Scattering reactive, results

ABSTRACT. Adiabatically adjusting Principal-axis Hyperspherical(APH) coordinates are used in a fully 3-dimensional quantum mechanical formulation of reactive scattering. Exact results will be presented for the following systems ... 

B. Density Coefficient A decrease in density decreases the macroscopic cross sections, which results in an increase of the mean free paths for absorption and scattering. The result is that the thermal diffusion length (L) and neutron age (t) increase. Because of the increase in L and T, the thermal and fast nonleakage probabilities are reduced. From Eq. (1) note that the reduced nonleakage probabilities decrease kg , which means that the reactivity effect is negative. A partial compensation for the effect of an increased L and t on the nonleakage if the core volume exp[Pg.193]

Reactive scattering or a chemical reaction is characterized by a rearrangement of the component particles within the collision system, thereby resulting in a change of the physical and chemical identity of the original collision reactants A + B into different collision products C + D. Total mass is conserved. The reaction is exothemiic when rel(CD) > (AB) and is endothermic when rel(CD) < (AB). A threshold energy is required for the endothemiic reaction. 

Bacic Z, Kress J D, Parker G A and Pack R T 1990 Quantum reactive scattering in 3 dimensions using hyperspherical (APH) coordinates. 4. discrete variable representation (DVR) basis functions and the analysis of accurate results for F + Hg d. Chem. Phys. 92 2344... 

The nuclear chain reaction can be modeled mathematically by considering the probable fates of a typical fast neutron released in the system. This neutron may make one or more coUisions, which result in scattering or absorption, either in fuel or nonfuel materials. If the neutron is absorbed in fuel and fission occurs, new neutrons are produced. A neutron may also escape from the core in free flight, a process called leakage. The state of the reactor can be defined by the multiplication factor, k, the net number of neutrons produced in one cycle. If k is exactly 1, the reactor is said to be critical if / < 1, it is subcritical if / > 1, it is supercritical. The neutron population and the reactor power depend on the difference between k and 1, ie, bk = k — K closely related quantity is the reactivity, p = bk jk. i the reactivity is negative, the number of neutrons declines with time if p = 0, the number remains constant if p is positive, there is a growth in population. 

Cross-sections for reactive scattering may exhibit a structure due to resonance or to other dynamical effects such as interference or threshold phenomenon. It is useful to have techniques that can identify resonance behavior in a system and distinguish it from other sorts of dynamics. Since resonance is associated with dynamical trapping, the concept of the collision time delay proves quite useful in this regard. Of course since collision time delay for chemical reactions is typically in the sub-picosecond domain, this approach is, at present, only useful in analyzing theoretical scattering results. Nevertheless, time delay is a valuable tool for the theoretical identification of reactive resonances. 

Fig. 6. The total differential cross-section in A2/sr for the HF D reactive channel, (a) Shows the experimental results while (b) presents the result of the scattering calculation. Note the ridge running from large 0 (backward) at low energies to small 0 (sideways) at higher Ec s.

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