Cross section, reaction

In a third step the S-matrix is related to state-selected reaction cross sections a., in principle observable in beam scattering experiments [28, 29, 30, 31, 32, 33, 34 and 35], by the fiindamental equation of scattering theory... 

A bimoleciilar reaction can be regarded as a reactive collision with a reaction cross section a that depends on the relative translational energy of the reactant molecules A and B (masses and m ). The specific rate constant k(E ) can thus fonnally be written in tenns of an effective reaction cross section o, multiplied by the relative centre of mass velocity... 

We use the symbol for Boltzmaim s constant to distingiush it from tire rate constant k. Equation (A3.4.85) defines the thennal average reaction cross section (a). 

In principle, the reaction cross section not only depends on the relative translational energy, but also on individual reactant and product quantum states. Its sole dependence on E in the simplified effective expression (equation (A3.4.82)) already implies unspecified averages over reactant states and sums over product states. For practical purposes it is therefore appropriate to consider simplified models for tire energy dependence of the effective reaction cross section. They often fonn the basis for the interpretation of the temperature dependence of thennal cross sections. Figure A3.4.5 illustrates several cross section models. 

The hyperbolic cross section model can be generalized fiirther by introducing a fiinction/(A ) (AE = E - Eq) to describe the reaction cross section above a tln-eshold ... 

A state-to-state integral reaction cross section from reactant level a to product level b takes the fomr... 

Light J C, Ross J and Shuler K E 1969 Rate coefficients, reaction cross sections and microscopic reversibility Kinetic Processes in Gases and Piasmas ed A R Hochstim (New York Academic) pp 281-320... 

Using a guided ion beam instrument the translational energy dependent reaction cross sections of endothemiic fragmentation processes can be detemiined [32]. Modelling these cross sections ultimately yields their energy tln-esholds and a great deal of valuable themiochemical infomiation has been derived with this teclmique. Precision of 0.2 eV can be obtained for reaction tln-esholds. Bimolecular reactions can also be studied and reaction enthalpies derived from the analysis of the cross section data. 

The big advantage of the Gaussian wavepacket method over the swarm of trajectory approach is that a wave function is being used, which can be easily manipulated to obtain quantum mechanical information such as the spechum, or reaction cross-sections. The initial Gaussian wave packet is chosen so that it... 

The technologically most important isotope, Pu, has been produced in large quantities since 1944 from natural or partially enriched uranium in production reactors. This isotope is characterized by a high fission reaction cross section and is useful for fission weapons, as trigger for thermonuclear weapons, and as fuel for breeder reactors. A large future source of plutonium may be from fast-neutron breeder reactors. 

When reaction cross sections are suflSciently large over an extended energy range, the entire depth profile may be obtained using a single incident beam energy. This is referred to as nonresonant profiling. 

The sensitivity of NRA is affected by reaction cross sections, interfering reactions and other background effects. Flence, it is impossible to make general statements as... 

NRA is an effective technique for measuring depth profiles of light elements in solids. Its sensitivity and isotope-selective character make it ideal for isotopic tracer experiments. NRA is also capable of profiling hydrogen, which can be characterized by only a few other analytical techniques. Future prospects include further application of the technique in a wider range of fields, three-dimensional mapping with microbeams, and development of an easily accessible and comprehensive compilation of reaction cross sections. 

NRA as in RBS or ERDA, and possible modification of the target composition as a result of irradiation must be considered. Nuclear reaction cross-sections are also usually not available in analytical form for direct evaluation of measured data. Concentrations are, therefore, often obtained by comparison of the measured data with results from standard samples of known concentration. 

Much of the interest of this symposium centers on the effect of the kinetic energy of the reacting ion on the reaction cross-section. A detailed examination of the effect of energy variations is essential to the development of a comprehensive theory for the kinetics of ion-molecule reactions. 

The reaction cross-section should therefore become zero for E Ec. By taking D = 5.0 e.v. and W = 0.5 e.v. for the reactions listed in Table II, the critical energies could be calculated (13,14). 

After identifying the reactant ion, reaction cross-sections were measured as a function of average reactant ion kinetic energy. Q experimental is measured for given values of (eEl) 1/2 in the spectrometer, and experimental values of k... 

Intramolecular isotope effect studies on the systems HD+ + He, HD+ + Ne, Ar+ + HD, and Kr + + HD (12) suggest that the E l dependence of reaction cross-section at higher reactant ion kinetic energy may be fortuitous. In these experiments the velocity dependence of the ratio of XH f /XD + cross-sections was determined. The experimental results are presented in summary in Figures 5 and 6. The G-S model makes no predictions concerning these competitive processes. The masses of the respective ions and reduced masses of the respective complex reacting systems are identical for both H and D product ions. Consequently, the intramolecular isotope effect study illuminates those... 

Reactions of Complex Ions. For reactions of systems containing H2 or HD the failure to observe an E 1/2 dependence of reaction cross-section was probably the result of the failure to include all products of ion-molecule reaction in the calculation of the experimental cross-sections. For reactions of complex molecule ions where electron impact ionization probably produces a distribution of vibrationally excited states, kinetic energy transfer can readily open channels which yield products obscured by primary ionization processes. In such cases an E n dependence of cross-section may be determined frequently n = 1 has been found. 

---