Sensitivity functions cross-section

When the variations in the detector response function affect the system, Eq. (206) represents only the direct contribution to the detector response. The indirect contributions can be taken into account as in the case of the cross-section sensitivity function which is discussed below. Equation (206) gives the exact contribution of different components of the detector to its response. 

The detailed form of cross-section sensitivity functions depends on the type of nuclear data under consideration. These special cases illustrate... 

Cross-section sensitivity studies have been performed for inhomogeneous systems since the late sixties ((S6). Their use has lately been promoted by the Oak Ridge group (5/, 59, 77, 72, 75, 79,80,87,88). This group refers to cross-section sensitivity spectra as sensitivity profiles. Other terminology used for cross-section sensitivity functions include perturbation functions (59) and sensitivity coefficients (56). 

The generalized-function formulation of OPT for inhomogeneous systems [Eq. (165)] is the source of sensitivity functions for various integral parameters that can be expressed as a composite functional. For example, the differential cross-section sensitivity function derived from Eq. (165) is... 

Cross-section sensitivity functions are very useful also for the adjustment of nuclear data so as to provide a best fit for measured integral parameters. Systematic adjustment of cross sections began in the middle sixties 103, 104) and has developed continuously. In fact, cross-section adjustment was one of the first applications of cross-section sensitivity functions (59). Descriptions of the activities in cross-section adjustment, including the application of perturbation theory, have been recently reported 76, 105-107). 

Many predictive applications of perturbation theory techniques for the design, analysis, and optimization of various nuclear systems, as well as for the evaluation and adjustment of nuclear data, are based on sensitivity functions. Section VI presents the fundamentals of perturbation-based sensitivity studies, describes the origin of sensitivity functions, and discusses several areas of application for sensitivity studies. These include cross-section sensitivity studies and optimization studies which are emerging as important fields for the application of perturbation theory. 

In this section we have tried to indicate the usefulness of sensitivity functions for the large number of applications. Considerable development is still required, however, before full benefit can be derived from perturbation theory methods for all these applications. Cross-section sensitivity studies, for example, will be more useful and reliable when cross-section error files supplement the cross-section files in present use. New computer code systems that can process these error files and perform sensitivity studies, allowing... 

Much work is still required before many of the perturbation theory formulations reviewed and presented here can be implemented in practice. If full benefit is to be drawn from perturbation theory techniques for a wide variety of problems concerned with the design, analysis, and optimization of nuclear systems, computer code systems of the future must include basic and specific modules for calculations based on perturbation theory formulations. The basic modules are intended for the calculation of different sensitivity functions. Specific modules should enable performanee of dilTerent studies sueh as cross-section sensitivity studies, analysis of alterations in the design or operating conditions of nuclear systems, and optimization studies. 

The lines of primary interest ia an xps spectmm ate those reflecting photoelectrons from cote electron energy levels of the surface atoms. These ate labeled ia Figure 8 for the Ag 3, 3p, and 3t7 electrons. The sensitivity of xps toward certain elements, and hence the surface sensitivity attainable for these elements, is dependent upon intrinsic properties of the photoelectron lines observed. The parameter governing the relative iatensities of these cote level peaks is the photoionization cross-section, (. This parameter describes the relative efficiency of the photoionization process for each cote electron as a function of element atomic number. Obviously, the photoionization efficiency is not the same for electrons from the same cote level of all elements. This difference results ia variable surface sensitivity for elements even though the same cote level electrons may be monitored. 

Two spectra of sulfided catalysts in Fig. 4.16 show that sulfur can also be detected, albeit with lower sensitivity, because of the Z2 dependence of the cross section in (4-6). Figure 4.17 gives the S/Mo atomic ratio as a function of sulfidation temperature. It indicates that sulfur uptake by M0O3 is already significant at room temperature and increases to the expected S/Mo ratio of 2 above 100 °C. Combination of these results with SIMS and XPS data have led to a detailed mechanism for the sulfidation of silica-supported molybdenum catalysts [21] (see also Chapter 9). 

Recently Schulz et aland Fischer et al have had some difficulty in applying the CDW-EIS theory successfully for fully differential cross sections in fast ion-atom collisions at large perturbations. These ionization cross sections are expected to be sensitive to the quality of the target wave function and therefore accurate wave functions are needed to calculate these cross sections. Thus one purpose of this paper is to address this problem theoretically by re-examining the CDW-EIS model and the assumptions on which it is based. We will explore this by employing different potentials to represent the interaction between the ionized electron, projectile ion and residual target ion. For other recent work carried out on fully differential cross sections see and references therein. This discussion is presented in section 4. 

Three-dimensional (3D) structuring of materials allows miniaturization of photonic devices, micro-(nano-)electromechanical systems (MEMS and NEMS), micro-total analysis systems (yu,-TAS), and other systems functioning on the micro- and nanoscale. Miniature photonic structures enable practical implementation of near-held manipulation, plasmonics, and photonic band-gap (PEG) materials, also known as photonic crystals (PhC) [1,2]. In micromechanics, fast response times are possible due to the small dimensions of moving parts. Femtoliter-level sensitivity of /x-TAS devices has been achieved due to minute volumes and cross-sections of channels and reaction chambers, in combination with high resolution and sensitivity of optical con-focal microscopy. Progress in all these areas relies on the 3D structuring of bulk and thin-fllm dielectrics, metals, and organic photosensitive materials. 

The probability of fusion is a sensitive function of the product of the atomic numbers of the colliding ions. The abrupt decline of the fusion cross section as the Coulomb force between the ions increases is due to the emergence of the deep inelastic reaction mechanism. This decline and other features of the fusion cross section can be explained in terms of the potential between the colliding ions. This potential consists of three contributions, the Coulomb potential, the nuclear potential, and the centrifugal potential. The variation of this potential as a function of the angular momentum l and radial separation is shown as Figure 10.26. 

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