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X-Ray Photoelectron and Auger Electron Spectroscopy
Published in Grinberg Nelu, Rodriguez Sonia, Ewing’s Analytical Instrumentation Handbook, Fourth Edition, 2019
C. R. Brundle, J. F. Watts, J. Wolstenholme
There are many factors which must be considered when attempting to quantify electron spectra. These are either sample-related factors or spectrometer-related factors. Sample-related factors include:1.The cross-section for emission, which is the probability of the emission of an electron owing to the effect of the incoming radiation (X-ray photon in XPS or electron in AES). The cross-section depends upon a number of factors such as the element under investigation, the orbital from which the electron is ejected, and the energy of the exciting radiation.2.The escape depth of the electron emitted from the atom, which depends upon its KE (the escape depth passes through a minimum with increasing KE. The minimum occurs in the region of 20-50 eV) and the nature of the specimen.3.The angle between the incoming X-ray beam and the emitted photoelectron. This affects the sensitivity to electrons in different orbitals in different ways via the angular asymmetry factor. It can be shown that if the angle is 55.7° (the so-called “magic angle”), this factor becomes unity and does not have to be taken into account.
Nuclear Cross Sections, Reaction Probabilities, and Reaction Rates
Published in Robert E. Masterson, Introduction to Nuclear Reactor Physics, 2017
Essentially, a nuclear cross section is a convenient way of measuring the probability that an incoming particle will hit the nucleus (or another comparably sized object like an electron) and, as the result of that collision, cause a particular nuclear reaction or set of reactions to occur. There is a direct correlation between the size of a nuclear cross section and the cross-sectional area of the nucleus that the incident particle is trying to hit. A larger cross-sectional area means that there will be a higher probability for a reaction to occur, and a smaller cross-sectional area means that the probability will be lower. The standard unit for measuring nuclear cross sections is a unit called the barn, (σ), which has a value of 10−24 cm2. Hence a barn is roughly equivalent to the cross-sectional area of an atomic nucleus (i.e., A = π*D2/4, where the diameter of the nucleus D is about 10–12 cm). (Refer to Figure 4.2 to get an idea of exactly how small a cross-sectional area of 10–24 cm can be.) In comparison, 1 Angstrom, a common unit for measuring the wavelength of light in the fields of chemistry and optics, is about 10–8 cm, and the atomic nucleus itself is about 1 femtometer (1 × 10–12 cm) in diameter. Hence the electron cloud in Figure 4.2 is about 1 Angstrom in diameter, while the nucleus is about 10,000 times smaller than this. Historically, the term “barn” was invented because it was believed that the early scientists who were shooting particles at the nucleus were having a hard time hitting the broad side of a barn. Over the years, the term became imbedded in the culture of the nuclear industry, and now all nuclear reaction probabilities are measured in this way.
Nuclear Cross Sections and Reaction Probabilities
Published in Robert E. Masterson, Nuclear Engineering Fundamentals, 2017
Essentially, a nuclear cross section is a convenient way of measuring the probability that an incoming particle will hit the nucleus (or another comparably sized object like an electron) and, as the result of that collision, cause a particular nuclear reaction or set of reactions to occur. There is a direct correlation between the size of a nuclear cross section and the cross-sectional area of the nucleus that the incident particle is trying to hit. A larger cross-sectional area means that there will be a higher probability for a reaction to occur, and a smaller cross sectional area means that the probability will be lower. The standard unit for measuring nuclear cross sections is a unit called the barn, (σ), which has a value of 10−24 cm2. Hence a barn is roughly equivalent to the cross-sectional area of an atomic nucleus (i.e., A = π*D2/4, where the diameter of the nucleus D is about 10–12 cm). (Refer to Figure 4.2 to get an idea of exactly how small a cross-sectional area of 10–24 cm can be.) In comparison, 1 Angstrom, a common unit for measuring the wavelength of light in the fields of chemistry and optics, is about 10–8 cm, and the atomic nucleus itself is about 1 femtometer (1 × 10–12 cm) in diameter. Hence the electron cloud in Figure 4.2 is about 1 Angstrom in diameter, while the nucleus is about 10,000 times smaller than this. Historically, the term “barn” was invented because it was believed that the early scientists who were shooting particles at the nucleus were having a hard time hitting the broad side of a barn. Over the years, the term became imbedded in the culture of the nuclear industry, and now all nuclear reaction probabilities are measured in this way.
Generation of Multigroup Cross Sections with an Improved Monte Carlo Algorithm
Published in Nuclear Science and Engineering, 2020
Li Cheng, Bin Zhong, Huayun Shen, Zehua Hu, Baiwen Li
The estimation of the scattering matrices is somehow complicated. In the current continuous cross-section libraries, only the total cross sections of scattering are given explicitly.dscattering cross section is the differential cross section that depends on incident, exiting energies and scattering angle. In this paper, “total scattering cross section” refers to the scattering cross section integrated over the exiting energy and angle, and “scattering matrix” refers to the group-to-group scattering cross section. The distributions over outgoing energy and angle are specified by various kinds of laws that could take different forms, continuous spectrum, or discrete cumulative probablities. They are usually assumed in a center-of-mass system and must be transformed into a laboratory system. Moreover, if a neutron becomes thermalized, target nuclides can no more be taken as stationary, and their velocities must be sampled. For these reasons, it is impossible to use the track-length method in the calculation of scattering matrices, whereas the collision estimator still works in this scenario. In the latter method, no extra effort is needed other than collecting the states of the neutrons before and after executions of the regular sacttering subroutine in a transport program and tallying the energy and angle bins accordingly. In Ref. 7, it is also referred to as the weight-to-flux–ratio method since the scattering rate in the numerator is evaluated by the sum of the neutron weights. The calculation could even be done by analyzing files that record events and tracks produced by transport simulation, which is practiced in Ref. 9.
Comparing the Effectiveness of Polymer and Composite Materials to Aluminum for Extended Deep Space Travel
Published in Nuclear Technology, 2020
Daniel K. Bond, Braden Goddard, Robert C. Singleterry, Sama Bilbao y León
To evaluate methods to increase thermal neutron absorption, layering configurations using materials with natural and 100% enriched compositions of 6Li and 10B are evaluated. To determine the thickness of the layers of each neutron-absorbing material, the thermal neutron absorption mean free path is calculated. Mean free path is the average distance that a particle moves between interactions and is the inverse of the sum of macroscopic cross sections for the constituents within a material:
A Unified Framework of Stabilized Finite Element Methods for Solving the Boltzmann Transport Equation
Published in Nuclear Science and Engineering, 2023
Qingming He, Chao Fang, Liangzhi Cao, Haoyu Zhang
which is the same as the ARE [Eq. (18)]. The dimension of is length, which is the same as IFP [Eq. (19)]. Given that the free path can be defined physically as the average distance between two interactions of particles and materials, it can be expressed as the reciprocal of the total cross section.