Photoeffect Cross Sections Research Articles

Implementation of ICRU report 90 to re-evaluate the dosimetry standards in Taiwan

The purpose of this investigation is to re-evaluate primary dosimetry standards at the National Radiation Standard Laboratory (NRSL/INER) according to the recommendation of the International Commission on Radiation Units and Measurements Report 90 (ICRU Report 90). These standards are air kerma (Kair) in X-rays, 60Co and 137Cs beams, absorbed dose to water (DW) in 60Co beam, as well as reference air kerma (RAKR) in 192Ir beam for brachytherapy in Taiwan.However, the Consultative Committee for Ionizing Radiation (CCRI) summarized the expected changes in ICRU Report 90 to primary standards. These include modifications to the mean excitation energy of water (Iw) and graphite (Ig), the application of the density effect correction for graphite, new combined correction factors and the uncertainty related to the average energy required to create an ion pair in air (Wair), improved calculations of the stopping power, and the adoption of renormalized photoeffect cross-section. The recommendations of the CCRI were adopted for recalculation regarding correction factors and radiation-matter interaction constants for NRSL/INER primary standards. Furthermore, a newer version of Monte Carlo software and the alternative measurements with new ionization chambers (ICs) of a similar design were used to reassess the impact on the NRSL/INER standards. Consequently, the impact of the new ICRU recommendation on dosimetry standards ranged from -0.8% to 0.1%. The changes to the primary standards are in good correlation with similar changes implemented for the BIPM primary standards. For international comparisons of these standards, adoption of the ICRU Report 90 would not change significantly the degree of equivalence stated in the Asia-Pacific Metrology Programme (APMP) key and supplementary comparison database considering the impacts of the BIPM standards in the comparisons of APMP.RI(I)-K3, APMP.RI(I)-K1.1, APMP.RI(I)-K4, APMP.RI(I)-K8 and APMP.RI(I)-S3. Therefore, the NRSL/INER has formally implemented the re-evaluation standards on the 1st January 2024.

Determining the ratio of the number of recoil electrons to the number of photoelectrons using a new method

The problem in question is relevant due to discrepancy between the results of theoretical and known experimental studies of various interactions of ionizing emission photons with substances, in particular, photo effect and Compton scattering of these photons. The study aimed at carrying out specific measurements using a new method of simultaneously determining the ratio of the number of recoil electrons to the number of photoelectrons. Analysis of the results showed that there are significant discrepancies between theoretical calculations and experimental data. New values of simultaneously measured ratios of cross-sections for heavy atoms using a method invented by the author, and old measurements of these ratios for light atoms usingWilson cloud chamber, when compared with theoretical calculations, show that a significant (by one order and more) one-direction discrepancy is seen for X-ray and gamma emissions over a range of energies in question.It is shown that these discrepancies might be attributed to the fact that an atomic electron is in a free state for a while. Compton scattering occurs with a free electron; photo effect involves only bound electrons. Therefore, Compton scattering cross section is proportional to a period of time, during which electron was in a free state, whereas photo effect cross section is proportional to a time period, during which electron was in a bound state. The article materials might be helpful to perform both fundamental, and applied studies on interaction of light quanta with substance including modelling the phenomena under examination.

INFLUENCE OF NEW MASS ENERGY-ABSORPTION COEFFICIENTS FROM ICRU REPORT NO. 90 ON AIR KERMA TO DOSE EQUIVALENT CONVERSION COEFFICIENTS.

In Report No. 90 of the International Commission on Radiation Units and Measurements (ICRU), new mass energy-absorption coefficients are listed which are based on renormalized Scofield photoeffect cross-sections. The mass energy-absorption coefficients are the basis for the conversion coefficients from air kerma to the operational quantities listed in ISO 4037-3. Although ICRU does not give a recommendation if these new mass energy-absorption coefficients should be applied instead of the values used so far, an examination of the possible consequences for radiation protection quantities is necessary. We calculated the conversion coefficients for the X-ray qualities specified in ISO 4037-1 with the new mass energy-absorption coefficients and with the mass energy-absorption coefficients used so far to determine the deviations. Our calculations show that the change of the conversion coefficients due to the new values from ICRU Report No. 90 is negligible.

Impact of new ICRU Report 90 recommendations on calculated correction factors for reference dosimetry

In 2016 the ICRU published a new report dealing with key data for ionizing radiation dosimetry (ICRU Report 90). New recommendations have been made for the mean excitation energies I for air, graphite and liquid water as well as for the graphite density to use when evaluating the density effect. In addition, the ICRU Report 90 discusses renormalized photoelectric cross sections, but refuses to give a recommendation on the use of renormalization factors. However, the Consultative Committee for Ionizing Radiation recommends to use renormalized photoeffect cross sections. Goal of the present work is to evaluate the impact of these new recommendations on clinical reference dosimetry for high energy photon and electron beams.The beam quality correction factor kQ was calculated by Monte Carlo simulations for compact and parallel plate ionization chambers. In case of photons seven phase space files from clinical accelerators and twelve spectra taken from literature from 4 MV to 24 MV and additionally a 60Co source were applied. As electron source thirteen electron spectra available in literature were used in the range of 4 MeV–21 MeV.The new ICRU recommendations have a small impact on Monte Carlo calculated kQ values for the chosen ionization chambers in the range of 0.1%–0.35% only—the difference increases for higher photon energies.The impact of the ICRU Report 90 recommendations on Monte Carlo calculated stopping power ratios sw,a, perturbation factors p and beam quality correction factors kQ was investigated and confirmed a decrese of sw,a by a fraction of a percent for photon and electron beams. This study indicates that the impact of the new ICRU recommendation is within 0.35%. The determined deviations should be taken into account, when widely published Monte Carlo calculated values are examined.

L subshell and total L shell photoeffect cross-sections of Sn, Sb, Te and I elements at 5.96 keV

In this study, L subshell and total L shell photoeffect cross-sections were determined for Sn, Sb, Te and I by using the Ll, Lγ1,5,8 and Lγ2,3 X-ray production cross-sections and atomic parameters at 5.96keV emitted from 55Fe radioisotope source. The results were compared with the theoretical values of Scofield. The values were plotted versus atomic number.

Rayleigh scattering of x-ray and γ-ray by 1s and 2s electrons in ions and neutral atoms

Using the Coulomb–Green function method and considering the nonrelativistic limit for the two-photon S-matrix element, the right nonrelativistic 2s Rayleigh scattering amplitudes are obtained. Our result takes into account all multipoles, retardation and relativistic kinematics contributions, and the old dipole approximation result of Costescu [1] is retrieved as a limit case. The total photoeffect cross-section which is related to the imaginary part of the Rayleigh forward scattering amplitude through the optical theorem is also obtained. Our Coulombian formulae are used in the more realistic case of elastic scattering of photons by bound 1s and 2s electrons in ions and neutral atoms. Screening effects are considered in the independent particle approximation through the Hartree–Fock method. The effective charge Zeff is obtained by fitting the Hartree–Fock charge distribution by a Coulombian one. Good agreement (within 10%) is found when comparing the numerical predictions given by our nonrelativistic formulae with the full relativistic numerical results of Kissel [2] in the case of elastic scattering of photons by 1s and 2s electrons and Scofield [3] in the case of K-shell and 2s subshell photoionization for neutral atoms with 18 ⩽ Z ⩽ 92 and photon energies ω ⩽ αZm.

K shell, L shell–subshell and M shell–subshell photoeffect cross-sections in elements between Tb ( Z=65) and U ( Z=92) at 123.6 keV

In this paper, we report on measurements of K shell, L shell–subshell and M shell–subshell photoeffect cross-sections for 21 high-atomic-number elements between Tb ( Z=65) and U ( Z=92) at 123.6 keV. These photoeffect cross-sections have been measured by using our earlier measurements of the K-shell X-ray production cross-sections. The measured photoeffect cross-sections have been compared with calculated theoretical values. It is clear that the results compare well with theoretical values within an experimental average error. At 123.6 keV, these cross-sections have been measured for the first time. The results have been plotted versus atomic number.

Dispersion corrections to the forward Rayleigh scattering amplitudes of tantalum, mercury and lead derived using photon interaction cross sections

Dispersion corrections to the forward Rayleigh scattering amplitudes of tantalum, mercury and lead in the photon energy range 24–136keV have been determined by a numerical evaluation of the dispersion integral that relates them through optical theorem to the photo effect cross sections. The photo effect cross sections have been extracted by subtracting the coherent and incoherent scattering contribution from the measured total attenuation cross section, using high-resolution high-purity germanium detector in a narrow beam good geometry set up. The real part of the dispersion correction to which the relativistic corrections calculated by Kissel and Pratt (S-matrix approach) or Creagh and McAuley (multipole corrections) have been included are in better agreement with the available theoretical values.

K shell and L subshell and L shell photoeffect cross-sections in the atomic region 40 ⩽ Z ⩽ 52 and 58 ⩽ Z ⩽ 68 at 59.537 keV

K and L shell photoeffect cross-sections have been measured by using our earlier measurements (A. Karabulut et al., Nucl. Instr. and Meth. B 152 (1999) 202 and G. Budak et al., Nucl. Instr. and Meth. B 149 (1999) 379) of total atomic photoeffect cross-sections in elements with 40⩽Z⩽52 and 58⩽Z⩽68 at 59.537keV photons. Fairly good agreement between the experimental and calculated values indicates indirectly the correctness of the theoretical calculations of the atomic coefficients in terms of which the experimental results have been interpreted.

Anomalous scattering factors of some rare earth elements evaluated using photon interaction cross-sections

The real and imaginary parts,f’(E) and”(E) of the dispersion corrections to the forward Rayleigh scattering amplitude (also called anomalous scattering factors) for the elements La, Ce, Pr, Nd, Sm, Gd, Dy, Ho and Er, have been determined by a numerical evaluation of the dispersion integral that relates them through the optical theorem to the photoeffect cross-sections. The photoeffect cross-sections are derived from the total attenuation cross-section data set experimentally determined using high resolution high purity germanium detector in a narrow beam good geometry set-up for these elements in the photon energy range 5 to 1332 keV and reported earlier by the authors. Below 5 keV, Scofield’s photoeffect cross-sections compiled in XCOM program have been interpolated and used. Simple formulae forf” in terms of atomic number and energy have also been obtained. The data cover the energy region from 6 to 85 keV and atomic numberZ from 57–68. The results obtained are found to agree fairly well with the other available data.

A method to determine the K-shell photoeffect cross sections of some rare earth elements

K-shell photoeffect cross sections of the rare earth elements La, Ce, Pr, Nd, Sm, Gd, Dy, Ho and Er have been obtained by a new method, for energies above the K-edge of these elements. In this method, the K-shell photoeffect cross sections of rare earth elements at energies above the K-shell threshold are obtained by using log–log plot of the experimentally measured total attenuation cross sections of their simple compounds. The method does not require any knowledge of the contributions of other competing processes. A simple formula has been obtained by studying the variation these K-shell photoeffect cross sections versus E and Z. This formula provides for an easy and rapid evaluation of the K-shell photoeffect cross sections for any element in the range >57 and <68 and for energies up to 84.3 keV.

L-subshell and total L-shell photoeffect cross-sections measurements for Pb, Au, W, and Ta at [formula omitted

L-subshell and total L-shell photoeffect cross-sections were experimentally determined at 59.5 keV using energy dispersive X-ray fluorescence spectrometry for Pb, Au, W, and Ta. The obtained experimental results were compared with theoretical and available experimental values.

Measurements of L subshell and total L shell photoeffect cross-sections for some elements in $ \sf 72\le Z\le 92$

We determined L subshell photoeffect cross-sections by using Lα, L γ , and L γ 2,3,6,8 X-ray fluorescence cross-sections and atomic parameters and total L shell photoeffect cross-sections for Hf, Hg, Tl, Bi, Tl, and U at 59.54 keV. These values were compared with the theoretical values of Scofield and experimental values that exist in the literature.

Studies on photon interaction around the K-edge of some rare-earth elements

The total attenuation cross sections of rare-earth elements have been measured in a narrow beam good geometry using a high-resolution hyper pure germanium detector in the energy range 6–85 keV. The data have been used to derive the K-shell photoeffect cross sections at the K-edge τ K, the oscillator strength g K and the K-jump ratio J K of the elements La, Ce, Pr, Nd, Sm, Gd, Dy, Ho and Er. The τ K and the g K values have been calculated by a method, which eliminates the requirement of subtracting the theoretical scattering contribution. The best-fit coefficients for the cross sections, jump ratios and oscillator strengths facilitate E- and Z-wise interpolation in the energy range 6–85 keV and Z range 57–68.

Studies on Photon Interaction Around the K-Edge of Some Elements

The total attenuation cross sections of the elements copper, zirconium, silver, and tin have been measured experimentally in a narrow beam good geometry set up by employing a high-resolution hyperpure germanium detector in the energy range 5 to 85 keV. The data have been used to derive the K-shell photoeffect cross sections at the K-edge, the oscillator strength gK, and the K-jump ratio of the elements copper, zirconium, silver, and tin. The photoeffect cross sections at the K-edge and the oscillator strengths of the element have been calculated by making use of a method that eliminates the requirement of subtracting the theoretical scattering contribution. The best-fit coefficients for the cross sections and the relations so obtained for the jump ratios and oscillator strengths facilitate a speedier E- and Z-wise interpolation of the data on total attenuation cross sections as well as JK and K-shell photo effect cross sections at the K-edge, respectively, in the range 5 to 85 keV, for elements in the atomic number range 25 to 55.

On discrepancies in atomic photoeffect cross sections in the low photon energy region

Studies on photon interaction with matter provide a wealth of data for various applied scientific fields. While large amounts of compiled data are available on photon cross sections, significant discrepancies have been observed at very low photon energies, especially in the region of absorption edges; the cross section in some elements shows approximately 10% variation with theory. In the present study, attenuation studies have been made for energies below 60 keV for the elements Zr, Pd, Cd, In, and Ta, these being situations in which discrepancies have been noted. Use has been made of a narrow beam, good geometry situation, coupled with a Freolectric cooled Si(Li) detector attached to a System 100 Canberra multichannel analyser. Total photon and total photoelectric cross sections have been deduced and compared with theory.

RTAB: the Rayleigh scattering database

Systematic tabulations of differential scattering cross sections for all atoms for photon energies 0.0543–2754.1 keV in various approximations are being made available, with a focus on the S-matrix approach of Kissel and Pratt. New tabulations are also being made available of: anomalous scattering factors for 0–10 MeV; total-atom, shell and subshell form factors; bound–bound oscillator strengths; total-atom, shell and subshell photoeffect cross sections; and Dirac–Slater potentials. Accurate interpolation of S-matrix cross sections to intermediate energies is investigated. Selected computer codes that generate or use these data are described.

Soft-photon emission in extreme-relativistic Compton scattering by K-shell electrons and connection to photoeffect

We have recently obtained cross-sections for Compton scattering by K-shell electrons at extreme-relativistic (ER) energies of the incoming photon. Our method is essentially analytical, and only at the end did it require a modest numerical computation. The results are valid for the Compton line of the scattered photon spectrum, but do not cover the infrared divergence at the soft-photon end of the spectrum. This case is treated in the present paper. The method we apply here is an adaptation of the one used for the Compton line. This allows us to make use of many previous results. The quadruply and doubly differential Compton cross-sections can be expressed in analytical forms which allow factorization of the ER photoeffect cross-sections (differential or total, respectively). This result is shown to be a manifestation of the soft-photon theorem connecting the Compton matrix element at low emitted photon frequencies to that of the photoeffect. The computation of ER Compton cross-sections with soft-photon emission is thereby reduced to that of the cross-sections for the ER photoeffect. We carry out a computation for the latter case and extend previously existing results.

Resonances in photoionization cross sections of inner subshells of atoms inside the fullerene cage

A model for the calculation of photoionization cross sections of an atom inside the fullerene cage is proposed. In the frame of this model the M@C60 endohedral is considered as an isolated M atom located in the centre of the spherically symmetrical fullerene shell. The potential of this shell is written as the Dirac delta function in the radial coordinate. On the basis of this model a comparative study of the photoionization cross sections of an isolated M atom and the same atom in M@C60 is carried out. It is shown that near the thresholds of ionization of atomic subshells the resonance peaks appear in the photoeffect cross sections. The positions of these resonances on the scale of photoelectron energy are defined by the fullerene radius and the affinity energy of an electron to C60. The general formulae derived are used to calculate the photoionization cross sections of the inner subshells of the He, Ne and Ca atoms inside the fullerene cage.

The Photon as a Soliton

Recently J. P. Vigier showed [1] that the photon can be reperesented as a solitary electromagnetic wave – a soliton. As a consequence one can ascribe to such a soliton effective volume, amplitude and frequency which coincide with the frequency of de Broglie's wave (measured by interference phenomena). In this paper we propose a soliton-like model for the photon. We show that the electromagnetic amplitude, the volume, the classical cross section and the photoeffect cross section of the photon-soliton can be estimated in an empirical as well as in an analytical way. In the framework of our model the relation between the electromagnetic amplitude of the soliton and its frequency that we found seams to be an universal one, in sense that it may not depend on the specific quantum system considered. We show that there are no essential contradictions between our photon-soliton and some well-known facts such as the interactions in the case of photoeffect and Compton effect.