Closely coupled states

For the case in which the set of closely coupled states is a finite number, the... 

If the number of closely coupled states is two, then the above matrix element reduces to... 

Solution of this set for F R) represents tire adiabatic close-coupling method. The adiabatic states are nomrally detennined (via standard computational teclmiques of quanUim chemistry) relative to a set of axes (X, Y, Z ) with the Z- axis directed along the nuclear separation R. On transfomring to this set which rotates during the collision, then /(r, / ), for the diatomic A-B case, satisfies... 

Numerical solution of this set of close-coupled equations is feasible only for a limited number of close target states. For each N, several sets of independent solutions F.. of the resulting close-coupled equations are detennined subject to F.. = 0 at r = 0 and to the reactance A-matrix asymptotic boundary conditions,... 

When the initial and final internal states of the system are not well-separated in energy from other states then the closed-coupling calculation converges very slowly. An effective strategy is to add a series of correlation temis involving powers of the distance r. between internal particles of projectile and target to the tmncated close-coupling expansion which already includes the important states. 

Mowrey R C and Kouri D J 1987 Application of the close coupling wave packet method to long lived resonance states in molecule-surface scattering J. Chem. Phys. 86 6140... 

Large towers often have the motor mounted horizontally connected to a right angle gear drive. The motor can be closely coupled- in the air stream- or connected with a drive shaft with the motor outside the air stream. Maintenance personnel typically prefer the external TEFC motor- when available- for its easier access. Cooling tower fans- like all fans- operate in accordance with the fan laws one of which states that the horsepower required to drive a fan increases to the cube of fan speed. 

Continua. The wavefunctions of scattering and bound states have been calculated numerically in the close coupled approximation [358]. Converged partial wave expansions of the elastic scattering solutions have been calculated for pairs of angular momenta 71/2 = 00, 02, 22, 10, 30, 12, 11, and 13 at several hundred energy points. Rotationally inelastic... 

Understanding the order of the hydrodynamics equations, continuity and momentum, can be somewhat confusing and possibly not the same from problem to problem. The continuity and momentum equations must be viewed as a closely coupled system. Again, it is clear that the momentum equations are second order in velocity and first order in pressure. The continuity equation is first order in density. However, an equation of state requires that density be a function of pressure, and vice versa. Density and pressure must be dependent on each other through an algebraic equation. Therefore a substitution could be done to eliminate either pressure or density. As a result the coupled system is third order, which can present some practical issues for boundary-condition assignment. The first-order behavior must carry information from some portions of the boundary into the domain, but it does not communicate information back. Therefore, over some portions of a problem... 

All other matrix elements of the perturbations, Vso and Fvlb, between the zero-order states, are taken to be zero. That is, we neglect the direct coupling of the singlet with the manifold of twisted triplets, and assume that all the zero-order states have been chosen such that there are no nonvanishing diagonal matrix elements of Fao or Fvlb, nor any vibronic interactions within the set of closely-spaced states, />. ... 

Quantally, this problem is in the usual close-coupled equations category. For analysis of product angular distributions, it seem reasonable that a two-state analysis might suffice, provided that the different product channels are not strongly coupled themselves and that the absorption into channels other than the one considered is weak. 

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