Threshold behaviour

The near-threshold behaviour of the positronium formation cross section has also been investigated for O2 (Laricchia, Moxom and Charlton,... 

Read, F.H. (1985). Threshold behaviour of ionization cross sections. In Electron Impact Ionization, eds. T.D. Mark and G.H. Dunn (Springer-Verlag) pp. 42-88. 

M. Gailitis, R. Damburg, The influence of close coupling on the threshold behaviour of cross sections of electron-hydrogen scattering, Proc. Phys. Soc. (London) 82 (1963) 192. 

The characteristic threshold behaviour of conductive composites is an unsatisfactory feature for many applications, both because the poor mechanical properties incurred at concentrations where conduction is obtained cannot be tolerated, and because the high level of conductivity above the threshold is not required or even not desirable. Thus a common requirement is for an antistatic material which has good plastics properties, sufficient conductivity to allow charges to leak away, and sufficient resistivity to prevent dangerous shocks to personnel who may become accidentally connected to mains electrical supplies through it. Unfortunately, the very steep slope of the conductivity versus filler concentration curve in the region of the threshold makes it very difficult to manufacture materials with reliable intermediate conductivities. 

It is demonstrated in the following section that quantum calculations in large basis sets are able to reproduce qualitatively the threshold behaviour of the ionization curves. This demonstrates that there is no mystery beyond quantum mechanics hidden in the experimental results. But although numerical quantum calculations reproduce the experimental results adequately, they are limited in that they do not provide us with any insight into the physical mechanisms responsible for the occurrence... 

Isotopic variations of H + H2, obtained by replacing hydrogens by deuteriums, were considered (Wu et al., 1973a) within a different computational scheme (Johnson, 1972) and, in connection with threshold behaviours and resonances for varying isotopic combinations. No significant reaction probabilities were found for total energies below the static barrier potential V s). One-dimensional barriers provided reasonable probabilities only... 

Walker and Wyatt (1972) have also performed a distorted-wave calculation for H + H2, based on the Porter-Karplus surface. They constructed reactant and product distortion potentials assuming adiabatic vibrational motion in each case, and obtained numerical solutions for the relative motions. Their results show that by choosing adequate potential parameters it is possible to reproduce the threshold behaviour, but that probabilities grow above unity soon after the threshold energy. 

In connection with the endoergicity of the processes which we are studying here, one problem remains to be discussed, viz. the threshold-behaviour of the total inelastic cross sections. This problem will turn out to be important because from the experimental threshold, information about the electron affinity can be obtained. 

In order to see the threshold behaviour of such a reaction and its marked contrast with the exothermic dissociative charge transfer, the cross-section curves for the two reactions... 

One of the nice aspects of classical variational TST is that the theory provides upper and lower bounds to the exact classical rate of reaction. To date, there is no such quantal theory. Quantally, transition state theory is an approximation - one of the objectives of the theorist is to optimize the approximation. The concept of a transition state remains though as an important guide towards understanding the quantal structure of the reaction probability. In this section we shall see that quantal barriers and wells and their associated properties determine both threshold behaviour and resonance phenomena in quantal reactive scattering. 

Photoelectrons released from a surface by light impact have very low kinetic energy, and thus they only travel any appreciable distance in a high-vacuum environment. The photoelectric effect exhibits threshold behaviour, i.e. light below a certain frequency, which depends on the material of the cathode being exposed, will not result in the emission of electrons, regardless of how high the irradiance is. 

Hutson, J.M., Feshbach resonances in ultracold atomic and molecular collisions threshold behaviour and suppression of poles in scattering lengths. New J. Phys., 9, 152, 2007. 

Hutson, J.M., Feshbach resonances in ultracold atomic and molecular collisions threshold behaviour and suppression of poles in scattering lengths. New. J. Phys., 9,152,2007. Maussang, K., Egorov, D., Helton, J.S., Nguyen, S.V., and Doyle, J.M., Zeeman relaxation of Cap in low temperature coUisions with heUum, Phys. Rev. Lett., 94, 123002, 2004. 

The r mass was first determined from the threshold behaviour of the cross-section (14.1.1). FVom (14.1.1) the quantity... 

In view of the findings of Knudsen et al. [3.45], it seems worthwhile to readdress the question of the near-threshold behaviour of the single-ionization cross section for positron impact on atoms and molecules. 

This discrepancy is in line with other observed quantitative discrepancies such as in the threshold behaviour when a stochastic component is present in the applied voltage [96]. As already mentioned, the most drastic non-standard behaviour, which is not understood from the SM, is the observed Hopf bifurcation in sufficiently thin and clean specimens [18, 41-43, 49-51] and the very small hysteresis sometimes observed at threshold [38-40, 47], In fact a little further above threshold (but still near it) the amplitude of the pattern does appear to coincide reasonably with the results of the weakly non-linear theory [59],... 

The above three critical fields He in equations (3.126), (3.140) and (3.143) give the classical results for measurements of the three Prank elastic constants Ki, K2 and Kz. Notice that K and K3 both contribute to the post-threshold behaviour in the splay and bend geometries. The constant K4 is not amenable to these set-ups. 

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