Close-coupling approximation

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... 

Sinha, P.K., Chaudhury, P. and Ghosh, A.S. (1997). Ps-H scattering using three-state positronium close-coupling approximation. J. Phys. B At. Mol. Opt. Phys. 30 4643-4652. 

P.G. Burke, S. Ormonde, W. Whitaker, Low-energy electron scattering by atomic hydrogen I. The close-coupling approximation, Proc. Phys. Soc. (London) 92 (1967) 319. 

This shows that the exponential model (see Section III) can be used to match nonresonant [equation (95)] and resonant [equation (85)] probabilities within the two-state close-coupling approximation. 

Theory. Usually we do not solve the fundamental equations directly. We use a theory, for example, Har-tree-Fock theory [3], Moller-Plesset perturbation theory [4], coupled-cluster theory [5], Kohn s [6, 7], Newton s [8], or Schlessinger s [9] variational principle for scattering amplitudes, the quasiclassical trajectory method [10], the trajectory surface hopping method [11], classical S-matrix theory [12], the close-coupling approximation... 

The close-coupling equations are also applicable to electron-molecule collision but severe computational difficulties arise due to the large number of rotational and vibrational channels that must be retained in the expansion for the system wavefiinction. In the fixed nuclei approximation, the Bom-Oppenlieimer separation of electronic and nuclear motion pennits electronic motion and scattering amplitudes f, (R) to be detemiined at fixed intemuclear separations R. Then in the adiabatic nuclear approximation the scattering amplitude for ... 

It is generally accepted that the centrifugal sudden (CS) approximation is the most reliable approximate method. Its results are usually very close to those obtained by ab initio close coupling (CC) calculations. The integral and differential cross-sections of Ar inelastic scattering on nitrogen were performed for a few low-frequency rotational transitions and four different interaction potentials [205]. Much better agreement of CC with CS results was found than with IOS calculations performed in... 

In order to describe the fluorescence radiation profile of scattering samples in total, Eqs. (8.3) and (8.4) have to be coupled. This system of differential equations is not soluble exactly, and even if simple boundary conditions are introduced the solution is possible only by numerical approximation. The most flexible procedure to overcome all analytical difficulties is to use a Monte Carlo simulation. However, this method is little elegant, gives noisy results, and allows resimulation only according to the method of trial and error which can be very time consuming, even in the age of fast computers. Therefore different steps of simplifications have been introduced that allow closed analytical approximations of sufficient accuracy for most practical purposes. In a first... 

Theory. The theory of collision-induced absorption profiles of systems with anisotropic interaction [43, 269] is based on Arthurs and Dalgamo s close coupled rigid rotor approximation [10]. Dipole and potential functions are approximated as rigid rotor functions, thus neglecting vibrational and centrifugal stretching effects. Only the H2-He and H2-H2 systems have been considered to date, because these have relatively few channels (i.e., rotational levels of H2 to be accounted for in the calculations). The... 

The rototranslational and fundamental absorption spectra of the H2-H complex have been obtained from first principles, for temperatures from 200 to 2500 K [21, 103]. Close-coupled and isotropic interaction approximation calculations give nearly identical values at frequencies from 0 to 6000 cm-1. No laboratory measurements exist for comparison with the calculations. The H2-H system is of considerable interest in stellar environments at such temperatures. 

Abstract. Cross sections for electron transfer in collisions of atomic hydrogen with fully stripped carbon ions are studied for impact energies from 0.1 to 500 keV/u. A semi-classical close-coupling approach is used within the impact parameter approximation. To solve the time-dependent Schrodinger equation the electronic wave function is expanded on a two-center atomic state basis set. The projectile states are modified by translational factors to take into account the relative motion of the two centers. For the processes C6++H(1.s) —> C5+ (nlm) + H+, we present shell-selective electron transfer cross sections, based on computations performed with an expansion spanning all states ofC5+( =l-6) shells and the H(ls) state. 

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. 

Figure 4.18 The near-threshold S-wave singlet (S = 0) and triplet (S = 1) absorption cross sections in e+ + H(1s) scattering, plotted versus reduced energy e = ( — th)/(r/2). The threshold energy th and the width T differ depending on the spin S. Full curves cross section 1,3(tabs °f Eq- (F5) from hyperspherical close-coupling calculations including the absorption potential —1(1,3 Vabs)- Dotted curves for e > 0 positronium formation cross section calculated without — / C Vabs). Broken curves for e < 0 absorption cross section 1,3a of Eq. (119) calculated without — Z(1,3Vabs) (first-order perturbation approximation). Circles Baz threshold formula fitted to the full curves. Figure from Ref. [16].

The B-spline K-matrix method follows the close-coupling prescription a complete set of stationary eigenfunctions of the Hamiltonian in the continuum is approximated with a linear combination of partial wave channels (PWCs) [Pg.286]

Delgado-Barrio, G., Mareca, P., Villarreal, P., Cortina, A.M., and Miret-Artes, S. (1986). A close-coupling infinite order sudden approximation (IOSA) to study vibrational predissociation of the Hel2 van der Waals molecule, J. Chem. Phys. 84, 4268-4271. 

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. 

The soot concentration, hydrocarbon species and soot temperature in the immediate vicinity of the droplet displayed closely coupled behavior. Hydrocarbon species, listed in approximate order of concentration were C2H2, CH4, C2H4, C2H6 and C3fs. Resolution of the propane and propylene peaks was not possible under current GC procedure, and these concentrations are reported merely as C3 compounds. The hydrocarbons were found to decay in the same time frame as the growth of the soot concentration. The zone of chemical activity, defined as where the vaporized hydrocarbon products react to form soot, is approximately 2 cm, which corresponds to 13 msec, after which the soot concentration decays due apparently to oxidation. 

---