Prior distribution internal states

In Section 6.4.1.1 we count the quantum states so as to derive the prior distribution for flux contour maps. Measurement of a flux map provides a relatively high resolution but it too implies grouping of final states all internal states of the products with energies in a narrow interval are counted together. The complementary experiment is to measure the internal state population of the nascent products. The prior distribution for this case is obtained in Section 6.4.1.2. 

Here we examine what modifications are required in the definition of the prior distribution when we explicitly take into account the conservation of angular momentum in addition to the conservation of energy. These modifications are required when, say, high final rotational states are being populated, which requires conversion of much angular momentum of initial relative motion to internal angular momentum of the products. As discussed in Section 10.2.2, when an... 

The U.S. titanium market distribution is shown in Table 18. Before 1970, more than 90% of the titanium produced was used for aerospace, which feU to ca 70—80% by 1982. Mihtary use has continually decreased from nearly 100% in the early 1950s to 20% in the 1990s. In contrast to the United States, aerospace uses in Western Europe and Japan account for only 40—50% of the demand (58). The CIS s consumption of titanium metal prior to the breakup was about one-half of the world consumption. In the 1980s, considerable amounts were used for submarine constmction. Since the breakup of the former Soviet Union, the internal consumption of titanium in the CIS is beheved to be a modest fraction of its former capacity, thus leaving a large capacity available for export. The world production faciUties for titanium metal and extraction are given in Table 19. 

The basic assumption in statistical theories is that the initially prepared state, in an indirect (true or apparent) unimolecular reaction A (E) —> products, prior to reaction has relaxed (via IVR) such that any distribution of the energy E over the internal degrees of freedom occurs with the same probability. This is illustrated in Fig. 7.3.1, where we have shown a constant energy surface in the phase space of a molecule. Note that the assumption is equivalent to the basic equal a priori probabilities postulate of statistical mechanics, for a microcanonical ensemble where every state within a narrow energy range is populated with the same probability. This uniform population of states describes the system regardless of where it is on the potential energy surface associated with the reaction. 

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