabor this point, let us consider in more detail a simple case, Refs. [78, 79], where the bound states of the Coulomb potential, through successive switching of a short-range barrier potential, becomes associated with resonances in the continuum. The simplicity of the problem demonstrates that resonances have decisively bound state properties, yields insights into the curve-crossing problem, and displays the tolerance of Jordan blocks. The potential has the form... 

Figure 2.11 3D plot of the Riemann sheet structure of the perturbed Coulomb potential as displayed in Eq (64) with a varying barrier height parameter The imaginary part of Vmax grows toward the viewer. 

Figure 2.12 Display of the first four bound states of the perturbed Coulomb potential, defined in Eq. (64) as a function of varying barrier heights. Note the dotted line above the continuum threshold at zero energy. Taken from Ref. [78] with permission of IJQC.

A.R. Engelmann, M.A. Natiello, M. Hoghede, E. Engdahl, E. Brandas, Association of Bound States of the Coulomb Potential with Resonances of the Coulomb Potential Perturbed by a Barrier, Int. J. Quant. Chem. 31 (1987) 841. 

Figure 2.1 shows the ionization mechanisms for atoms in high intensity laser fields. Non-resonant multiphoton ionization (NRMPI) is expected at an irradiation intensity of around 1013 W cm 2. Optical field ionization (OFI), which comprises tunneling ionization (TI) and barrier suppression ionization (BSI), occurs at an intensity above 1014Wcm 2. The original Coulomb potential is distorted enough for the electron to either tunnel out through or escape over the barrier. The threshold intensity of BSI for atoms can be estimated by (2.1) [14] ... 

A chemical molecule, by contrast consists of many particles. In the most general case N independent constituent electrons and nuclei generate a molecular Hamiltonian as the sum over N kinetic energy operators. The common wave function encodes all information pertaining to the system. In order to constitute a molecule in any but a formal sense it is necessary for the set of particles to stay confined to a common region of space-time. The effect is the same as on the single confined particle. Their behaviour becomes more structured and interactions between individual particles occur. Each interaction generates a Coulombic term in the molecular Hamiltonian. The effect of these terms are the same as of potential barriers and wells that modify the boundary conditions. The wave function stays the same, only some specific solutions become disallowed by the boundary conditions imposed by the environment. 

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