Scattering, asymptotic

On the other hand, Cassassa and Berry32,129 conclude from their LS measurements on rod-like fibrinogen in solution that Eq. (86) is followed very well, but the intercept is extremely small or effectively zero. A rather trivial change in the model can be shown to produce a theoretical intercept of zero. Accordingly, they consider that the asymptotic scattering data reveal nothing about M but do give information from the slope on the ratio Ln/Mn. 

When the incident electric field is polarized perpendicular to the xz plane (Case II), the asymptotic scattered field is given by (8.33) with anl replaced by -anll and bnl replaced by -bnll. 

Note that the center-of-mass motion drops out in these operators and in the following it is understood that the Hamiltonians refer to the relative motion the subscript reI will consequently be dropped. Thus, according to Eq. (4.132), the relation between the scattering state at f = 0 and the asymptotic scattering states can be illustrated in the following way ... 

The coefficient <, -( ) can be easily evaluated from the free asymptotic scattering function as follows ... 

Here we discuss only the very simple case of zero final state interaction, which corresponds to the asymptotic scattering problem. In this case the motion of the products AB and C is completely decoupled. The corresponding wavefunctions are the wavefunctions for the separated fragments. If the internal motion of AB is described by AB>, the internal motion in C by C> and the relative motion by AB-C>, the solution f> for the asymptotic scattering problem becomes... 

This is a special solution for the full scattering problem in the trivial case where the asymptotic scattering wavefunction is not changed at all by the interaction potential, i.e., for the case of zero final state interaction. This implies that the full scattering solution can be replaced by the asymptotic wavefunction f>. This yields the state to state photodissociation cross section in the FC-limit ... 

FIGURE 3.24 Comparison between the resonance (upper) and Gaussian (lower) curves wile the last is fast decreasing to zero outside of the resonance (central) region, the first one presents the long (asymptotical) tail specific for (asymptotic) scatterings. 

Scattering from the drawn samples in the higher- region was greater than for identical undrawn samples and was nearer to that expected for an adjacent re-entry model (all isotropic polypropylene samples, regardless of their thermal histories, have approximately the same asymptotic scattering level). A tentative interpretation of this result is that the stems come closer together as the polymer is drawn. 

The first term is a plane wave of incoming reactants in channel Nr, and the second term is a sum of outgoing spherical waves in all open channels. The asymptotic scattering amplitude /n t. Nti which has units of length, can also be expressed as... 

The task in QRS, then, is to compute the asymptotic scattering amplitudes given the system masses and the PES. 

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