Close-coupling calculation

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. 

Bray, I. and Stelbovics, A.T. (1993). Convergent close-coupling calculation of low-energy positron-atomic hydrogen scattering. Phys. Rev. A 48 4787-4789. 

Zhou, Y. and Lin, C.D. (1994). Hyperspherical close-coupling calculation of positronium formation cross sections in positron-hydrogen scattering at low energies. J. Phys. B At. Mol. Opt. Phys. 27 5065-5081. 

Figure 4.4 shows another example, also from close-coupling calculations by Burke et al. [43], for and 2P electron scattering by the helium atom near... 

Figure 4.12 Photoionization spectrum of HeO1 S) between the thresholds for He+(n = 4) and He+(n = 6). Dots Experiment [126]. Curve Hyperspherical close-coupling calculations convoluted with an experimental energy resolution of 6 meV and the background linear in photon energy subtracted. This background is caused mostly by the decay of the electron current in the storage ring. Figure from Ref. [51].

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].

Figure 4.20 The S-wave annihilation function P[p) defined by Eq. (126), p being the hyperradius, for e+ + H(1s) scattering at an energy of 10 6 a.u. above the positronium formation threshold. The total P[p) is decomposed into the contributions from the direct channels e+ + H, the positronium formation channels p + Ps, and the interference between them. Results of hyperspherical close-coupling calculations including the absorption potential —iVabs in the Hamiltonian. Figure from Ref. [16].

Fig. 10.20. Rotational state distribution of CN following the photodissociation of C1CN at 191.5 nm. Comparison between exact close-coupling calculations using the full ab initio PES of Waite and Dunlap (1986) (solid curve) and the impulsive model (IM, dashed curve). Adapted from Schinke (1990).

Figure 12.9 depicts a comparison between classical trajectory results and exact close-coupling calculations for He--Cl2 and Ne- -Cl2, respectively. In both cases, the classical procedure reproduces the overall behavior of the final state distributions satisfactorily. Subtle details such as the weak undulations particularly for He are not reproduced, however. As shown by Gray and Wozny (1991), who treated the dissociation of van der Waals molecules in the time-dependent framework, the bimodality for He CI2 is the result of a quantum mechanical interference between two branches of the evolving wavepacket and therefore cannot be obtained in purely classical calculations. 

Gianturco, FA. and Stoecklin, T. (1996). Hie elastic scattering of electrons from CO2 molecules I. Close coupling calculations of integral and differential cross sections, J. Phys. B 29, 3933-3954. 

The reliability of the newly-developed rigid-rotor potential was tested by means of close-coupling calculations of rotational state-to-state integral cross sections. The MOLSCAT code was used [66]. The results were compared with those obtained using the semiempirical potential of Buck, and with the available experimental data. 

Close-coupling calculations for the photodissociation cross-sections of CH+ C+pP) + H( S)... 

It is perhaps as interesting to compare the approximate calculations with the convergent-close-coupling calculation as with experiment. The one that takes all channels into account most completely is the coupled-channels-optical calculation (Bray, Konovalov and McCarthy, 1991c) in which P space consists of the n=l, 2 and 3 channels. It agrees closely, but not completely, with the convergent calculation and similarly with... 

The comparison of theory and experiment in table 8.3 is somewhat unsatisfactory. The coupled-channels-optical and pseudostate calculations agree with each other and with the convergent-close-coupling calculation within a few percent, yet there are noticeable discrepancies with the experimental estimates. The convergent-close-coupling method calculates total ionisation cross sections in complete agreement with the measurements... 

Laniiay, J.M. and le Domnenf, M. (1989) Hyperspherical close-coupling calculations of integral cross sections for the reactions H L H2 H2 + H, Chem. Phys. Lett. 163. 178-188. 

Results and Predictions. Detailed close coupling calculations for "real" Av<0 vibrational predissociation of weak-coupling systems such as the hydrogen-inert gas complexes are more difficult and computationally more expensive than those for predissociation by internal rotation. The computational expense arises simply from the very large increase in the nvmber of channels which must be included in order to obtain converged results. The difficulty, on the other hand, arises from the fact that these resonances have very small widths, usually 10 cm , %jhich makes them very difficult to find. 

For the prototype level (n,Jl,v, j, J)=(0,0,1,0,0T"of H2-, D2-and HD-Ar, the results of close coupling calculations for the partial and total predissociation widths are listed in Table V. Tests showed that the angular basis sets used to obtain these results were fully converged (25) they included diatom rotation states up to j 8 for v l and up to j" 10 for v -O. The absence of odd-j" dissociation products for H2- and D2-Ar merely reflects the fact that their potentials have no odd-j anisotropy terms. 

On the theoretical side, both quantal and semlclasslcal methods have been used to calculate resonance energies and widths, principally for colllnear reactions, although there are a few studies of 3D reactions. In quantal studies of 3D reactions, some close-coupling calculations on H+H2 have been reported (If), (li), but the large number of channels has necessitated approaches based upon the J -conserving (3),... 

The model described is in agreement with the major features of the observations and is consistent with the data available for the predissociation of Hel van der Waals complexes. It remains to be seen if detailed close coupling calculations will provide quantitative verification of all of its features. Although there are not now data to support a generalization, it seems plausible that the zero energy orbiting resonance mechanism for efficient collision-induced vibrational relaxation will occur in all systems. It will be particularly interesting to see what selectivity of vibrational pathway exists in the case of relaxation of a polyatomic molecule. 

Different theoretical methods have been used to calculate the complex energies, Eq. (8.1), for compound-state resonances. They can be divided into time-independent and time-dependent methods. A standard quantum mechanical time-independent method is a close-coupling calculation (Stechel et al., 1978) which considers resonant state formation as a result of a collision such as A + BC —> ABC AB + C. Determined... 

Another interesting system is C1H- -Ar. Although it has not been studied experimentally, a close coupling calculation has shown that this cluster dissociates with a rate of 4 X 10 sec (Hutson, 1984). The HCl bond absorbs infrared radiation at 2886 cm f Since the binding energy is 116 cm, we have a total of 2770 cm" of energy to dispose. Suppose first that the decay converts all of this energy into translations. If... 

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