Bohr criterion

The Bohr criterion k I depends on the projectile speed rather than its kinetic energy. This, together with the fact that Zi — l, implies that for electrons or positrons the validity of semiclassical collision theory becomes... 

Straight simulation of collision processes relevant to stopping by solution of the classical equations of motion has been common for about two decades [64]. Although the necessary computational effort is considerable, remarkable results have been found in comparisons with experimental results such as emitted-electron spectra [65]. The main application area of this method refers to very heavy ions at not too high speeds where the Bohr criterion is well satisfied yet relativistic effects are insignificant. 

The values of the parameter y corresponding to experimental dependences of zeff on the charge Z, have been found in Ref. 178. Using the statistical Fermi-Thompson model of an atom, the authors have calculated the velocity distribution of external electrons for atoms of heavy elements. Using the Bohr criterion, they have obtained a formula for zeff of the form (5.7) with the exponent of Z, equal to For this value of y the calculated values of zeff for heavy fission fragments in a hydrogen medium practically coincide with the experimental ones. 

For media more complicated than hydrogen, where the electrons may have different orbital velocities, the Bohr criterion alone is not enough. At present we have no good theory that would explain the influence of a... 

DSO term is very small. However, as we will see latter, the DSO contribution is significant for certain coupling constants and cannot be discarded. Note that our criterion to estimate the order of magnitude of the individual terms is based on an electron in a Bohr orbit of the hydrogen atom. On some occasions this estimate may not give a good indication of the actual magnitude. 

Isosurfaces of electron density are obtained from the probability density isosurfaces for molecules described in Chapter 6. These are surfaces in three-dimensional space that include all the points at which has a particular value. The value of electron density chosen to define the isosurface is selected by some definite, though arbitrary, criterion. There is broad acceptance of a standard density of 0.002 el ao), where is the Bohr radius. This value is thought to best represent the sizes and shapes of molecules because it corresponds to the van der Waals atomic radii discussed earlier in the context of repulsive forces. These are the same dimensions depicted in space-filling models of molecules. 

There is no allowance in this model for more than one electron. Some researchers tried to accommodate the extra electrons by using elliptical orbits, but that didn t work. How do we know it failed We could use the same criterion we used for hydrogen. The question to ask is Can we reproduce the experimental spectrum For multi-electron atoms there are far too many lines of nearly the same wavelength. The Bohr model cannot predict the occurrence of these transitions. We need a new model the new quantum mechanics. We shall use a formulation due to Schrodinger. 

The criterion (43) differs significantly from the Bohr s criterion [8], 17 1, which ensures a small quantum uncertainty of the angle of electron... 

Figure 6(a). Diagram of core as a function of velocity. The critical velocity separating the conical and cylindrical regions is 2.28 X 109 cm./sec. At this velocity the core radius computed from Bohr s criterion for maximum impact parameter is equal to our estimated range of 100 e.v. electrons in water... 

According to the Bohr-Wheeler criterion and an approach of Werner (1997) the mean (Sauter) size d 2 is given by... 

Bohr radius crit Chauvanet s criterion (outlier test)... 

Experiments are not only difficult to perform but also lead to alternative interpretations and consequently controversies (Criterion 3). Davisson-Germer had considerable difficulty in understanding their experimental data before it could be accepted as evidence for wave-particle duality. Even leading scientists (Planck, Bohr) were reluctant to accept the wave-particle duality as it conflicted with some of the predictions based on the previous dominant paradigm, namely the wave theory of light. 

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