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Scr."],"published-print":{"date-parts":[[2024,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The main objective of this study is to obtain three-dimensional empirical K-shell x-ray fluorescence cross-section (<jats:inline-formula>\n                     <jats:tex-math>\n\n<\/jats:tex-math>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:msub>\n                           <mml:mrow>\n                              <mml:mi>\u03c3<\/mml:mi>\n                           <\/mml:mrow>\n                           <mml:mrow>\n                              <mml:msub>\n                                 <mml:mrow>\n                                    <mml:mi>K<\/mml:mi>\n                                 <\/mml:mrow>\n                                 <mml:mrow>\n                                    <mml:mi>\u03b1<\/mml:mi>\n                                 <\/mml:mrow>\n                              <\/mml:msub>\n                           <\/mml:mrow>\n                        <\/mml:msub>\n                        <mml:mo>,<\/mml:mo>\n                        <mml:msub>\n                           <mml:mrow>\n                              <mml:mi>\u03c3<\/mml:mi>\n                           <\/mml:mrow>\n                           <mml:mrow>\n                              <mml:msub>\n                                 <mml:mrow>\n                                    <mml:mi>K<\/mml:mi>\n                                 <\/mml:mrow>\n                                 <mml:mrow>\n                                    <mml:mi>\u03b2<\/mml:mi>\n                                 <\/mml:mrow>\n                              <\/mml:msub>\n                           <\/mml:mrow>\n                        <\/mml:msub>\n                     <\/mml:math>\n                  <\/jats:inline-formula> and <jats:inline-formula>\n                     <jats:tex-math>\n\n<\/jats:tex-math>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:msub>\n                           <mml:mrow>\n                              <mml:mi>\u03c3<\/mml:mi>\n                           <\/mml:mrow>\n                           <mml:mrow>\n                              <mml:msub>\n                                 <mml:mrow>\n                                    <mml:mi>K<\/mml:mi>\n                                 <\/mml:mrow>\n                                 <mml:mrow>\n                                    <mml:mi mathvariant=\"italic\">tot<\/mml:mi>\n                                 <\/mml:mrow>\n                              <\/mml:msub>\n                           <\/mml:mrow>\n                        <\/mml:msub>\n                        <mml:mo stretchy=\"false\">)<\/mml:mo>\n                     <\/mml:math>\n                  <\/jats:inline-formula> values for a wide range of elements <jats:inline-formula>\n                     <jats:tex-math>\n\n<\/jats:tex-math>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                           <mml:mfenced close=\")\" open=\"(\">\n                              <mml:mrow>\n                                 <mml:mn>16<\/mml:mn>\n                                 <mml:mo>\u2264<\/mml:mo>\n                                 <mml:mi>Z<\/mml:mi>\n                                 <mml:mo>\u2264<\/mml:mo>\n                                 <mml:mn>92<\/mml:mn>\n                              <\/mml:mrow>\n                           <\/mml:mfenced>\n                        <\/mml:mrow>\n                     <\/mml:math>\n                  <\/jats:inline-formula> for photons with energies from 5.46 keV to 123.6 keV, using more than 3300 experimental data values published between 1985 and 2023 by numerous researchers. These data values are fitted using an interpolation method including a three-dimensional function against atomic number <jats:italic>Z<\/jats:italic> and excitation energy <jats:italic>E<\/jats:italic>, resulting in a three-dimensional plot to estimate empirically a three-dimensional set of <jats:inline-formula>\n                     <jats:tex-math>\n\n<\/jats:tex-math>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:msub>\n                           <mml:mrow>\n                              <mml:mi>K<\/mml:mi>\n                           <\/mml:mrow>\n                           <mml:mrow>\n                              <mml:mi>\u03b1<\/mml:mi>\n                           <\/mml:mrow>\n                        <\/mml:msub>\n                        <mml:mo>,<\/mml:mo>\n                        <mml:msub>\n                           <mml:mrow>\n                              <mml:mi>K<\/mml:mi>\n                           <\/mml:mrow>\n                           <mml:mrow>\n                              <mml:mi>\u03b2<\/mml:mi>\n                           <\/mml:mrow>\n                        <\/mml:msub>\n                     <\/mml:math>\n                  <\/jats:inline-formula> and <jats:inline-formula>\n                     <jats:tex-math>\n\n<\/jats:tex-math>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:msub>\n                           <mml:mrow>\n                              <mml:mi>K<\/mml:mi>\n                           <\/mml:mrow>\n                           <mml:mrow>\n                              <mml:mi mathvariant=\"normal\">tot<\/mml:mi>\n                           <\/mml:mrow>\n                        <\/mml:msub>\n                     <\/mml:math>\n                  <\/jats:inline-formula> x-ray fluorescence cross sections. The results of this empirical calculation are compared, for selected elements, with other empirical and experimental values reported in the literature, and a reasonable agreement is observed.<\/jats:p>","DOI":"10.1088\/1402-4896\/ad720e","type":"journal-article","created":{"date-parts":[[2024,8,21]],"date-time":"2024-08-21T23:03:55Z","timestamp":1724281435000},"page":"105402","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Empirical calculation of K-shell fluorescence cross sections for elements in the atomic range 16 \u2264 Z \u2264 92 by photon effects ranging from 5.46 to 123.6 keV (Three-dimensional formulae)"],"prefix":"10.1088","volume":"99","author":[{"given":"K","family":"Amari","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6043-4316","authenticated-orcid":true,"given":"Kahoul","family":"A","sequence":"additional","affiliation":[]},{"given":"J M","family":"Sampaio","sequence":"additional","affiliation":[]},{"given":"Y","family":"Kasri","sequence":"additional","affiliation":[]},{"given":"J P","family":"Marques","sequence":"additional","affiliation":[]},{"given":"F","family":"Parente","sequence":"additional","affiliation":[]},{"given":"A","family":"Hamidani","sequence":"additional","affiliation":[]},{"given":"S","family":"Croft","sequence":"additional","affiliation":[]},{"given":"A","family":"Favalli","sequence":"additional","affiliation":[]},{"given":"S","family":"Daoudi","sequence":"additional","affiliation":[]},{"given":"B","family":"Deghfel","sequence":"additional","affiliation":[]},{"given":"A","family":"Zidi","sequence":"additional","affiliation":[]},{"given":"B","family":"Berkani","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2024,9,4]]},"reference":[{"key":"psad720ebib1","doi-asserted-by":"publisher","author":"Scofield","year":"1973","DOI":"10.2172\/4545040"},{"key":"psad720ebib2","doi-asserted-by":"publisher","first-page":"5632","DOI":"10.6028\/nist.ir.5632","author":"Hubbell","year":"1995"},{"key":"psad720ebib3","first-page":"2333","volume":"58","author":"Berger","year":"2010","journal-title":"J. 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