Cross sections isotope effects

Almost all of the practical calculations of the Doppler effect in fast reactors are carried out by the conventional method, which consists of tracing through the expressions for the effective cross sections, as developed in this paper for the different fuel isotopes and energy ranges. Then, one can either run two multigroup diffusion calculations with the effective cross sections at different temperatures and obtain the reactivity changes associated with the Doppler effect as the difference of the two criticality factors, or else one can do only one multigroup calculation and find the Doppler coefficient by the use of perturbation theory. Both ways are, of course, equivalent from a mathematical point of view. 

The ratio factors R in O Eq. (30.35) are ideally unity, but small deviations and their uncertainties must be considered. Rg is the ratio of isotopic abundances for the unknown and standard, R, is the ratio of neutron fluences (including fluence drop off, self-shielding, and scattering), is the ratio of effective cross sections if the shape of neutron spectrum differs from the unknown sample to standard, Re is the ratio of counting efficiencies (differences due to geometry, y-ray self-shielding, and dead-time effects). 

The traditional way to calculate the physical characteristics of a fast reactor is to carry out the following steps (1) preparation of the effective cross sections for regions of the reactor (2) a three-dimensional calculation to obtain k-eff, and real and adjoint fluxes (3) edit the results of the previous steps to estimate the power and reaction rate distributions, neutron kinetics parameters, control rod effectiveness, etc., and (4) a bumup analysis, calculating the variation of the isotopic composition with time, and then recalculating the results obtained in the previous steps for particular bumup states. This scheme has been implemented, for example, in the TRIGEX code [4.49]. This code calculates k-eff, few group real and adjoint fluxes, power spatial distribution, dose factor and reaction rates distributions, breeding parameters, bumup effects, and kinetics parameters (effective delayed neutron Auction, etc.). 

Ongoing work suggests that the 2.1-s activity may be an observation of and that the ground state may be significandy shorter lived. The isotope Th2 = 8 s) can only be produced indirectly. At first it was reported as a 15-min SF activity in the " Bk( 0,4n) reaction, as the decay daughter of a small EC branch in 27-sec Db. However, 3% of the 6 nb evaporation-residue cross section results in an effective cross section of 180 pb for the production of the 15-min activity [161]. A single event consistent with an 8-s half-hfe was observed in an a decay chain of Hs (see below), which is considered to be the more reliable observation of Rf. Work is needed to sort out the decay properties of this isotope. Several of the Rf isotopes are also produced indirectly in hot-fusion reactions as daughters of the a decays of Sg isotopes (see below). 

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. 

Intramolecular Isotope Effects. The data in Figure 2 clearly illustrate the failure of the experimental results in following the predicted velocity dependence of the Langevin cross-section. The remark has been frequently made that in the reactions of complex ions with molecules, hydrocarbon systems etc., experimental cross-sections correlate better with an E l than E 112 dependence on reactant ion kinetic energy (14, 24). This energy dependence of reaction presents a fundamental problem with respect to the nature of the ion-molecule interaction potential. So far no theory has been proposed which quantitatively predicts the E l dependence, and under these circumstances interpreting the experiment in these terms is questionable. 

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... 

Rare-Gas-Hydrogen Reactions. Ion-molecule reactions in the rare gas-hydrogen system are of great interest both theoretically and experimentally. The properties of the reactants and products are well known or may be calculated, and the properties of the intermediate three-body complex pose a tractable theoretical problem. Systematic studies of cross-section energy dependence and isotope effects in these systems have been undertaken by Friedman and co-workers (29, 47, 49, 67), by Koski and co-workers (2, 3), and by Giese and Maier (15, 16). 

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