Coupled-state approximation

The coupled-state approximation has also been applied to the other alkali atoms, by Ward et al. (1988, 1989), McEachran, Horbatsch and Stauffer (1991), Hewitt, Noble and Bransden (1993, 1994), Kernoghan, McAlinden and Walters (1996) and McAlinden, Kernoghan and Walters (1996). As with lithium, the neglect of positronium terms in the wave function has a serious influence on the very-low-energy elastic scattering cross section. 

Fig. 3.11. Calculations of the positron-hydrogen elastic scattering cross sections ----, 18-coupled-state approximation (Kernoghan et al., 1995) (a 33-...

Kernoghan, Robinson, McAlinden and Walters (1996) for the total positronium formation cross section together with the experimental points of Zhou et al. (1997). (b) Helium the theoretical results were obtained by Campbell et al. (1998a) using a 27-coupled-state approximation — —, ground state formation ... 

Fig. 5.1. Cross sections for the excitation of atomic hydrogen obtained using the coupled-state approximation with 30 hydrogen states and pseudostates plus three positronium states (a) 1S-2S (b) 1S-2P (Kernoghan et al., 1996).

McGuire, P. and Kouri, D.J. (1974). Quantum mechanical close coupling approach to molecular collisions, -conserving coupled states approximation, J. Chem. Phys. 60, 2488-2499. 

In the centrifugal sudden approximation (CSA), which is also known as the coupled states approximation, the operator j j is replaced by a value such as [j +j - 2 J j ] such that there is no coupling between different" 2 states 07 4,25]. The S matrix elements are then of the form... 

The numerical treatment of the triatom reactions (I) was carried out within the coupled states approximation. Consequently the Hamiltonian takes the form ... 

Neglect of these particular operators removes the coupling in basis functions with different Q. quantum numbers and drastically reduces the size of die basis set[7,25]. This is the centrifugal sudden approximation (CSA) and is often known as the coupled-states approximation, although that is a term we prefer not to use as it is easily confused with "close-coupling". The basis set expansion for a CSA calculation of vibrational-rotational excitation cross sections would thus be... 

CSA Centrifugal Sudden Approximation (Coupled States Approximation) V xjxk Fixed0... 

To simplify the problem, the K-conserving, centrifugal sudden, or coupled states approximation [19, 20, 21] is frequently employed. Within this approximation, K is considered to be a good quantum number and all terms in the Hamiltonian which couple different K values are disregarded. Then the thermal rate constant can be written as the sum ... 

J. Kouri, Quantum mechanical approach to mole-j -Conserving coupled states approximation,... 

D. J. Kouri and Y. Shimoni, On the j -conserving coupled states approximation Magnetic transitions and angular distributions in rotating and fixed frames, J. Chem. Phys. 67 86 (1977). 

L. Monchick and S. Green, Validity of approximation methods in molecular scattering. III. Effective potential and coupled states approximations for differential and gas kinetic cross sections,... 

In addition to reference 10, three other studies of Li" -C0 have been done. In reference 11 classical partial cross sections (fixed impact parameter) were compared with the coupled states approximation. More recently, classical calculations were done for... 

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