Coupled-channel results

Fig. 11. (a) Coupled-channel results for the electronic stopping cross section of H and beams incident on He vs. incident energy (solid and dashed lines). Ionization and excitation of projectiles, in the case of the charge-state fraction, is accounted for by considering the collision system He + H (dot-dashed line), (b) Experimental equilibrium fractions for hydrogen beams in helium gas, from Ref. [63]. 

Fig. 14. Non-perturbative results for the energy loss at a small impact parameter in 500 keV/u + He collisions, compared to the values from first-order perturbation theory (SCA, dashed line). Atomic orbital (AO) coupled-channel results for positively charged particles (open circles) and for anti-nuclei (closed squares). Results using the UCA model solid curve.

We had earlier vindicated treating one of the OH bonds in the H2O molecule as a spectator bond in studying the abstraction reaction. Another key assumption that needed to be checked was the centrifugal sudden (CS) approximation which was invoked to reduce the number of rotational basis functions used in the computations.28 Under the CS approximation and using only the K = 0 rotational basis functions, there was a total of 220 million basis functions for J = 15 alone. Relaxing the CS approximation, for example, with K = 0,1 and J = 15 led to 650 million basis functions. To approach the fully coupled-channel (CC) results, i.e. without... 

In the CT-VPP-REDOR experiment (cf. Figure 3), the positions of the 7t-pulses on the /-channel which are applied at Tr/2 in conventional REDOR are changed stepwise over the complete rotor period, leading to but a partial reintroduction of the heteronuclear dipolar coupling. The resulting AS/So curve depends on the pulse position fpp according to... 

The results of HSCC calculations have proved much more rapid convergence with the number of coupled channels than the conventional close-coupling equations in terms of the independent-particle coordinates or the Jacobi coordinates based on them. This is considered to be because of the particle-particle correlations considerably taken into account already in the choice of the hyperspherical coordinate system. The results suggest an approximate adiabaticity with respect to the hyperradius p, even when the mass ratios might appear to violate the conditions for the adiabaticity, for example, for Ps- with three equal masses. Then, it makes sense to study an adiabatic approximation with p adopted as the adiabatic parameter. 

An example for one of the first applications of the coupled-channel equations y with quantized fields for photodissociation problems is shown in Figure 12.1, where, the dissociation of the IBr molecule by a two-photon (visible + IR) process wasJS studied [388], The results of the calculations, shown in Figure 12.2, demonstrate 3 how the strong IR photon broadens the transition ( power broadening ) allowing th system to be dissociated even if the first photon is tuned substantially away from, 7 resonance. This illustrates how multiphoton transitions induced by strong fields [392] are less restricted insofar as they need not be very close to an intermediate T resonance, the situation described in Section 3.3. 

Absolute measurements of total cross sections have been made by beam-transmission techniques. The results of Kwan et al. (1991) are compared with the coupled-channels-optical calculation in table 8.7. In most cases the coupled-channels-optical cross section is within one standard deviation of the experimental result. 

Figure 7. The coupled channel (CC) and centrifugal sudden (CS) integral cross section for the H + H20f00)f0) abstraction reaction. Other results x CS, Ref. 44 QCT, Ref. 54.

A review is given on the application of the coupled-channel method for the calculation of the electronic energy loss of ions as well as ionization in matter. This first principle calculation, based on the solution of the time-dependent Schrodinger equation, has been apphed to evaluate the impact parameter and angular dependence of the electronic and nuclear energy losses of ions as well as the ionization due to high-power short laser pulses. The results are compared to experimental data as well as to other current theoretical models. 

The chapter is organized as follows. The principle of the coupled-channel method is reviewed in detail in Section 2. The results are discussed in connection to higher order terms in Section 3. The application to multiphoton ionization is described in Section 4. Comparisons with measurements are provided in Section 5. A simple model for the electronic energy loss is... 

A direct measurement of the electronic energy loss as a function of the impact parameter is a hard task to be performed from the experimental point of view and only a few experiments have been performed for fast light ions. Experiments in gas targets under single collision condition provide a more direct and precise comparison of the theoretical results with the experimental data. Here we compare the results of the coupled-channel method for collisions of protons with He as a function of the projectile scattering angle. 

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