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An Introduction to the Passage of Energetic Particles through Matter

N J, Carron (2021) An Introduction to the Passage of Energetic Particles through Matter. Taylor & Francis Group, LLC. (Submitted)

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The subject of the passage of neutral and charged particles through matter has been studied for a century. After decades of much early experimental work and nonquantum mechanical calculation, the basic physics of the passage of photons, electrons, protons, and heavier charged particles through matter was worked out theoretically in the decades following the completion of quantum mechanics, largely in the 1930’s, and neutron diffusion shortly thereafter. There is excellent summary documentation, from the 1950’s and later. The early, basic theoretical treatments, now textbook material, were compared with data available at the time. Today, one has available large data libraries with cross sections compiled from decades of measurements and sophisticated calculations. The accuracy of data in current libraries, based on modern computations and continually accumulating experimental measurements, far surpasses that of the early, relatively elementary, calculations. As one example, below 100 keV the standard, original Bethe mean stopping power formula for electrons is less than 85% of the actual stopping power, and below 10 keV may be less than 60% of the correct value in some materials. At still lower energies it is effectively inapplicable. Today’s computing capabilities have allowed accurate calculations (although electron stopping power below a few keV is still somewhat problematical). Given the long history of work on the passage of energetic particles through matter, there is little new that can be said of a fundamental nature. And almost all the data collected here are available elsewhere, often on the Web, or in journal articles. However, workers in need of certain parameters (cross sections, stopping powers, etc.) may not be aware of the availability of the needed data, which can be well-known to other disciplines. While nuclear physicists may be very familiar with the cross section compilation in the evaluated nuclear data files (ENDF), solid-state physicists and electronic engineers studying the effects of cosmic rays on satellites or micro-electronics may be less so. It is not widely known that photo-atomic and electro-atomic cross sections are also tabulated in ENDF, or that models for electron multiple scattering are available on the Web. Knowing where to access those and other data, extracting a needed subset from all that is available, knowing how to interpret the format in which it is presented, can be time-consuming tasks. That has often been the experience of the author and, according to a short, informal survey, the author’s colleagues as well. Graphs of parameters as a function of the relevant independent variable (cross sections vs. energy or vs. scattering angle, etc.) are sometimes what is wanted, and occasionally are sufficient for the purpose at hand. It seemed worthwhile to try to collect in one place as much of these often needed data as possible, together with enough background physics so the reader can feel comfortable applying them, having some understanding of where they come from and why they have the order of magnitude they have. The idea is to make up-to-date data available and understandable to nonspecialists. The book and its accompanying data CD and contour plots are intended to be a working reference for scientists and engineers in industry, educational institutions, and laboratories, providing ready access to useful data. We have also tried to digest the data in the form of useful graphs, showing dependencies over a wide range of the independent variable(s), allowing quick approximations of a quantity. And it was decided to include much of the numerical data on a CD-ROM included with the book. Throughout, we include references to where the data came from, and where updates to them, and related information, can be found. While there are many articles and treatises on individual projectiles, there are fewer if any introductions providing an overview of the entire subject for photons, electrons, ions, and neutrons; we attempt to provide such an introduction here. It will be useful to practitioners of radiation physics, but the level of analysis is not intended to satisfy the expert. It is intermediate between a text book and usual reference. It is not intended to be a comprehensive treatise on the subject; that would be too vast a task. References that together may be taken to constitute such a treatise are given throughout. And the book may serve as an introduction to the massive, invaluable ENDF data library. In addition, certain features of particles interacting with matter are not so well known, and worth bringing to a wider audience. It is widely appreciated, for example, that when a photon Compton scatters from a free electron, its angular distribution peaks in the forward direction. But it is less widely recognized that when a photon Compton scatters from an atom, its angular distribution vanishes in the forward direction. For electrons, it is common knowledge that the Coulomb cross section for scattering from an isolated charge (nucleus) diverges. Screening of atomic electrons makes the electron-atom elastic scattering cross section finite. But its sharp forward peaking, even on a screened atom, is remarkable. The elastic differential cross section in exactly the forward direction (u ¼ 0) increases in proportion to the square of the incident electron energy, while the total elastic cross section saturates to a constant as energy increases. On Fe, the forward differential cross section rises to a value of 1013 barn=sr at 100 MeV. At an angle of only 18 it has fallen 9 orders of magnitude to 104 b=sr. At that energy 99% of the scattering occurs at angles less than 0.18, in a solid angle of only 10�8 of a sphere. Any cross section, say the photon-atom Compton cross section s(E), is a function of incident photon energy E for each target material. It is therefore clear that the cross section on all elements, s(Z,E), is a function of atomic number Z and E, and so forms a surface over the Z-E plane. That surface can be represented by a contour plot in the Z-E plane. One thereby displays an interaction for all elements over all energies of interest on a single graph. Numerical values of cross sections and=or stopping powers can be read quickly, often to quite useful accuracy, from such a graph, especially from the large, color 11001700 plots. These plots are considered an integral part of this book. They are included as high resolution Portable Document Format (pdf) files on the accompanying CD-ROM, appropriate for printing on 11001700 paper. Such a contour plot assists in understanding the overall process, enables global trends to be discerned, and helps one choose a material with desired characteristics. In addition, there is satisfaction in knowing more than just the immediate number one needs; one develops more confidence in each number when it is viewed along side its neighbors.* For a photon cross section such a plot brings to light the difference between the atomic cross section s(barn=atom) as a function of Z and E, and the bulk matter cross section s(cm2 =gram) as a function of Z and E. In the conversion between the two the atomic weight A(Z) of elements in their natural isotopic composition enters the conversion factor. Since A(Z) has irregular behavior as a function of Z, contours of s(cm2 =gm) exhibit an irregular pattern that does not occur in the smooth s(barn=atom). Similar graphs can be constructed for any cross section or for stopping powers or ranges of charged particles. Cross section or stopping power contour plots are more than of academic interest. Not only does one see the full span of physics on a single page for, say, the total photon cross section, as the dominant process passes from photoelectric absorption to Compton scattering to pair production as energy increases, but in addition one can read the numerical value of the cross section often to better than a few percent. The author uses them routinely. It seems worthwhile to bring these and other features to the attention of a wider audience, and to provide comments clarifying and emphasizing important points. Further, some published data are based on quite sophisticated calculations (for example self-consistent relativistic Dirac-Hartree-Fock models) that generally give a very believable result for cross sections, but may produce other unrealistic features. The self-consistent DHF model of elastic photon-atom scattering produces detailed form factors, but can be inaccurate for absorption edges. Such published data are most meaningful to other specialists in the field. The general user may wonder why a seemingly elementary quantity like the photo-ionization edge in Fe, which is given as 7.9024 eV in most tabulations, is given as 7.530 eV in LLNL’s Evaluated Photon Data Library (EPDL) data base, and appears as 3.60 eV in calculations of elastic form factors [C.T. Chantler J. Phys. Chem. Ref. Data 24:71 (1995)]. Likewise the separation of edges, such as LII to LIII, may not be calculated accurately. The reason is that detailed models accurate for their intended purpose (calculation of scattering cross sections) are not necessarily accurate for bound energies; they tend to break down at the 3–5 eV level. The resulting photo-ionization edge may be off by more than 1 eV. In particular, Livermore’s EPDL photo-atomic library was constructed together with its EEDL electro-atomic counterpart for the purpose of having a consistent set of cross sections for electron-photon transport calculations. Here consistency between data sets is more important than absolute accuracy. The library documentation makes that purpose clear, and cautions against using the cross sections for other purposes without checking other sources. Merely bringing these and other related facts to the attention of a wider audience seemed sensible. Fortunately for the author the U.S. Air Force Office of Scientific Research agreed that this was a worthwhile undertaking, it hopefully being helpful to those unfamiliar with the data and saving workers much time. AFOSR has funded its writing for some time. The author is grateful for that support; there is no way the book could have been written without it. Sources for data and their updates are given as Web addresses. Unfortunately, internet URLs change over time. We have found no simple way around this dilemma except to note that each address is usually associated with a particular organization which survives longer than the specific address for the data in question. Creative hunting for the new address within that organization may be necessary. The address for photo-nuclear cross sections at the International Atomic Energy Agency may change, but the IAEA will still be there. Time and support limitations have resulted in photons and electrons being discussed more thoroughly than ions and neutrons. The former are important in their wide occurrence, are more penetrating than ions, and are a common source of effects. There are already a number of good reviews of heavy ion transport, and excellent, readily available calculational tools. Neutron interactions are too varied and numerous to attempt a full compilation. And the author is more familiar with photon and electron effects. A broad discussion is given of the effects of multiple scattering on electron trajectories. We include a derivation and discussion of the conversion of a photon flux to an electron flux, via photoelectric, Compton, and pairproduction interactions (the ‘‘1% Rule’’), relevant, for example, to noise in pixellated detectors. Its opposite, the conversion of electrons to photons via Bremsstrahlung, is also discussed, with emphasis on the photon number flux in addition to the common energy flux, relevant, for example, to the problem of electrons penetrating material thicker than their range.

Item Type: Book
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Depositing User: user user2 2
Date Deposited: 09 May 2022 00:11
Last Modified: 09 May 2022 00:11

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