Total reaction cross section

Table I. Total Reaction Cross-Sections of Ions with CH4...

The total reaction cross-sections of the individual primary and secondary species were derived and are compared in Table III with reactivities determined from previous electron impact studies (10, 31). 

Fig. 2.5. Dependence of total reaction cross-section on the angular momentum quantum number.

Focusing on comparisons to measurable quantities, the relative probability of a reaction (exit) channel can be written as the ratio of the cross section for that channel, (r to the total reaction cross section, 07. The ratios are labeled as the relative decay widths, T, in a notation that is, unfortunately, easy to confuse with the number of states discussed above. The sum of the decay widths is the total width of the state and can be used to calculate the lifetime of the excited state. Thus,... 

The total reaction cross section is obtained by summing over all l values as ... 

The total cross section is proportional to the size of the target nucleus and the size of the projectile nucleus. Since the wavelength of the projectile, X, goes to infinity as the projectile energy goes to zero, the cross sections for neutrons at low energies can be very large. The above discussion is based upon semiclassical mechanics. We need to indicate how the problem would look if we used quantum mechanics to treat it. In quantum mechanics, we can write a similar expression for the total reaction cross section ... 

Example Problem Calculate the energy dependence of the total reaction cross section for the 48Ca + 208Pb reaction. 

What do we typically measure when we study a nuclear reaction We might measure aR, the total reaction cross section. This might be measured by a beam attenuation method ( transmitted vs- incident) or by measuring all possible exit channels for a reaction where... 

One reaction proposed for the synthesis of element 110 is the reaction of 59Co with 209Bi at a laboratory energy of 295 MeV. Calculate the expected total reaction cross section. 

Consider the Ca + Cm reaction where the lab energy of the Ca is 300 MeV. What is the excitation energy of the putative compound nucleus 296116 What is the expected total reaction cross section ... 

Scattering of Noble-Gas Metastable Atoms in Molecular Beams velocity. The total reaction cross section is... 

Fig. 4.1.12 Total reaction cross-sections for the reaction H + H2 (n, J = 0) — 112 I 11 as functions of the total energy Etot for initial vibrational states n 0, 1,2 n 0, xn = l, n = 2. The energies of the 0 levels of H2 are indicated by arrows. [Adapted from Barg et al., J. Chem. Phys. 74, 1017 (1981).]...

Model calculations usually divide the reaction into two parts and make various assumptions about the nature of the entrance channel (or reactant) and exit channel (or product) interactions. In some models, these interactions are treated independently and in others some degree of coupling is introduced. Not all reaction models are capable of describing the nature of the product energy disposal many are concerned only with the total reaction cross section or the product angular scattering distributions. 

Various electronic states of CaO are populated in the reactions Ca (3P, lD) + N20, although none of the observed states is adiabatically accessible [385] and they thus occur as the result of several surface crossings. It appears that product channels which involve a small number of such crossings are favoured. The total reaction cross sections and the chemiluminescence cross sections are 70 A2, 4 A2 and 67 A2, 5 A2 for the reactions of Ca (1D) and Ca (3P) with N20, respectively. 

In the last step, the MX molecule acts as a chaperone to bring the M and Y together to form the electronically excited halide MY. The chemiluminescent cross sections are about two orders of magnitude smaller than the total reaction cross sections. For the K2 reactions, the cross sections are 0.3—3 A2 for M emission and smaller for MX emission for Rb2 and Cs2, the MX emission becomes stronger. 

Statistical methods represent a background for, e.g., the theory of the activated complex (239), the RRKM theory of unimolecular decay (240), the quasi-equilibrium theory of mass spectra (241), and the phase space theory of reaction kinetics (242). These theories yield results in terms of the total reaction cross-sections or detailed macroscopic rate constants. The RRKM and the phase space theory can be obtained as special cases of the single adiabatic channel model (SACM) developed by Quack and Troe (243). The SACM of unimolecular decay provides information on the distribution of the relative kinetic energy of the products released as well as on their angular distributions. 

Greene, Ross, and their co-workers [15,40] have found the following total reaction cross sections for reactions of K atoms with hydrogen halides ... 

Many trajectories were integrated to obtain either total reaction cross sections for comparison with molecular beams experiments rotational and... 

The total reaction cross section (4.95b) is zero if Sl is real. 

Fig. 14.2 (a) Energy dependence of the total reaction cross sections for with ethylene for the theoretical model (solid line) and experimental measurements (diamonds), (b) Energy profile for the reaction of with C H. Reprinted with permission from [40]. Copyright 2006... 

---