Kinematical effects

In heavy-particle collisions it is often not the resolving power of the electron spectrometer that limits the accuracy with which structures in ejected electron spectra can be measured, but the Doppler effect broaden-ings and shifts of the electron peaks severely influence the spectra and have to be taken into account in the analysis, or to be avoided by special means in the experimental setup. Since electron spectra due to heavy-particle collisions are treated in some detail in the following sections, we will briefly discuss the various kinematical effects. 

An electron, emitted with a velocity v with respect to the emitter, which in turn moves at a velocity V in the laboratory, will have a velocity v = Ve + V and a corresponding energy of 

An additional broadening of electron peaks is caused by the fact that, after a collisional excitation process, the electron-emitting atoms do not move into one well-defined direction. If they are scattered (or recoiled) at an angle (0, ) with respect to the projectile beam direction, and the electrons are detected at p), Eq. (3) can be written more precisely as 

Gordeev and Ogurtsov were the first ones to point out that the term b cos p - t ) in Eq. (S) is responsible for a considerable peak-broadening if there is no selection of the azimuth angle of the atoms, all if will occur with the same probability and the shape of the peaks of the energy scale, for the case t) V, is given by 

For constant I p - i ) this is a doubly peaked shape with its center at (e + a) and singularities at energy separations b from this center. Actually measured peaks consist of superpositions of such shapes with different b, depending on 0 as given by (7). 

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The fraction of released energy that passes into translational and vibrational energies of product depends to a quite significant extent on the mass combination of reactant atoms. This mass effect is referred as kinematic effect. In order to understand mass effect, at least for a collinear reaction, we can transform the motion of the three particles on PES to that of a single... 

These results indicate that both electronic and kinematic effects are important in determining the frequency of the C—N vibration. The masses of the alkyl substituents also were found to affect the mixing of the asymmetric /V-alkyl and the symmetric C-S modes. The mixing was found to increase with increasing substituent mass. 

The thermal motion of the atoms in the source volume leads to a broadening of the observed line, because the thermal velocity vth of the electron-emitting atom is added to the electron velocity v0. For an estimation of the resulting disturbance by this kinematical effect it is sufficient to select for the thermal velocity the two directions at which the Doppler effect becomes extreme, i.e.,... 

A remarkable fact about the true metric is that it is essentially non-Euclidean for three- or more-atom systems [7]. This implies that metric forces should be arising inevitably in the internal dynamics of polyatomic molecules independently of the forces arising from the potential. Kinematic effects owing to such a metric force and the non-Euclidean nature of internal space are our main concern in this review. 

Finally, we would like to point out that the kinematic effects of DCF inducing an asymmetry in mass balance in a many-body system should be of universal significance not only in molecular systems but also in a wide variety of many-body systems. This is because the DCF originates not from the interaction potential but from the intrinsic metric of internal space, which is uniquely determined from the shape and mass balance of a system. It is therefore anticipated that the DCF should be an important factor not only in molecular dynamics but in collective motions in nuclear, celestial, and biological many-body systems. 

Phenomenologically, dispersion occurs because different solute molecules take different times to move from point A to point 5 in a convective flow. The difference in transit times is attributed to a combination of kinematic and dynamic effects. Kinematic effects stem from tortuosity and the splitting and joining of stream tubes during flow, so that different particles traverse paths of different length. Dynamic effects stem from the distribution of velocities that a particle encounters on its path. Mechanical dispersion consists of the combined effects associated purely with convection (i.e., velocity variations due to hydrodynamics). Nonmechanical effects are associated with the diffusion of solutes from one streamline to another and into stagnant regions. 

Relativistic effects in atoms and molecules are commonly separated in kinematical effects, which do not cause a splitting of energy levels due to the spin degrees of freedom, and the effects of spin-orbit coupling. This separation is not unambiguously defined (Visscher and van Lenthe 1999), but is nevertheless extremely convenient when discussing effects on phenomenology. 

The many-body approach (impulsive models, Paddeev-Watson equations) represent a new direction in the development of chemical collision theory,in which the kinematic effects appear in addition to the molecular interactions. An excellent review of all these new methods is given by MICHA /89a/. In particular, the effective Hamiltonian methods have been considered by MICHA /89b/ with a detailed discussion of different approximations to optical potentials. 

The confinement in such a sector sets boundaries to the dynamics, which physically correspond to the prohibition, for masses on a line, to overcome each other. It also shows that very different kinematic effects are likely to be associated with different mass combinations. 

Calculation of pixel parameters for stereograms or kinematic effects is similar to the considered case. It is only necessary to take into account a new position of observation of the hologram that can be achieved by replacing the old variables (x,y) in formulas (4)-(7) by the new ones (x-Ax,y-Ay), where (Ax, Ay) indicate displacement of the observer in the observation plane. 

In seismic design practice it is common to neglect the influence of soil-pile interactimi oti the motimi applied to the superstructure (i.e. the earthquake excitation is assumed to be equal to the free-field ground motion), except for important structures (NEHRP 2003 Eurocode 8 2004 Norme Tecniche per le Costruzioni 2008 Greek National Code, EAK 2000). It is worth discussing the relevant clauses from Eurocode 8 (EN 1998-5, 2004). The code prescribes that kinematic effects... 

The various kinematical effects can best be observed in energy spectra of electrons due to collision processes with well-defined kinematics. Figure 4, which will be discussed in the following section, shows an example. 

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