A new version of the Fortran program sbethe is presented. This program calculates the stopping power of materials for swift charged particles with small charges (electrons, muons, protons, their antiparticles, and alphas). The electronic stopping power is computed from the corrected Bethe formula, with the shell correction derived from numerical calculations with the plane-wave Born approximation (PWBA) for atoms, which were based on an independent-electron model with the Dirac–Hartree–Fock–Slater self-consistent potential for the ground-state configuration of the target atom. The density effect correction is evaluated from an empirical optical oscillator strength (OOS) model based on atomic subshell contributions obtained from PWBA calculations. For projectiles heavier than the electron, the Barkas correction is evaluated from the OOS model, and the Lindhard–Sørensen correction is estimated from an accurate parameterization of its numerical values. The calculated electronic stopping power is completely determined by a single empirical parameter, the mean excitation energy or I value of the material. The radiative stopping power for electrons, and positrons, is evaluated by means of Seltzer and Berger's cross section tables for bremsstrahlung emission. The radiative contribution to the stopping power of muons is obtained from interpolation of tables given by Groom et al. (2001) [5]. The program yields reliable stopping powers and particle ranges for arbitrary materials and projectiles with kinetic energy larger than a certain cutoff value Ecut, which is specific of each projectile kind. The program is accompanied by an extensive database that contains tables of relevant energy-dependent atomic quantities for all the elements from hydrogen to einsteinium. sbethe may be used to generate basic information for dosimetry calculations and Monte Carlo simulations of radiation transport, and as a pedagogical tool. New version program summary Program Title: sbetheCPC Library link to program files: https://doi.org/10.17632/7zw25f428t.2Licensing provisions:: CC By NC 3.0Programming language:: Fortran 90Journal reference of previous version:: Comput. Phys. Commun. 287 (2023) 108697Does the new version supersede the previous version?:: YesReasons for the new version:: The present version extends the original Fortran code by implementing a more realistic extension formula for low-energy protons and alphas in various materials. The program now accounts for radiative effects for high-energy muons. It also produces additional output files with relevant data.Summary of revisions:: The present program differs from the one published by Salvat and Andreo [1] in the following aspects: 1) The program uses a fitted extension formula for low-energy protons and alphas in various materials for which enough measured stopping-power data are available. 2) Sbethe generates the output file named PENstp.dat with values of the stopping power tabulated at the energy grids used by the Monte Carlo simulation codes penelope and penhan [2,3]. 3) The modified program accounts for radiative effects for high-energy muons. 4) The manual of the code has been expanded to describe the new features covered by the program.Nature of problem:: The program calculates the stopping power of arbitrary materials for swift charged projectiles with small charges. The material is characterized by its chemical composition, mass density, and the empirical I value. The considered projectiles are electrons, positrons, negative muons, antimuons, protons, antiprotons, and alphas, which are described as point particles characterized by their mass and charge. If the actual I value of the material is known, the results from the program are expected to be reliable for projectiles with kinetic energy higher than a value Ecut, of the order of 1 keV for electrons and positrons, 150 keV for muons and antimuons, 0.75 MeV for protons and antiprotons, and 5 MeV for alpha particles.Solution method:: The electronic stopping power is calculated by means of a corrected Bethe formula [1], which combines the conventional Bethe logarithm with the following corrections,1)the shell correction obtained from calculations based on the plane-wave Born approximation with the self-consistent Dirac–Hartree–Fock–Slater (DHFS) potential of neutral atoms in their ground-state configuration,2)the density effect correction, which accounts for the reduction of the stopping power caused by the dielectric polarization of the medium,3)a parameterization of the Lindhard–Sørensen correction, which generalizes the Bloch correction for relativistic projectiles, and4)the Barkas correction, which accounts for differences between the stopping powers of particles and their antiparticles. The density-effect and the Barkas corrections are calculated from a model of the optical oscillator strength (OOS) of the material, which combines the contributions of inner atomic subshells calculated with the DHFS potential, with a classical oscillator model for the contribution of valence electrons.An extrapolation formula is used to extend the calculated electronic stopping power to energies less than Ecut to allow the calculation of particle ranges.For electrons and positrons, the radiative stopping power is calculated from numerical tables prepared by Seltzer and Berger [4], while radiative stopping powers for muons are obtained from tables derived by cubic spline interpolation from tables in Groom et al. [5].Additional comments including restrictions and unusual features:: The calculated stopping power is determined by a single parameter, the mean excitation energy or I value. The program assigns to each material a default I value, derived from the recommendations in the ICRU Reports 37 and 49 [6], which can be changed by the user. The distribution package includes text files with tables of atomic energy-dependent quantities (subshell optical oscillator strengths, shell corrections, scaled cross sections for bremsstrahlung emission by electrons, tables of radiative stopping powers of muons) that are used in the calculations. References [1]F. Salvat, P. Andreo, SBETHE: Stopping powers of materials for swift charged particles from the corrected Bethe formula, Comput. Phys. Commun. 287 (2023) 108697.[2]F. Salvat, penelope-2024: A Code System for Monte Carlo Simulation of Electron and Photon Transport, OECD Nuclear Energy Agency, document NEA/MBDAV/R(2024)1, OECD Publishing, Paris, 2025, https://doi.org/10.82155/1vk5-0513.[3]F. Salvat, C. Heredia, Electromagnetic interaction models for Monte Carlo simulation of protons and alpha particles, Nucl. Instrum. Meth. B 546 (2023) 165157.[4]S.M. Seltzer, M.J. Berger, Bremsstrahlung spectra from electron interactions with screened atomic nuclei and orbital electrons, Nucl. Instrum. Meth. B 12 (1985) 95–134; S.M. Seltzer, M.J. Berger, Bremsstrahlung energy spectra from electrons with kinetic energy 1 keV–10 GeV incident on screened nuclei and orbital electrons of neutral atoms with Z= 1–100, At. Data Nucl. Data Tables 35 (1986) 345–418.[5]D.E. Groom, N.V. Mokhov, S.I. Striganov, Muon Stopping power and range tables 10 MeV-100 TeV, At. Data Nucl. Data Tables 78 (2001) 183–356.[6]ICRU Report 37, Stopping Powers for Electrons and Positrons (ICRU, Bethesda, MD, 1984); ICRU Report 49, Stopping Powers and Ranges for Protons and Alpha Particles (ICRU", Bethesda, MD, 1993).

The Fortran program SBETHE calculates the stopping power of materials for swift charged particles with small charges (electrons, muons, protons, their antiparticles, and alphas). The electronic stopping power is computed from the corrected Bethe formula, with the shell correction derived from numerical calculations with the plane-wave Born approximation (PWBA) for atoms, which were based on an independent-electron model with the Dirac-Hartree-Fock-Slater self-consistent potential for the ground -state configuration of the target atom. The density effect correction is evaluated from an empirical optical oscillator strength (OOS) model based on atomic subshell contributions obtained from PWBA calculations. For projectiles heavier than the electron, the Barkas correction is evaluated from the OOS model, and the Lindhard-Sorensen correction is estimated from an accurate parameterization of its numerical values. The calculated electronic stopping power is completely determined by a single empirical parameter, the mean excitation energy or I value of the material. The radiative stopping power for electrons, and positrons, is evaluated by means of Seltzer and Berger's cross section tables for bremsstrahlung emission. The program yields reliable stopping powers and particle ranges for arbitrary materials and projectiles with kinetic energy larger than a certain cutoff value Ecut, which is specific of each projectile kind. The program is accompanied by an extensive database that contains tables of relevant energy-dependent atomic quantities for all the elements from hydrogen to einsteinium. sbethe may be used to generate basic information for dosimetry calculations and Monte Carlo simulations of radiation transport, and as a pedagogical tool.Program summaryProgram title: SBETHECPC Library link to program files: https://doi .org /10 .17632 /7zw25f428t .1Licensing provisions: CC by NC 3.0 Programming language: Fortran 90/95 Nature of problem: The program calculates the stopping power of arbitrary materials for swift charged projectiles with small charges. The material is characterized by its chemical composition, mass density, and the empirical I value. The considered projectiles are electrons, positrons, negative muons, antimuons, protons, antiprotons, and alphas, which are described as point particles characterized by their mass and charge. If the actual I value of the material is known, the results from the program are expected to be reliable for projectiles with kinetic energy higher than a value Ecut, of the order of 1 keV for electrons and positrons, 150 keV for muons and antimuons, 0.75 MeV for protons and antiprotons, and 5 MeV for alpha particles.Solution method: The electronic stopping power is calculated by means of a corrected Bethe formula [1], which combines the conventional Bethe logarithm with the following corrections,1) the shell correction obtained from calculations based on the plane-wave Born approximation with the self-consistent Dirac-Hartree-Fock-Slater (DHFS) potential of neutral atoms in their ground-state configuration [2],2) the density effect correction, which accounts for the reduction of the stopping power caused by the dielectric polarization of the medium,3) a parameterization of the Lindhard-Sorensen correction, which generalizes the Bloch correction for relativistic projectiles, and4) the Barkas correction, which accounts for differences between the stopping powers of particles and their antiparticles. The density-effect and the Barkas corrections are calculated from a model of the optical oscillator strength (OOS) of the material, which combines the contributions of inner atomic subshells calculated with the DHFS potential, with a classical oscillator model for the contribution of valence electrons, A simple extrapolation formula is used to extend the calculated electronic stopping power to energies less than Ecut to allow the calculation of particle ranges. For electrons and positrons, the radiative stopping power is calculated from numerical tables prepared by Seltzer and Berger [3].Additional comments including restrictions and unusual features: The calculated stopping power is determined by a single parameter, the mean excitation energy or I value. The program assigns to each material a default I value, derived from the recommendations in the ICRU Report 37, which can be changed by the user. The distribution package includes text files with tables of atomic energy-dependent quantities (subshell optical oscillator strengths, shell corrections, scaled cross sections for bremsstrahlung emission) that are used in the calculations.References [1] F. Salvat, Phys. Rev. A 106 (2022) 032809. [2] F. Salvat, L. Barjuan, P. Andreo, Phys. Rev. A 105 (2022) 042813. [3] S.M. Seltzer, M.J. Berger, Nucl. Instrum. Methods B 12 (1985) 95-134.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by/4.0/).

The relativistic plane-wave Born approximation is applied to the study of inelastic collisions of charged particles with atoms, by considering atomic wave functions calculated from the independent-electron approximation with the self-consistent Dirac-Hartree-Fock-Slater potential. A database of longitudinal and transverse generalized oscillator strengths (GOSs) has been computed by using accurate numerical methods for all the subshells of the ground-state configurations of the elements with atomic numbers from 1 (hydrogen) to 99 (einsteinium). The calculated GOS do not satisfy the Bethe sum rule; departures from the sum rule are in accordance with previous theoretical estimates. Asymptotic high-energy formulas for the total cross section, the stopping cross section, and the energy-straggling cross section are derived with proper account of the relativistic departure from the Bethe sum rule. The shell correction is calculated as the energy-dependent term that, when added to the asymptotic formula, reproduces the value of the atomic cross section calculated by integrating the energy-loss differential cross section. Shell corrections to the stopping cross section obtained from the present approach are presented and compared with previous estimates.

Objective. To review the currently available data on beam quality correction factors, kQ, for ionization chambers in clinical proton beams and derive their current best estimates for the updated recommendations of the IAEA TRS-398 Code of Practice. Approach. The reviewed data come from 20 publications from which kQ values can be derived either directly from calorimeter measurements, indirectly from comparison with other chambers or from Monte Carlo calculated overall chamber factors, fQ. For cylindrical ionization chambers, a distinction is made between data obtained in the centre of a spread-out Bragg peak and those obtained in the plateau region of single-energy fields. For the latter, the effect of depth dose gradients has to be considered. To this end an empirical model for previously published displacement correction factors for single-layer scanned beams was established, while for unmodulated scattered beams experimental data were used. From all the data, chamber factors, fQ, and chamber perturbation correction factors, pQ, were then derived and analysed. Main results. The analysis showed that except for the beam quality dependence of the water-to-air mass stopping power ratio and, for cylindrical ionization chambers in unmodulated beams, of the displacement correction factor, there is no remaining beam quality dependence of the chamber perturbation correction factors pQ. Based on this approach, average values of the beam quality independent part of the perturbation factors were derived to calculate kQ values consistent with the data in the literature. Significance. The resulting data from this analysis are current best estimates of kQ values for modulated scattered beams and single-layer scanned beams used in proton therapy. Based on this, a single set of harmonized values is derived to be recommended in the update of IAEA TRS-398.

Calculating x-ray tube spectra provides a comprehensive review of the modelling of x-ray tube emissions, with a focus on medical imaging and radiotherapy applications. It begins by covering the relevant background, before discussing modelling approaches, including both analytical formulations and Monte Carlo simulation. Historical context is provided, based on the past century of literature, as well as a summary of recent developments and insights. The book finishes with example applications for spectrum models, including beam quality prediction and the calculation of dosimetric and image-quality metrics. This book will be a valuable resource for postgraduate and advanced undergraduate students studying medical radiation physics, in addition to those in teaching, research, industry and healthcare settings whose work involves x-ray tubes. Key Features: Covers simple modelling approaches as well as full Monte Carlo simulation of x-ray tubes. Bremsstrahlung and characteristic contributions to the spectrum are discussed in detail. Learning is supported by free open-source software and an online repository of code. An online repository of the code that accompanies this book can be found here: https://bitbucket.org/caxtus

Objective.Experimental determination of beam qualitykQfactors for two types of Farmer ionization chambers, NE2571 and IBA FC65-G, in a scanned proton beam for three nominal energies (140 MeV, 180 MeV and 220 MeV) based on water calorimetry.Approach.Beam quality correction factors were determined comparing the results obtained with water calorimetry and ionometry. Water calorimetry was performed to determine the absorbed dose at a depth of measurement in water of 5 g cm-2, limited by the extension of the calorimeter glass vessel used. For the ionometry, two chambers of each type were included in the study. The ionization chambers were calibrated in terms of absorbed dose to water in60Co at the Swedish Secondary Standard Dosimetry Laboratory, directly traceable to the BIPM, and were used according to the IAEA TRS-398 Code of Practice.Main results. ThekQvalues determined in the present work have been compared with the values tabulated in TRS-398 and its forthcoming update and also with those obtained in previous water calorimetric measurements and Monte Carlo calculations. All results were found to agree within the combined uncertainties of the different data.Significance. It is expected that the present work will serve as an experimental contribution tokQ-factors for the two chamber types and three scanned proton beam qualities used.

PURPOSE:Determination of absorbed dose is well established in many dosimetry protocols and considered to be highly reliable using ionization chambers under reference conditions. If dosimetry is performed under other conditions or using other detectors, however, open questions still remain. Such questions frequently refer to appropriate correction factors. A converted energy per mass (cema)-based approach to formulate such correction factors offers a good understanding of the specific response of a detector for dosimetry under various measuring conditions and thus an estimate of pros and cons of its application. METHODS:Determination of absorbed dose requires the knowledge of the beam quality correction factor kQ,Qo , where Q denotes the quality of a user beam and Qo is the quality of the radiation used for calibration. In modern Monte Carlo (MC)-based methods, kQ,Qo is directly derived from the MC-calculated dose conversion factor, which is the ratio between the absorbed dose at a point of interest in water and the mean absorbed dose in the sensitive volume of an ion chamber. In this work, absorbed dose is approximated by the fundamental quantity cema. This approximation allows the dose conversion factor to be substituted by the cema conversion factor. Subsequently, this factor is decomposed into a product of cema ratios. They are identified as the stopping power ratio water to the material in the sensitive detector volume, and as the correction factor for the fluence perturbation of the secondary charged particles in the detector cavity caused by the presence of the detector. This correction factor is further decomposed with respect to the perturbation caused by the detector cavity and that caused by external detector properties. The cema-based formalism was subsequently tested by MC calculations of the spectral fluence of the secondary charged particles (electrons and positrons) under various conditions. RESULTS:MC calculations demonstrate that considerable fluence perturbation may occur particularly under non-reference conditions. Cema-based correction factors to be applied in a 6-MV beam were obtained for a number of ionization chambers and for three solid-state detectors. Feasibility was shown at field sizes of 4 × 4 and 0.5 cm × 0.5 cm. Values of the cema ratios resulting from the decomposition of the dose conversion factor can be well correlated with detector response. Under the small field conditions, the internal fluence correction factor of ionization chambers is considerably dependent on volume averaging and thus on the shape and size of the cavity volume. CONCLUSIONS:The cema approach is particularly useful at non-reference conditions including when solid-state detectors are used. Perturbation correction factors can be expressed and evaluated by cema ratios in a comprehensive manner. The cema approach can serve to understand the specific response of a detector for dosimetry to be dependent on (a) radiation quality, (b) detector properties, and (c) electron fluence changes caused by the detector. This understanding may also help to decide which detector is best suited for a specific measurement situation.

An error has been found in the footnote of page 9 of this paper, where a typographical error infigure 3 of AAPM TG-61 (Ma et al 2001)was incorrectly indicated. The footnote points at an incorrect labeling of the 300 kV curve in TG-61ʼsfigure, but the label is correct. It is emphasized that TG-61ʼs figure 3 illustrates thefield size dependence of m r = z en w,air 2 [ ] values relative to those of a 100cmfield area, whilefigure 7 in this paper shows absolute values. The author is indebted to ProfessorDave Rogers for pointing this error.

Purpose SpekPy is a free toolkit for modeling x‐ray tube spectra with the Python programming language. In this article, the advances in version 2.0 (v2) of the software are described, including additional target materials and more accurate modeling of the heel effect. Use of the toolkit is also demonstrated. Methods The predictions of SpekPy are illustrated in comparison to experimentally determined spectra: three radiation quality reference (RQR) series tungsten spectra and one mammography spectrum with a molybdenum target. The capability of the software to correctly model changes in tube output with tube potential is also assessed, using the example of a GE Revolution TM CT scanner (GE Healthcare, Waukesha, WI, USA) and specifications in the system's Technical Reference Manual. Furthermore, we note that there are several physics models available in SpekPy. These are compared on and off the central axis, to illustrate the differences. Results SpekPy agrees closely with the experimental spectra over a wide range of tube potentials, both visually and in terms of first and second half‐value layers (HVLs) (within 2% here). The CT scanner spectrum output (normalized to 120 kV tube potential) agreed within 4% over the range of 70 to 140 kV. The default physics model ( casim ) is adequate in most situations. The advanced option ( kqp ) should be used if high accuracy is desired for modeling the anode heel effect, as it fully includes the effects of bremsstrahlung anisotropy. Conclusions SpekPy v2 can reliably predict on‐ and off‐axis spectra for tungsten and molybdenum targets. SpekPy's open‐source MIT license allows users the freedom to incorporate this powerful toolkit into their own projects.

Three different correction factors for measurements with the parallel-plate ionization chamber PTW T34013 on the Esteya electronic brachytherapy unit have been investigated. This chamber type is recommended by AAPM TG-253 for depth-dose measurements in the 69.5 kV x-ray beam generated by the Esteya unit. Monte Carlo simulations using the PENELOPE-2018 system were performed to determine the absorbed dose deposited in water and in the chamber sensitive volume at different depths with a Type A uncertainty smaller than 0.1%. Chamber-to-chamber differences have been explored performing measurements using three different chambers. The range of conical applicators available, from 10 to 30 mm in diameter, has been explored. Using a depth-independent global chamber perturbation correction factor without a shift of the effective point of measurement yielded differences between the absorbed dose to water and the corrected absorbed dose in the sensitive volume of the chamber of up to 1% and 0.6% for the 10 mm and 30 mm applicators, respectively. Calculations using a depth-dependent perturbation factor, including or excluding a shift of the effective point of measurement, resulted in depth-dose differences of about ± 0.5% or less for both applicators. The smallest depth-dose differences were obtained when a shift of the effective point of measurement was implemented, being displaced 0.4 mm towards the center of the sensitive volume of the chamber. The correction factors were obtained with combined uncertainties of 0.4% (k = 2). Uncertainties due to chamber-to-chamber differences are found to be lower than 2%. The results emphasize the relevance of carrying out detailed Monte Carlo studies for each electronic brachytherapy device and ionization chamber used for its dosimetry.

PurposeTo develop an analytical model for bremsstrahlung production in a thick x‐ray target (i.e., the x‐ray tube anode) that takes into account the intrinsic bremsstrahlung angular distribution.MethodsX‐ray spectrum models developed from theoretical principles have traditionally treated the angular distribution of the bremsstrahlung production as spherically uniform. This assumption stems from the rationale that electrons promptly attain a diffuse directional distribution in an x‐ray target due to multiple scattering, thereby effectively masking the intrinsic bremsstrahlung angular distribution. In this work, a model that explicitly accounts for the angular distribution of the bremsstrahlung production is presented. The model combines Monte Carlo‐calculated depth, energy, and angular distributions of electrons penetrating the x‐ray target, and incorporates theoretical results for the differential bremsstrahlung cross section. The effects of using different simplified model assumptions for the electron penetration and the intrinsic bremsstrahlung angular distribution are analyzed for tungsten and molybdenum targets in the energy range 20–300 keV.ResultsTypical assumptions of previous models are shown to introduce errors in calculated spectra. Particularly, it is shown that predictions of fluence and air kerma free‐in‐air can be overestimated by 15–30% (2–3% in aluminum half‐value layer thickness) for clinically relevant beam qualities. The present model is able to reproduce comprehensive Monte Carlo calculations of the bremsstrahlung production generally to within 1%.ConclusionsThe bremsstrahlung model developed in this work is an improvement over previous models in that the main features of the electron penetration and the resulting bremsstrahlung are considered in detail. The model can be used for more accurate predictions of the energy and angular distribution of x rays emitted from an x‐ray tube.