Scattering energy-normalized

Figure 32. Scattering intensity / ( normalized to I as function of light-incidence angle 0 for the e + Na(3/>)—>Na(3.s) + e process at incident energy of IN= 10 eV for various collision angles dcol.

Figure 14 Role of e-h pairs in the scattering and sticking of CO/Cu(l 11) at a surface temperature of Ts = 100 K (a) sticking probability for CO/Cu(l 1 1) under normal incidence calculated without and with electronic friction, (b) energy distribution of CO molecules scattered under normal incidence from Cu(l 11) in percent of the initial kinetic energy (after [110]).

The mean free path A may be determined by many different scattering mechanisms but the dominant one at temperatures not too close to o °K is phonon-phonon scattering, the coupling taking place through the anharmonicity of the lattice vibrations. There are two possible types of phonon-phonon scattering processes normal processes in which total phonon wave vector is conserved, and umklapp processes in which the total wave vector after collision differs from that before collision by a vector of the reciprocal lattice. Since normal processes do not affect the total phonon momentum or energy, they do not contribute to thermal resistance and only umklapp processes need be considered. For an umklapp process to occur between two phonons of wave vectors q and q we must have a relation of the form... 

The choices that we made in Ref. [54] [the electric dipole approximation (EDA) in the "velocity" form] and in Refs. [55-57] (full interaction in the multipolar form [75-77, 106]) were based on this extensive literature and on our analysis as regards the proper nonperturbative solution of the TDSE for specific problems. Elements of this work are presented here and in Section 6. Eurthermore, in Ref. [105] we discussed the computation of free-free coupling matrix elements in the EDA, when using, on the one hand energy-normalized scattering functions and on the other hand box-normalized discrete representations of the continuous spectrum. 

Due to their simple structure, the core wavefunctions ls 2s and ls 2p P° were represented by HP wavefunctions. The basis set of bound orbitals and of the energy-normalized scattering orbitals, si and s t, were computed numerically from separate calculations via the term-dependent HE scheme. 

In process (A), the 2s subshell of the ground state is ionized by the electromagnetic pulse. In the EDA, two final LS-coupled core states are reached, each with its own self-consistent field and its own correlation effects. (The approximation which is often made in various types of calculations, namely taking the same orbital and N-electron functions for such multiplet terms, contains errors.) The corresponding energy-normalized scattering orbitals are labeled by iPj and 2P2 and are computed as term-dependent functions in the fixed HE potential of the core. 

The energy-normalized scattering wavefunctions, Isel, were computed numerically by the fixed-core HF method, for energies up to 4.03 a.u. in steps of 0.004 a.u. and for angular momenta Z = 0,1,..., 15. 

Obviously, there is much room for further development of the basic concepts of the SSEA and for improvement of its methodology, as well as for additional applications to new and challenging TDMEPs. In all cases, the fundamental issue is how to identify and construct the wavefunctions that are considered relevant to each problem. For example, the possibility of treating correctly the contribution from two-electron continue is an open question. Even if two-electron products of energy-normalized scattering states are used as basis sets, the computational requirements of this (multichannel in general) problem are huge, and so its solution would require dedicated effort and powerful computers. 

The reaction probability is defined as the expectation value of this flux operator in the basis of energy normalized time-independent reactive scattering wave function evaluated at the dividing surface.2 34-38 write this... 

The quantity on the right hand side of the above equation is integrated over the entire range of R and 7. The energy-normalized time-independent reactive scattering wave function is calculated along the dividing surface at... 

Defining the energy normalized time-independent reactive scattering wave function in the adiabatic electronic basis as... 

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