Perturbations cross-section

GPT is a method of evaluating the effects of cross-section perturbations on quantities that can be formulated as integral responses, such as reactivity and power density. An initial requirement is an exact solution of a reactor physics model for a reference core configuration. In FORMOSA-P the reference neutronics model is a two-dimensional Cartesian [x-y] geometry implementation of the nodal expansion method (NEM) to solve the two-group, steady-state neutron diffusion equation ... 

System perturbations can usually be expressed as perturbations in the macroscopic cross sections. The operators of the perturbation integrals of the different formulations depend on these cross-section perturbations the functional dependence varies with the formulation. The simplest dependence is found in the integrodifferential formulation in which the perturbation operators are the cross-section perturbations. Conversely, the integral transport theory formulations include kernel perturbations that do not depend linearly on cross-section perturbations. Consequently, it is necessary to evaluate the perturbation in the kernels before applying integral pertur-... 

For two Bom-Oppenlieimer surfaces (the ground state and a single electronic excited state), the total photodissociation cross section for the system to absorb a photon of energy ai, given that it is initially at a state x) with energy can be shown, by simple application of second-order perturbation theory, to be [89]... 

When high-energy electrons are injected into thin specimen, most of them tend to pass through without any perturbation occurring from the substances, because the cross section of atomic nuclei is small enough to such electrons. Some of the incident electrons are elastically scattered to be diffracted, and the others... 

Laminar flow ceases to be stable when a small perturbation or disturbance in the flow tends to increase in magnitude rather than decay. For flow in a pipe of circular cross-section, the critical condition occurs at a Reynolds number of about 2100. Thus although laminar flow can take place at much higher values of Reynolds number, that flow is no longer stable and a small disturbance to the flow will lead to the growth of the disturbance and the onset of turbulence. Similarly, if turbulence is artificially promoted at a Reynolds number of less than 2100 the flow will ultimately revert to a laminar condition in the absence of any further disturbance. 

In connection with the transition, Ryan and Johnson l0) have proposed a stability parameter Z. If the critical value Zc of that parameter is exceeded at any point on the cross-section of the pipe, then turbulence will ensue. Based on a concept of a balance between energy supply to a perturbation and energy dissipation, it was proposed that Z could be defined as ... 

Within the semiclassical, perturbational treatment of the interaction of radiation with matter [77,78] and within the dipole approximation [79], the total energy absorption cross section may be written in the form [11,12,20,80]... 

The differential cross section for the photoelectron can be calculated using first-order time-dependent perturbation theory (see Cardona and Ley, 1978). The incident light is treated as a perturbation. 

The first (and still the foremost) quantum theory of stopping, attributed to Bethe [19,20], considers the observables energy and momentum transfers as fundamental in the interaction of fast charged particles with atomic electrons. Taking the simplest case of a heavy, fast, yet nonrelativistic incident projectile, the excitation cross-section is developed in the first Born approximation that is, the incident particle is represented as a plane wave and the scattered particle as a slightly perturbed wave. Representing the Coulombic interaction as a Fourier integral over momentum transfer, Bethe derives the differential Born cross-section for excitation to the nth quantum state of the atom as follows. 

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. 

To get accurate results from this approach, it is necessary that the collisional changes in the internal energy be small compared to the translational energy. Then one can accurately assume a common translation path for all coupled internal states. In the usual applications of this method, one does not include interference effects between different classical paths, so that translational quantum effects, including total elastic cross sections, are not predicted. If the perturbation approximation is also used, accuracy can be guaranteed only when the sum of the transition probabilities remains small throughout the collision. 

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