Capture to the continuum

Figs. 10 and 11 for helium. This feature is closely analogous to the one observed for ve = vp for electron capture to the continuum mechanism or to electron loss to the continuum which is often referred to as the cusp. The electrons with v, vr 0 in the low-lying continuum states of the target ion also form a sharp peak known as the target cusp. ... 

In Figs. 24 and 25 we show the measured double differential cross sections for electron emission at zero degrees in collisions of 100-keV protons with He and H2 [39] compared to CDW-EIS predictions [39]. Uncertainties associated with the experimental results vary from 1% near the electron capture to the continuum peak to about 15% near the extreme wings of the distribution. These results have been scaled to provide a best fit with CDW-EIS calculations. In both cases there is satisfactory agreement between the CDW-EIS calculations and experiment, particularly with excellent agreement for electrons with velocities greater than v, where v is the velocity of the projectile. For lower-energy electrons the eikonal description of the initial state may have its limitations, especially for lower-impact parameters. 

The first reported study of the behaviour of double differential cross sections for positron impact ionization was that of Moxom et al. (1992) these workers conducted a search for electron capture to the continuum (ECC) in positron-argon collisions. In this experiment electrons ejected over a restricted angular range around 0° were energy-analysed to search for evidence of a cusp similar to that found in heavy-particle collisions (e.g. Rodbro and Andersen, 1979 Briggs, 1989, and references therein), which would be the signature of the ECC process. 

Schultz, D.R. and Reinhold, C.O. (1990). Electron capture to the continuum and binary ridge structures in positron-hydrogen collisions. J. Phys. B At. Mol. Opt. Phys. 23 L9-L14. 

Charge Capture to Bound States Plus Capture to the Continuum... 

Below roughening, pronounced lattice effects show up in the simulations, as in the case of wires. The meandering of the top(bottom) steps and the islanding on the top(bottom) terrace leads to slow and fast time scales in the decay of the amplitude. The profile shapes near the top(bottom) broaden at integer values of the amplitude and acquire a nearly sinusoidal form in between. Again, these features are not captured by the continuum theory. For evaporation kinetics, continuum theory suggests that the decay of the profile amplitude z scales like z t,L) = where g =... 

Fig. 6. Probability (per unit time) of Auger capture to the L shell of a N ion embedded in a FEG 7 us a function of the number of L-shell electrons bound to the ion before the capture. Fl is in atomic units. Two different values of the electronic density = 1.5 and 2 are shown. For ml > 5 the 2p KS orbital merges into the continuum and is no longer bound.

This comparison illustrates that the lateral drift in the lower part of the wall has more flexibility and ductility in MDFEA than in the ZEUS-NL analysis. This is mainly due to the much larger shear deformation contributions that are captured in the continuum model of the MDFEA. At higher load levels, the ZEUS-NL model exhibits lower stiffness and ultimately less strength than the MDFEA model. This is mainly because, the plane section assumption in the fiber approach leads to concrete crushing at wall s base earlier than the concrete compressive capacity is reached in the continuum model. 

If two electrons are transferred to bound states on the projectile, as opposed to the continuum, once again a clear signature of a multifermion process is present. However for charge transfer there is no simple identification of the strength of the external probe to see if EIMP or IIMP is dominant. Thus one must rely on theory to see whether correlation plays a role, or not, in such collisions. And everyone must agree on what correlation is. See for example, Stohlterfoht et al. [7.1], for a discussion of electron correlation in double capture. 

The wavefunctions for the initial bound state the resonant states , and the neutral thresholds are generated in separate valence RCI calculations. The valence RCI calculation for the resonant state yields energy positions of unperturbed resonant states, i.e., the E s in equation 1.3. Since virtual orbitals are used for the correlation configurations that capture not only the bound orbitals but also a portion of the continuum orbitals, it s important to avoid in cj) the correlation configurations that are equivalent to the continuum state. For example, in Ce [5], 4/ 5d 6s vp and 4/ 5d 6s vf were excluded from the basis set for resonant state 4/ 5d 6p. Otherwise, the variational optimization for 4/ 5d 6s 6p may collapse into the continuum 4/ 5d 6s ep (f) in which it lies. 

To capture the essence of the Feshbach resonance phenomenon, we will need to understand what happens to the ground vibrational state 4>o(R) of the ground electronic state, also depicted in Figure 1.13, because of the interaction with the continuum of states excited electronic state. The physical process described above can be formulated as a two coupled channels problem where the solution irg(R) in the closed channel (the ground state) depends on the solution ire(R) in the open channel (the excited state) and vice-versa. The coupled Schrodinger equations read... 

Another class of systems for which the use of the continuum dielectric theory would be unable to capture an essential solvation mechanism are supercritical fluids. In these systems, an essential component of solvation is the local density enhancement [26,33,72], A change in the solute dipole on electronic excitation triggers a change in the extent of solvent clustering around the solute. The dynamics of the resulting density fluctuations is unlikely to be adequately modeled by using the dielectric permittivity as input in the case of dipolar supercritical fluids. 

---