{"id":13479,"date":"2017-01-02T09:25:35","date_gmt":"2017-01-02T09:25:35","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=13479"},"modified":"2022-10-19T11:37:30","modified_gmt":"2022-10-19T11:37:30","slug":"microscopic-cross-section","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/microscopic-cross-section\/","title":{"rendered":"Microscopic Cross-section"},"content":{"rendered":"<div   id="8n9s8rpp6h"    class=\"su-quote su-quote-style-default\"><div   id="8n9s8rpp6h"    class=\"su-quote-inner su-u-clearfix su-u-trim\">The effective target area in m<sup>2<\/sup> presented by a single nucleus to an incident neutron beam is denoted the <strong>microscopic cross-section<\/strong>, <strong>\u03c3<\/strong>. The microscopic cross-sections characterize interactions with single isotopes and are a part of data libraries, such as ENDF\/B-VII.1.<\/p>\n<\/div><\/div>\n<h2>Barn &#8211; Unit of Cross-section<\/h2>\n<p>The cross-section is typically denoted <strong>\u03c3<\/strong> and measured in units of the area [m<sup>2<\/sup>]. But a square meter (or centimeter) is tremendously large compared to the effective area of a nucleus. It has been suggested that a physicist once referred to the measure of a square meter as being &#8220;as big as a barn&#8221; when applied to nuclear processes. The name has persisted, and microscopic cross-sections are expressed in terms of barns. The standard unit for measuring a nuclear cross-section is the <strong>barn<\/strong>, equal to <strong>10<sup>\u221228<\/sup> m\u00b2 or 10<sup>\u221224<\/sup> cm\u00b2<\/strong>. It can be seen the concept of a nuclear cross-section can be quantified physically in terms of <strong>&#8220;characteristic target area&#8221;,<\/strong> where a larger area means a larger probability of interaction.<\/p>\n<figure id=\"attachment_13580\" aria-describedby=\"caption-attachment-13580\" style=\"width: 290px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/01\/nuclear-cross-section-min.png\"><img loading=\"lazy\" class=\"wp-image-13580 size-medium\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/01\/nuclear-cross-section-min-300x300.png\" alt=\"nuclear cross-sections, microscopic cross-sections\" width=\"300\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/01\/nuclear-cross-section-min-300x300.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/01\/nuclear-cross-section-min-150x150.png 150w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/01\/nuclear-cross-section-min-66x66.png 66w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/01\/nuclear-cross-section-min.png 900w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-13580\" class=\"wp-caption-text\">The various microscopic cross-section for uranium-235 and incident thermal neutron.<\/figcaption><\/figure>\n<h3>Typical Values of Microscopic Cross-sections<\/h3>\n<ul>\n<li><strong>Uranium 235<\/strong> is a\u00a0<a title=\"Fissile Material\" href=\"http:\/\/sitepourvtc.com\/glossary\/fissile-material\/\">fissile isotope<\/a>,\u00a0and its\u00a0<a title=\"Cross-sections of Uranium\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/cross-sections-of-uranium\/\">fission cross-section<\/a>\u00a0for thermal neutrons is about\u00a0<strong>585 barns<\/strong> (for 0.0253 eV neutron). For fast neutrons, its fission cross-section is\u00a0<strong>on the order of barns<\/strong>.<\/li>\n<li><strong>Xenon-135<\/strong>\u00a0is a product of<a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/uranium-235-fission\/\">\u00a0U-235 fission<\/a>\u00a0and has a\u00a0<strong>very large\u00a0<\/strong><a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-capture-radiative-capture\/neutron-capture-cross-section\/\"><strong>neutron capture cross-section<\/strong><\/a>\u00a0(about<strong>\u00a02.6 x 10<\/strong><strong><sup>6<\/sup><\/strong><strong>\u00a0barns<\/strong>).<\/li>\n<li><strong>Boron<\/strong> is commonly used as a <strong>neutron absorber<\/strong>\u00a0due to the high\u00a0<a title=\"Neutron cross-section\" href=\"http:\/\/sitepourvtc.com\/neutron-cross-section\/\">neutron cross-section<\/a>\u00a0of isotope \u00a0<strong><sup>10<\/sup>B<\/strong>. Its\u00a0<strong>(n,alpha) reaction<\/strong>\u00a0cross-section for\u00a0<a title=\"Neutron Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/neutron-energy\/\">thermal neutrons<\/a>\u00a0is about\u00a0<strong>3840 barns<\/strong>\u00a0(for 0.025 eV neutron).<\/li>\n<li><strong>Gadolinium<\/strong> is commonly used as a<strong>\u00a0neutron absorber<\/strong> due to the very high neutron absorption <a title=\"Neutron cross-section\" href=\"http:\/\/sitepourvtc.com\/neutron-cross-section\/\">cross-section<\/a>\u00a0of two isotopes\u00a0<strong><sup>155<\/sup>Gd<\/strong>\u00a0and\u00a0<strong><sup>157<\/sup>Gd<\/strong>. \u00a0<sup>155<\/sup>Gd\u00a0has 61 000 barns for\u00a0<a title=\"Neutron Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/neutron-energy\/\">thermal neutrons\u00a0<\/a>(for 0.025 eV neutron) and\u00a0<sup>157<\/sup>Gd\u00a0has even 254 000 barns.<\/li>\n<\/ul>\n<p>See also: <a href=\"https:\/\/www.oecd-nea.org\/jcms\/pl_39910\/janis\">JANIS (Java-based Nuclear Data Information Software)<\/a><\/p>\n<div   id="8n9s8rpp6h"    class=\"collapsible-container\">\n<h2>Theory of Microscopic Cross-section<\/h2>\n<p>The extent to which <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutrons<\/a> interact with nuclei is described in terms of quantities known as <strong>cross-sections<\/strong>. <strong>Cross-sections<\/strong> are used to express the <strong>likelihood of particular interaction<\/strong> between an incident neutron and a target nucleus. It must be noted this likelihood does not depend on real target dimensions. In conjunction with the neutron flux, it enables the calculation of the reaction rate, for example, to derive the <strong>thermal power of a nuclear power plant<\/strong>. The standard unit for measuring the <strong>microscopic cross-section<\/strong> (\u03c3-sigma) is the <strong>barn<\/strong>, equal to <strong>10<sup>-28<\/sup> m<sup>2<\/sup><\/strong>. This unit is very small. Therefore barns (abbreviated as \u201cb\u201d) are commonly used.<\/p>\n<p><strong>The cross-section \u03c3<\/strong> can be interpreted as the <strong>effective \u2018target area\u2019<\/strong> that a nucleus interacts with an incident neutron. The larger the effective area, the greater the probability of reaction. This cross-section is usually known as <strong>the microscopic cross-section<\/strong>.<\/p>\n<p>The concept of the microscopic cross-section is therefore introduced to represent the probability of a <a title=\"Neutron Nuclear Reactions\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/\">neutron-nucleus reaction<\/a>. Suppose that a thin \u2018film\u2019 of atoms (one atomic layer thick) with N<sub>a<\/sub> atoms\/cm<sup>2<\/sup> is placed in a monodirectional beam of intensity I<sub>0<\/sub>. Then the number of interactions C per cm<sup>2<\/sup> per second will be proportional to the intensity I<sub>0<\/sub> and the atom density N<sub>a<\/sub>. We define the proportionality factor as the microscopic cross-section \u03c3:<\/p>\n<p style=\"text-align: center;\"><strong>\u03c3<sub>t<\/sub> = C\/N<sub>a<\/sub>.I<sub>0<\/sub><\/strong><\/p>\n<p>To be able to determine the microscopic cross-section, <strong>transmission measurements<\/strong> are performed on plates of materials. Assume that if a neutron collides with a nucleus, it will either be <a title=\"Neutron Elastic Scattering\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-elastic-scattering\/\">scattered<\/a> into a different direction or be <a title=\"Neutron Absorption\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-absorption\/\">absorbed<\/a> (without fission absorption). Assume that N (nuclei\/cm<sup>3<\/sup>) of the material will then be N.dx per cm<sup>2<\/sup> in the layer dx.<br \/>\nOnly the neutrons that have not interacted will remain traveling in the x-direction. This causes the intensity of the un-collided beam will be attenuated as it penetrates deeper into the material.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/CR.png\"><img loading=\"lazy\" class=\" size-medium wp-image-13408 aligncenter\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/CR-300x249.png\" alt=\"CR\" width=\"300\" height=\"249\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/CR-300x249.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/CR.png 391w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>Then, according to the definition of the microscopic cross-section, the reaction rate per unit area is N\u03c3 \u0399(x)dx. This is equal to the decrease of the beam intensity, so that:<\/p>\n<p style=\"text-align: center;\"><strong>-dI = N.\u03c3.\u0399(x).dx<\/strong><\/p>\n<p>and<\/p>\n<p style=\"text-align: center;\"><strong>\u0399(x) = \u0399<sub>0<\/sub>e<sup>-N.\u03c3.x<\/sup><\/strong><\/p>\n<p>It can be seen that whether a neutron will interact with a certain volume of material depends not only on <strong>the microscopic cross-section<\/strong> of the individual nuclei but also on <strong>the density of nuclei<\/strong> within that volume. It depends on the <strong>N.\u03c3 factor<\/strong>. This factor is therefore widely defined, and it is known <strong>as the macroscopic cross-section<\/strong>.<\/p>\n<p>The difference between the microscopic and macroscopic cross-sections is extremely important. The <strong>microscopic cross-section<\/strong> represents the effective target area of a\u00a0<strong>single nucleus<\/strong>. In contrast,\u00a0the <strong>macroscopic cross-section<\/strong> represents the effective target area of\u00a0<strong>all of <\/strong><strong>the nuclei<\/strong> contained in a certain volume.<\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Nuclear Radius<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Typical nuclear radii<\/strong> are of the order <strong>10<sup>\u221214<\/sup> m<\/strong>. Assuming spherical shape, nuclear radii can be calculated according to following formula:<\/p>\n<p>r = r<sub>0<\/sub> . A<sup>1\/3<\/sup><\/p>\n<p>where r<sub>0<\/sub> = 1.2 x 10<sup>-15\u00a0<\/sup>m = 1.2 fm<\/p>\n<p>If we use this approximation, we, therefore, expect the <strong>geometrical cross-sections<\/strong> of nuclei to be of the order of \u03c0r<sup>2<\/sup> or <strong>4.5 x 10<sup>\u221230\u00a0<\/sup>m\u00b2 for hydrogen<\/strong> nuclei or <strong>1.74 x 10<sup>\u221228<\/sup> m\u00b2 for <a title=\"Uranium 238\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-238\/\"><sup>238<\/sup>U<\/a><\/strong> nuclei.<\/p>\n<p>Since there are many nuclear reactions from the incident particle point of view but, in nuclear reactor physics, neutron-nuclear reactions are of particular interest. In this case, the neutron cross-section must be defined.<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Total Cross-section<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In general, <strong>nuclear cross-sections<\/strong> can be measured for all possible interaction processes together, in this case they are called <strong>total cross-sections (\u03c3<sub>t<\/sub>)<\/strong>. The total cross-section is the sum of all the partial cross-sections such as:<\/p>\n<ul>\n<li><a title=\"Elastic Scattering Cross-section\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-elastic-scattering\/elastic-scattering-cross-section\/\">elastic scattering cross-section<\/a> (\u03c3<sub>s<\/sub>)<\/li>\n<li><a title=\"Inelastic Scattering Cross-section\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-inelastic-scattering\/inelastic-scattering-cross-section\/\">inelastic scattering cross-section<\/a> (\u03c3<sub>i<\/sub>)<\/li>\n<li><a title=\"Neutron Absorption Cross-section\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-absorption\/neutron-absorption-cross-section\/\">absorption cross-section<\/a> (\u03c3<sub>a<\/sub>)<\/li>\n<li><a title=\"Neutron Capture Cross-section\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-capture-radiative-capture\/neutron-capture-cross-section\/\">radiative capture cross-section<\/a> (\u03c3<sub>\u03b3<\/sub>)<\/li>\n<li><a title=\"Nuclear Fission\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/\">fission cross-section<\/a>\u00a0(\u03c3<sub>f<\/sub>)<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><strong>\u03c3<sub>t<\/sub> = \u03c3<sub>s<\/sub> + \u03c3<sub>i<\/sub> + \u03c3<sub>\u03b3<\/sub> + \u03c3<sub>f<\/sub> + \u2026&#8230;<\/strong><\/p>\n<p>The total cross-section measures the probability that interaction of any type will occur when neutron interacts with a target.<\/div><\/div>\n<\/div>\n<p><strong>Microscopic cross-sections<\/strong> constitute key parameters of <a title=\"Nuclear Fuel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/\">nuclear fuel<\/a>. In general, neutron cross-sections are essential for reactor core calculations and part of data libraries, such as ENDF\/B-VII.1.<\/p>\n<p>The neutron cross-section is variable and depends on:<\/p>\n<ul>\n<li><strong><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/11\/cross-sections_nuclides.png\"><img loading=\"lazy\" class=\"size-full wp-image-381 alignright\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/11\/cross-sections_nuclides.png\" alt=\"Table of cross-sections\" width=\"732\" height=\"441\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/11\/cross-sections_nuclides.png 732w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/11\/cross-sections_nuclides-300x180.png 300w\" sizes=\"(max-width: 732px) 100vw, 732px\" \/><\/a>Target nucleus<\/strong> (hydrogen, <a title=\"Boron 10\" href=\"http:\/\/sitepourvtc.com\/glossary\/boron-10\/\">boron<\/a>, <a title=\"Uranium\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/\">uranium<\/a>, etc.). Each isotope has its own set of cross-sections.<\/li>\n<li><strong>Type of the reaction<\/strong> (<a title=\"Neutron Capture \u2013 Radiative Capture\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-capture-radiative-capture\/\">capture<\/a>, <a title=\"Nuclear Fission\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/\">fission<\/a>, etc.). Cross-sections are different for each nuclear reaction.<\/li>\n<li><strong><a title=\"Neutron Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/neutron-energy\/\">Neutron energy<\/a> <\/strong>(<a title=\"Thermal Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/thermal-neutron\/\">thermal neutron<\/a>, resonance neutron, fast neutron). For a given target and reaction type, the cross-section is strongly dependent on the neutron energy. In the common case, the cross-section is usually much larger at low energies than at high energies. This is why most nuclear reactors use a <a title=\"Neutron Moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">neutron moderator <\/a>to reduce the neutron&#8217;s energy and thus increase the probability of fission, essential to produce energy and sustain the chain reaction.<\/li>\n<li><strong>Target energy<\/strong> (temperature of target material \u2013 <a title=\"Doppler Broadening\" href=\"http:\/\/sitepourvtc.com\/glossary\/doppler-broadening\/\">Doppler broadening<\/a>). This dependency is not so significant, but the target energy strongly influences the inherent safety of <a title=\"Nuclear Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/\">nuclear reactors <\/a>due to a Doppler broadening of resonances.<\/li>\n<\/ul>\n<p><strong>Microscopic cross-section varies with incident neutron energy<\/strong>. Some nuclear reactions exhibit <strong>very specific dependency<\/strong> on incident neutron energy. This dependency will be described in the example of the <a title=\"Neutron Capture \u2013 Radiative Capture\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-capture-radiative-capture\/\">radiative capture reaction<\/a>. The radiative capture cross-section represents the likelihood of a neutron radiative capture as <strong>\u03c3<sub>\u03b3<\/sub><\/strong>. The following dependency is typical for radiative capture. It definitely does not mean that it is typical for other types of reactions (see <a title=\"Elastic Scattering Cross-section\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-elastic-scattering\/elastic-scattering-cross-section\/\">elastic scattering cross-section<\/a> or <a title=\"Charged Particle Ejection\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/charged-particle-ejection\/\">(n, alpha) reaction cross-section<\/a>).<\/p>\n<p>The capture cross-section can be divided into three regions according to the incident neutron energy. These regions will be discussed separately.<\/p>\n<ul>\n<li><strong>1\/v Region<\/strong><\/li>\n<li><strong>Resonance Region<\/strong><\/li>\n<li><strong>Fast Neutrons Region<\/strong><\/li>\n<\/ul>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\">\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Charts of Cross-sections<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/neutron-absorption-capture-scattering-fission-min.png\"><img loading=\"lazy\" class=\"aligncenter size-medium wp-image-13131\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/neutron-absorption-capture-scattering-fission-min-300x144.png\" alt=\"Uranium 238. Neutron absorption and scattering. Comparison of cross-sections.\" width=\"300\" height=\"144\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/neutron-absorption-capture-scattering-fission-min-300x144.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/neutron-absorption-capture-scattering-fission-min-1024x491.png 1024w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/neutron-absorption-capture-scattering-fission-min.png 1248w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><div   id="8n9s8rpp6h"    class=\"su-spacer\" style=\"height:10px\"><\/div><div   id="8n9s8rpp6h"    class=\"su-spacer\" style=\"height:10px\"><\/div><a title=\"Uranium 238\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-238\/\">Uranium 238<\/a>. Comparison of cross-sections.<br \/>\nSource: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library<div   id="8n9s8rpp6h"    class=\"su-spacer\" style=\"height:15px\"><\/div><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/08\/gadolinium-cross-sections.png\"><img loading=\"lazy\" class=\"aligncenter size-medium wp-image-12520\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/08\/gadolinium-cross-sections-300x206.png\" alt=\"Gadolinium 155 and 157. Comparison of radiative capture cross-sections.\" width=\"300\" height=\"206\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/08\/gadolinium-cross-sections-300x206.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/08\/gadolinium-cross-sections.png 889w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><div   id="8n9s8rpp6h"    class=\"su-spacer\" style=\"height:10px\"><\/div><div   id="8n9s8rpp6h"    class=\"su-spacer\" style=\"height:10px\"><\/div><a title=\"Gadolinium\" href=\"http:\/\/sitepourvtc.com\/glossary\/gadolinium\/\">Gadolinium <\/a>155 and 157. Comparison of radiative capture cross-sections.<br \/>\nSource: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library<div   id="8n9s8rpp6h"    class=\"su-spacer\" style=\"height:15px\"><\/div>\n<figure id=\"attachment_12069\" aria-describedby=\"caption-attachment-12069\" style=\"width: 290px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/1v-Law.png\"><img loading=\"lazy\" class=\"size-medium wp-image-12069\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/1v-Law-300x221.png\" alt=\"1\/v Law\" width=\"300\" height=\"221\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/1v-Law-300x221.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/1v-Law-220x161.png 220w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/05\/1v-Law.png 737w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-12069\" class=\"wp-caption-text\">For thermal neutrons (in 1\/v region), absorption cross-sections increase as the neutron&#8217;s velocity (kinetic energy) decreases.<br \/>Source: JANIS 4.0<\/figcaption><\/figure>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>1\/v Region<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In the common case, the cross-section is usually <strong>much larger at low energies<\/strong> than at high energies. For <a title=\"Thermal Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/thermal-neutron\/\">thermal neutrons<\/a> (in 1\/v region), radiative capture cross-sections also increase as the neutron&#8217;s velocity (kinetic energy) decreases. Therefore the <a title=\"Law 1\/v\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/interactions-neutrons-matter\/law-1v\/\">1\/v Law<\/a> can be used to determine the shift in capture cross-section if the neutron is in equilibrium with a surrounding medium. This phenomenon is because the nuclear force between the target nucleus and the neutron has a longer time to interact.<\/p>\n<p><img class=\"mathtex-equation-editor aligncenter\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%5Csigma_a%20%5Csim%20%5Cfrac%7B1%7D%7Bv%7D%7D%7D%20%5Csim%20%5Cfrac%7B1%7D%7B%5Csqrt%7BE%7D%7D%7D%7D%7D%20%5Csim%20%5Cfrac%7B1%7D%7B%5Csqrt%7BT%7D%7D%7D%7D%7D\" alt=\"\\sigma_a \\sim \\frac{1}{v}}} \\sim \\frac{1}{\\sqrt{E}}}}} \\sim \\frac{1}{\\sqrt{T}}}}}\" align=\"absmiddle\" \/><\/p>\n<p>This law is applicable only for absorption cross-section and only in the 1\/v region.<\/p>\n<p><strong>Example of cross-sections in 1\/v region:<\/strong><\/p>\n<p>The absorbtion cross-section for 238U at 20\u00b0C = 293K (~0.0253 eV) is:<\/p>\n<p><img class=\"mathtex-equation-editor\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%5Csigma_a(293K)%20%3D%202.68b%20\" alt=\"\\sigma_a(293K) = 2.68b \" align=\"absmiddle\" \/>.<\/p>\n<p>The absorption cross-section for 238U at 1000\u00b0C = 1273K is equal to:<\/p>\n<p><img class=\"mathtex-equation-editor alignleft\" src=\"http:\/\/chart.apis.google.com\/chart?cht=tx&amp;chl=%5Csigma_a(1273K)%20%3D%20%5Csigma_a(293K)%20%5Ccdot%20%5Cfrac%20%7BT_0%7D%7BT_1%7D%20%3D%202.68%20%5Ccdot%20%5Cfrac%7B293%7D%7B1273%7D%20%3D%20%200.617b\" alt=\"\\sigma_a(1273K) = \\sigma_a(293K) \\cdot \\frac {T_0}{T_1} = 2.68 \\cdot \\frac{293}{1273} = 0.617b\" align=\"absmiddle\" \/><\/p>\n<p>This cross-section reduction is caused only due to the shift of temperature of the surrounding medium.<\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Resonance Region<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_12633\" aria-describedby=\"caption-attachment-12633\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/09\/Compound_nucleus.png\"><img loading=\"lazy\" class=\"size-medium wp-image-12633\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/09\/Compound_nucleus-300x199.png\" alt=\"Compound state - resonance\" width=\"300\" height=\"199\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/09\/Compound_nucleus-300x199.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/09\/Compound_nucleus.png 719w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-12633\" class=\"wp-caption-text\">Energy levels of the compound state. For neutron absorption reaction on 238U, the first resonance E1 corresponds to the excitation energy of 6.67eV. E0 is a base state of 239U.<\/figcaption><\/figure>\n<p><strong>The largest cross-sections<\/strong> are usually at neutron energies that lead to long-lived states of the <a title=\"What is Nuclear Resonance \u2013 Compound Nucleus\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/compound-nucleus-reactions\/what-is-nuclear-resonance-compound-nucleus\/\">compound nucleus<\/a>. The compound nuclei of these certain energies are called <strong>nuclear resonances,<\/strong> and their formation is typical <strong>in the resonance region<\/strong>. The widths of the resonances increase in general with increasing energies. At higher energies, the widths may reach the order of the distances between resonances, and then no resonances can be observed. The narrowest resonances are usually compound states of heavy nuclei (such as <a title=\"Fissionable Material\" href=\"http:\/\/sitepourvtc.com\/glossary\/fissionable-material\/\">fissionable nuclei<\/a>).<\/p>\n<p>Since the <strong>mode of decay<\/strong> of the compound nucleus <strong>does not depend on the way the compound nucleus was formed<\/strong>, the nucleus sometimes emits a <a title=\"Gamma Rays \/ Gamma Radiation\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/photon\/gamma-ray\/\">gamma-ray<\/a> (radiative capture) or sometimes emits a <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutron<\/a> (<a title=\"Elastic and Inelastic Scattering\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-elastic-scattering\/elastic-and-inelastic-scattering\/\">scattering<\/a>). To understand how a nucleus will stabilize itself, we have to understand the behavior of the compound nucleus.<\/p>\n<figure id=\"attachment_12819\" aria-describedby=\"caption-attachment-12819\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/10\/ground-state-compound-nucleus.png\"><img loading=\"lazy\" class=\"size-medium wp-image-12819\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/10\/ground-state-compound-nucleus-300x163.png\" alt=\"ground state compound nucleus - excitation\" width=\"300\" height=\"163\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/10\/ground-state-compound-nucleus-300x163.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/10\/ground-state-compound-nucleus.png 736w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-12819\" class=\"wp-caption-text\">The position of the energy levels during the formation of a compound nucleus. Ground state and energy states.<\/figcaption><\/figure>\n<p>The compound nucleus emits a neutron only after one neutron obtains energy in collision with another nucleon greater than its <a title=\"Nuclear Binding Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/binding-energy\/nuclear-binding-energy\/\">binding energy<\/a> in the nucleus. It has some delay because the excitation energy of the compound nucleus <strong>is divided<\/strong> among several nucleons. The average time that elapses before a neutron can be emitted is much longer for nuclei <strong>with many nucleons<\/strong> than when only a few nucleons are involved. It is a consequence of sharing the excitation energy among a large number of nucleons.<\/p>\n<p>This is why the <strong>radiative capture<\/strong> is comparatively <strong>unimportant in light nuclei<\/strong> but becomes increasingly <strong>important in heavier nuclei<\/strong>.<\/p>\n<p>The compound states (resonances) are observed at low excitation energies. This is due to the fact, the energy gap between the states is large. At high excitation energy, the gap between two compound states is very small, and the widths of resonances may reach the order of the distances between resonances. Therefore, no resonances can be observed at high energies, and the cross-section in this energy region is continuous and smooth.<\/p>\n<p>The lifetime of a compound nucleus is inversely proportional to its total width. <strong>Narrow resonances,<\/strong> therefore, correspond to capture, while the wider resonances are due to scattering.<\/p>\n<p>See also: <a title=\"What is Nuclear Resonance \u2013 Compound Nucleus\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/compound-nucleus-reactions\/what-is-nuclear-resonance-compound-nucleus\/\">Nuclear Resonance<\/a><\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Fast Neutron Region<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>The radiative capture cross-section<\/strong> at energies above the resonance region <strong>drops rapidly<\/strong> to very small values. This rapid drop is caused by the compound nucleus, which is formed in more highly excited states. In these <strong>highly excited states,<\/strong> it is more likely that one neutron obtains <strong>energy<\/strong> in collision with another nucleon <strong>greater than its <a title=\"Nuclear Binding Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/binding-energy\/nuclear-binding-energy\/\">binding energy<\/a><\/strong> in the nucleus. <strong>The neutron emission becomes dominant,<\/strong> and gamma decay becomes less important. Moreover, at high energies, <a title=\"Neutron Inelastic Scattering\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-inelastic-scattering\/\">the inelastic scattering<\/a> and<strong> (n,2n) reaction<\/strong> are highly probable at the expense of both <a title=\"Neutron Elastic Scattering\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-elastic-scattering\/\">elastic scattering<\/a> and radiative capture.<\/p>\n<\/div><\/div>\n<\/div>\n<h2>Doppler Broadening of Resonances<\/h2>\n<p>In general, <a title=\"Doppler Broadening\" href=\"http:\/\/sitepourvtc.com\/glossary\/doppler-broadening\/\">Doppler broadening<\/a> is the broadening of spectral lines due to the <strong>Doppler effect<\/strong> caused by a distribution of kinetic energies of molecules or atoms. In reactor physics, a particular case of this phenomenon is the <strong>thermal Doppler broadening of the resonance capture cross-sections<\/strong> of the <a title=\"Fertile Material\" href=\"http:\/\/sitepourvtc.com\/glossary\/fertile-material\/\">fertile material<\/a> (e.g.,,<a title=\"Uranium 238\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-238\/\"> <sup>238<\/sup>U<\/a> or<a title=\"Plutonium 240\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/plutonium-240\/\"> <sup>240<\/sup>Pu<\/a>) caused by the <strong>thermal motion of target nuclei<\/strong> in the <a title=\"Nuclear Fuel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/\">nuclear fuel<\/a>.<\/p>\n<figure id=\"attachment_378\" aria-describedby=\"caption-attachment-378\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/11\/Doppler_broadening.jpg\"><img loading=\"lazy\" class=\"size-medium wp-image-378\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/11\/Doppler_broadening-300x161.jpg\" alt=\"Doppler effect\" width=\"300\" height=\"161\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/11\/Doppler_broadening-300x161.jpg 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/11\/Doppler_broadening.jpg 624w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-378\" class=\"wp-caption-text\">Doppler effect improves reactor stability. Broadened resonance (heating of a fuel) results in a higher probability of absorption, thus causing negative reactivity insertion (reduction of reactor power).<\/figcaption><\/figure>\n<p>The Doppler broadening of resonances is an important phenomenon that\u00a0<strong>improves reactor stability<\/strong>\u00a0because it accounts for the dominant part of the<strong> fuel temperature coefficient<\/strong> (the change in reactivity per degree change in fuel temperature) in thermal reactors and makes a substantial contribution in <a title=\"Fast Neutron Reactor\" href=\"http:\/\/sitepourvtc.com\/fast-neutron-reactor\/\">fast reactors<\/a> as well. This coefficient is also called the <strong>prompt temperature coefficient<\/strong> because it causes an <strong>immediate response<\/strong> to changes in fuel temperature. The prompt temperature coefficient of most thermal reactors<strong> is negative<\/strong>.<\/p>\n<p>See also: <a title=\"Doppler Broadening\" href=\"http:\/\/sitepourvtc.com\/glossary\/doppler-broadening\/\">Doppler Broadening.<\/a><\/p>\n<h2>Self-Shielding<\/h2>\n<p>It was written, in some cases, the amount of absorption reactions is dramatically reduced despite the <strong>unchanged microscopic cross-section<\/strong> of the material. This phenomenon is commonly known as <strong>the <a title=\"Self-shielding\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/self-shielding\/\">resonance self-shielding<\/a><\/strong> and also <strong>contributes to reactor stability<\/strong>. There are two types of self-shielding.<\/p>\n<ul>\n<li><strong>Energy Self-shielding.<\/strong><\/li>\n<li><strong>Spatial Self-shielding.<\/strong><\/li>\n<\/ul>\n<p>See also: <a title=\"Self-shielding\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/self-shielding\/\">Resonance Self-shielding<\/a><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-min.png\"><img loading=\"lazy\" class=\"aligncenter size-large wp-image-13381\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-min-1024x512.png\" alt=\"Self-shielding - neutron cross-section\" width=\"1024\" height=\"512\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-min-1024x512.png 1024w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-min-300x150.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/12\/self-shielding-min.png 1200w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/a>An increase in temperature from T<sub>1<\/sub> to T<sub>2<\/sub> causes the broadening of spectral lines of resonances. Although the area under the resonance remains the same, the broadening of spectral lines causes an<strong> increase in <a title=\"Neutron Flux \u2013 Neutron Intensity\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-flux-neutron-intensity\/\">neutron flux<\/a><\/strong> in the fuel \u03c6<sub>f<\/sub>(E), increasing the absorption as the temperature increases.<\/p>\n<\/div>\n<div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:20px 0;border-width:2px;border-color:#999999\"><\/div>\n<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\u00a0 <div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>References:<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Nuclear and Reactor Physics:<\/strong>\n<ol>\n<li>J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading,\u00a0MA (1983).<\/li>\n<li>J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.<\/li>\n<li>W. M. Stacey, Nuclear Reactor Physics, John Wiley &amp; Sons, 2001, ISBN: 0- 471-39127-1.<\/li>\n<li>Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering,\u00a0Springer; 4th edition, 1994, ISBN:\u00a0978-0412985317<\/li>\n<li>W.S.C. Williams. Nuclear and Particle Physics.\u00a0Clarendon Press; 1 edition, 1991, ISBN:\u00a0978-0198520467<\/li>\n<li>G.R.Keepin. Physics of Nuclear Kinetics.\u00a0Addison-Wesley Pub. Co; 1st edition, 1965<\/li>\n<li>Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.<\/li>\n<li>U.S. Department of Energy, Nuclear Physics and Reactor Theory.\u00a0DOE Fundamentals Handbook,\u00a0Volume 1 and 2.\u00a0January\u00a01993.<\/li>\n<\/ol>\n<p><strong><\/strong><strong>Advanced Reactor Physics:<\/strong><\/p>\n<ol>\n<li>K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.<\/li>\n<li>K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.<\/li>\n<li><span style=\"font-weight: 400;\">D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.\u00a0<\/span><\/li>\n<li>E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.<\/li>\n<\/ol>\n<\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-default\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See previous:<\/h2>\n<a href=\"\" class=\"su-button su-button-style-flat\" style=\"color:#606060;background-color:#ffffff;border-color:#cccccc;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px\" target=\"_self\"><span style=\"color:#606060;padding:7px 20px;font-size:16px;line-height:24px;border-color:#ffffff;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px;text-shadow:0px 0px 0px #000000;-moz-text-shadow:0px 0px 0px #000000;-webkit-text-shadow:0px 0px 0px #000000\"><i class=\"sui sui-link\" style=\"font-size:16px;color:#5d5d5d\"><\/i> <\/span><\/a><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See above:<\/h2>\n<p>Neutron Nuclear Reactions<a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/\" class=\"su-button su-button-style-flat\" style=\"color:#606060;background-color:#ffffff;border-color:#cccccc;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px\" target=\"_self\"><span style=\"color:#606060;padding:7px 20px;font-size:16px;line-height:24px;border-color:#ffffff;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px;text-shadow:0px 0px 0px #000000;-moz-text-shadow:0px 0px 0px #000000;-webkit-text-shadow:0px 0px 0px #000000\"><i class=\"sui sui-link\" style=\"font-size:16px;color:#5d5d5d\"><\/i> <\/span><\/a><\/p><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See next:<\/h2>\n<a href=\"\" class=\"su-button su-button-style-flat\" style=\"color:#606060;background-color:#ffffff;border-color:#cccccc;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px\" target=\"_self\"><span style=\"color:#606060;padding:7px 20px;font-size:16px;line-height:24px;border-color:#ffffff;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px;text-shadow:0px 0px 0px #000000;-moz-text-shadow:0px 0px 0px #000000;-webkit-text-shadow:0px 0px 0px #000000\"><i class=\"sui sui-link\" style=\"font-size:16px;color:#5d5d5d\"><\/i> <\/span><\/a><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Barn &#8211; Unit of Cross-section The cross-section is typically denoted \u03c3 and measured in units of the area [m2]. But a square meter (or centimeter) is tremendously large compared to the effective area of a nucleus. It has been suggested that a physicist once referred to the measure of a square meter as being &#8220;as &#8230; <a title=\"Microscopic Cross-section\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/microscopic-cross-section\/\" aria-label=\"More on Microscopic Cross-section\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":12656,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"generate_page_header":""},"_links":{"self":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/13479"}],"collection":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/comments?post=13479"}],"version-history":[{"count":4,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/13479\/revisions"}],"predecessor-version":[{"id":32815,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/13479\/revisions\/32815"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/12656"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=13479"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}