Close-coupling expansion

Since only a relatively small number of coupled equations can be solved in practice, the target states p must be selected carefully. Virtual target excitation into the ionization continuum must be approximated by inclusion of closed-channel pseudostates that cannot be target eigenstates but have the character of wave packets in the continuum. Target polarization response is treated by including polarization pseudostates y(P). 

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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. 

Let s now consider several examples. The simplest of all reactions is the H+H reaction. The vibrational levels are fairly widely spaced, but we must also include the rotational manifold of levels associated with each vibrational level. (See Fig. 9.) Now, it is this rotational manifold of levels (and the degeneracies of states associated with each vibration-rotation level) which ultimately breaks the bank in the size of the close coupling expansion. 

The starting point is the Bom-Oppenheimer-Huang (BOH) close coupling expansion ... 

RG. Burke, The convergence of the close coupling expansion, Proc. Phys. Soc. Lond. 82 (1963) 443. 

In the close-coupling expansion, basis functions with different states are coupled together and this can lead to an enormous basis set being required Expansion of the I J-jr operator gives... 

The combination of the Azimuthal method of Section He with close-coupling expansions in the vy=0, vy=l and v q=1 vibrations enables vibrational predissociation resonances to be predicted. Por the reasons given above these predicted resonances are quite broad for the Ne complex( -- 10" cm ) but are much narrower for Ar(- 10" cm" ). This prediction remains to be verified in experiments. Furthermore, methods similar to those described for Ne-HF, but with the inclusion of Ae sudden approximation, have been used very recently to predict the full infrared spectrum for Ne-C2H4[71]. 

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