Scattering, reactive energy dependence

The initial state-selected total dissociation probability of the diatom is obtained by projecting out the energy-dependent reactive flux. If i /,) denotes the time-independent (TI) full scattering wavefunction, where the labels i and E denote the initial state and energy, the total dissociation probability from an initial state i can be obtained by the flux formula (95). We choose the diatomic distance r to be the 5 coordinate in Eq. (96). The full TI scattering wave function is normalized as (if/,) NV/. ) = 2/nhh(E - E ). The total dissociation probability, according to Eq. (98), is given by... 

Figure 7. Complete in-plane laboratory angular distribution of reactively scattered T atoms formed in the reaction of D atoms (at 2120 K) with T, molecules (at 300 K) (16/ Energy-dependent total reaction cross sections for D + T2 used for weighting in the energy averaging are from (19/ Other notation as in Figure 6.

The conditions required by (ii) are not allowed quantum mechanically the sharp discontinuity would be smoothed. Indeed, what few examinations there have been of the nature of P(fe, ), either by analysis of reactive scattering using the optical potential model or by trajectory calculation, show a different dependence than that required by (ii). This is merely support for the familiar idea that, even in the absence of energy barriers, reactivity is dependent upon the total angular momentum. 

When collisions release energy, the energy dependence of the scattering cross-sections near threshold does not depend on the angular momentum in the final collision channel. For example, the cross-section for inelastic energy transfer in three-dimensional collisions is proportional to [52]. For reactive or inelastic... 

To the extent that K(t) is constant throu out a time interval that is comparable to then the correct time dependent rate expression can be replaced by an approximate quasi steady state analog. Even in the absence of a true steady state, certain features of an average rate coefficient formulation will continue to be applicable (23.25.27,51,32). This conclusion is insensitive to the present assumptions concerning nonreactive scattering. It would be strengthened by the inclusion of a more realistic representation of the energy dependent nonreactive cross section, since a relative reactivity increase would lead to ccmipression of the time and ranges sampled by nonthermal reaction. 

One of the key aspects of time-dependent reactive scattering theory arises from the conservation of the total energy. This has the consequence that each energy... 

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