{"id":83,"date":"2015-10-28T10:17:00","date_gmt":"2015-10-28T10:17:00","guid":{"rendered":"http:\/\/sitepourvtc.com\/?p=83"},"modified":"2022-01-29T13:10:57","modified_gmt":"2022-01-29T13:10:57","slug":"neutron-moderator","status":"publish","type":"post","link":"https:\/\/sitepourvtc.com\/neutron-moderator\/","title":{"rendered":"Neutron Moderator"},"content":{"rendered":"<div   id="8n9s8rpp6h"    class=\"sue-shadow-wrap sue-content-wrap sue-shadow-inline-no\"><div   id="8n9s8rpp6h"    class=\"sue-shadow sue-shadow-style-vertical\">\n<div   id="8n9s8rpp6h"    class=\"sue-panel\" data-url=\"\" data-target=\"self\" style=\"background-color:#ffffff;color:#333333;border-radius:0px;-moz-border-radius:0px;-webkit-border-radius:0px;box-shadow:none;-moz-box-shadow:none;-webkit-box-shadow:none;border:1px solid #cccccc\"><div   id="8n9s8rpp6h"    class=\"sue-panel-content sue-content-wrap\" style=\"padding:15px;text-align:left\">\n<div class=\"su-heading su-heading-style-modern-1-dark su-heading-align-left\" id=\"\" style=\"font-size:13px;margin-bottom:20px\"><div   id="8n9s8rpp6h"    class=\"su-heading-inner\">\n<h2>Article Summary &amp; FAQs<\/h2>\n<\/div><\/div>\n<h3>What is neutron moderator?<\/h3>\n<p>In nuclear reactors, the <strong>neutron moderator<\/strong> is any material used to slow down high-energy\u00a0<a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutrons<\/a> to lower energies (e.g., fission neutrons to thermal neutrons). Neutron moderators are also used for shielding of neutron radiation.<\/p>\n<h3>Key Facts<\/h3>\n<ul>\n<li>Almost all <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/fission-neutron\/\">prompt fission neutrons<\/a> have\u00a0<strong>energies between 0.1 MeV and 10 MeV<\/strong>.<\/li>\n<li>High-energy neutrons scatter with heavy nuclei <strong>very elastically<\/strong>. Heavy nuclei very hard slow down a neutron let alone absorb a fast neutron.<\/li>\n<li>The probability of the <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/\">fission<\/a>\u00a0<a title=\"Uranium 235\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\">U-235<\/a> is very small at these energies and it becomes very large <strong>at the thermal energies<\/strong>. This fact implies increase of <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/six-factor-formula-effective-multiplication-factor\/\">multiplication factor<\/a> of the reactor (i.e., lower fuel enrichment is needed to sustain chain reaction).<\/li>\n<li>For U-235, the <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>\u00a0(for 0.0253 eV neutron). For fast neutrons its fission cross-section is\u00a0<strong>on the order of barns<\/strong>.<\/li>\n<li>For iron, a 2MeV neutron must undergo about 400 elastic scattering reactions to slow down to 1 eV.<\/li>\n<li>To be\u00a0<strong>an effective\u00a0<a title=\"Neutron moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">moderator<\/a>:<\/strong>\n<ul>\n<li>The probability of <a title=\"Neutron Elastic Scattering\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-elastic-scattering\/\">elastic reaction<\/a>\u00a0between neutron and the nucleus must be high.<\/li>\n<li>Moderator must be made of low atomic number material.<\/li>\n<li>Moderator must have low absorption cross-section.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Light water<\/strong>\u00a0has the\u00a0<strong>highest \u03be and \u03c3<\/strong><sub><strong>s<\/strong>\u00a0<\/sub>among the moderators (resulting in the highest MSDP) shown in the table, but its moderating ratio is low due to its relatively\u00a0<strong>higher absorption cross section<\/strong>.<\/li>\n<li>On the other hand,\u00a0<strong>heavy water<\/strong>\u00a0has\u00a0<strong>lower \u03be and \u03c3s<\/strong>, but it has the\u00a0<strong>highest moderating ratio<\/strong>\u00a0owing to its\u00a0<strong>lowest neutron absorption cross-section<\/strong>.<\/li>\n<li><strong>Graphite<\/strong>\u00a0has much heavier nuclei than hydrogen in water, despite the fact graphite has\u00a0<strong>much lower \u03be and \u03c3<sub>s<\/sub><\/strong>, it is\u00a0<strong>better moderator than light water<\/strong>\u00a0due to its lower absorption cross-section compared to that of light water.<\/li>\n<li>Most common nuclear reactors are\u00a0<a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/reactor-types\/lwr-light-water-reactor\/\"><strong>light water reactors<\/strong><\/a>\u00a0(LWR), where light water is used as a\u00a0<a title=\"Neutron moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">moderator<\/a> and coolant.<\/li>\n<li>In case of <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/shielding-neutron-radiation\/\">shielding of neutrons<\/a>, the principles are the same, but higher absorption cross-section are desirable.<\/li>\n<\/ul>\n<div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:10px 0;border-width:2px;border-color:#999999\"><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\">\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-modern-light 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>What are thermal neutrons?<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>What are thermal neutrons?<\/strong><\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/thermal-neutron\/\"><strong>Thermal neutrons<\/strong><\/a>\u00a0are\u00a0neutrons in thermal equilibrium\u00a0<strong>with a surrounding medium of temperature 290K (17 \u00b0C or 62 \u00b0F)<\/strong>. Most probable energy at 17\u00b0C (62\u00b0F) for Maxwellian distribution is\u00a0<strong>0.025 eV<\/strong>\u00a0(~2 km\/s). This part of neutron\u2019s energy spectrum constitutes most important part of spectrum\u00a0<strong>in thermal reactors<\/strong>.<\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-modern-light 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>Why fast reactor does not need a neutron moderator?<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<strong>Why fast reactor does not need a neutron moderator?<\/strong><\/p>\n<div   id="8n9s8rpp6h"    class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights lgc-first lgc-last\">\n<div   id="8n9s8rpp6h"    class=\"inside-grid-column\">\n<p>A\u00a0<strong>fast neutron reactor<\/strong>\u00a0is a\u00a0<a title=\"Nuclear Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/\" target=\"_blank\" rel=\"noopener\">nuclear reactor<\/a>\u00a0in which the<a title=\"Nuclear Fission\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/\" target=\"_blank\" rel=\"noopener\">\u00a0fission chain reaction<\/a>\u00a0is sustained by\u00a0<strong>fast neutrons<\/strong>. That means the\u00a0<a title=\"Neutron moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\" target=\"_blank\" rel=\"noopener\">neutron moderator<\/a>\u00a0(slowing down) in such reactors is undesirable. This is a key advantage of fast reactors, because fast reactors\u00a0have a significant\u00a0<strong>excess of neutrons<\/strong>\u00a0(due to low parasitic absorbtion), unlike\u00a0<a title=\"PWR \u2013 Pressurized water reactor\" href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\" target=\"_blank\" rel=\"noopener\">PWRs<\/a>\u00a0(or LWRs).<\/p>\n<\/div>\n<\/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 lgc-first lgc-last\">\n<div   id="8n9s8rpp6h"    class=\"inside-grid-column\">\n<figure id=\"attachment_263\" class=\"wp-caption alignright\" aria-describedby=\"caption-attachment-263\"><figcaption id=\"caption-attachment-263\" class=\"wp-caption-text\"><\/figcaption><\/figure>\n<p>On the other hand such reactors\u00a0must compensate for the\u00a0<strong>missing reactivity<\/strong>\u00a0from\u00a0<a title=\"Neutron moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">neutron moderator<\/a>\u00a0efect. They use fuel with\u00a0<strong>higher enrichment<\/strong>\u00a0when compared to that required for a thermal reactor.<\/p>\n<\/div>\n<\/div>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-modern-light 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>What is the moderator temperature coefficient?<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<strong>What is the moderator temperature coefficient?<\/strong><\/p>\n<p>The moderator temperature coefficient \u2013 MTC is defined as the change in reactivity per degree change in moderator\u00a0temperature.<\/p>\n<p>\u03b1<sub>M<\/sub>\u00a0=\u00a0<sup>d\u03c1<\/sup>\u2044<sub>dT<\/sub><sub>M<\/sub><\/p>\n<p>It is expressed in units of pcm\/\u00b0C or pcm\/\u00b0F.<\/p>\n<\/div><\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-60 lgc-tablet-grid-60 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><div   id="8n9s8rpp6h"    class=\"su-spacer\" style=\"height:10px\"><\/div>\n<h2>Neutron Moderators in Nuclear Reactors<\/h2>\n<p><strong>The moderator<\/strong>, which is of importance\u00a0in thermal reactors, is used to moderate, that is, <strong>to slow down<\/strong>, <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutrons<\/a> from fission to thermal energies. The probability that fission will occur depends on incident neutron energy. Physicists calculate with fission <a title=\"Neutron cross-section\" href=\"http:\/\/sitepourvtc.com\/neutron-cross-section\/\" target=\"_blank\" rel=\"noopener\">cross-section<\/a>, which determines this probability.<\/p>\n<p>Nuclei with low mass numbers are most effective for this purpose, so the moderator is always a low-mass-number material. In a fast reactor there is no moderator, only fuel and coolant. The moderation of neutrons is undesirable in fast reactors.\u00a0Commonly used moderators include regular (light) water (roughly 75% of the world&#8217;s reactors), solid graphite (20% of reactors) and\u00a0heavy water (5% of reactors). Beryllium and beryllium oxide (BeO) have been used occasionally, but they are very costly.<\/p>\n<h2>Why the moderator is needed?<\/h2>\n<p>The probability of the fission\u00a0<a title=\"Uranium 235\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/uranium-235\/\">U-235<\/a> becomes very large <strong>at the thermal energies<\/strong> of slow neutrons. This fact implies increase of multiplication factor of the reactor (i.e., lower fuel enrichment is needed to sustain chain reaction)<\/p>\n<h2>Why fast reactors don&#8217;t need moderator?<\/h2>\n<p><a title=\"Fast Neutron Reactor\" href=\"http:\/\/sitepourvtc.com\/fast-neutron-reactor\/\">Fast reactors<\/a> use fast neutrons to split <a title=\"Uranium\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/uranium\/\">uranium<\/a> or <a title=\"Plutonium\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/plutonium\/\">plutonium<\/a> nuclei. They use higher fuel enrichment to sustain chain reaction.\u00a0The moderation of neutrons is undesirable in fast reactors.<\/p><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-40 lgc-tablet-grid-40 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<figure id=\"attachment_90\" aria-describedby=\"caption-attachment-90\" style=\"width: 390px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/10\/neutron_moderator.gif\"><img loading=\"lazy\" class=\"size-full wp-image-90\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/10\/neutron_moderator.gif\" alt=\"How does the neutron moderator work?\" width=\"400\" height=\"348\" \/><\/a><figcaption id=\"caption-attachment-90\" class=\"wp-caption-text\">How does the neutron moderator work?<br \/>Source: http:\/\/hyperphysics.phy-astr.gsu.edu\/<\/figcaption><\/figure>\n<div   id="8n9s8rpp6h"    class=\"su-spacer\" style=\"height:10px\"><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div>\n<figure id=\"attachment_89\" aria-describedby=\"caption-attachment-89\" style=\"width: 444px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/10\/neutron_moderator_fuel.gif\"><img loading=\"lazy\" class=\"size-full wp-image-89\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2014\/10\/neutron_moderator_fuel.gif\" alt=\"How does the neutron moderator work? Fuel pin\" width=\"454\" height=\"419\" \/><\/a><figcaption id=\"caption-attachment-89\" class=\"wp-caption-text\">How does the neutron moderator work? Fuel pin<br \/>Source: http:\/\/hyperphysics.phy-astr.gsu.edu\/<\/figcaption><\/figure>\n<div   id="8n9s8rpp6h"    class=\"su-spacer\" style=\"height:10px\"><\/div><\/div><\/div><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\"><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=\"lgc-column lgc-grid-parent lgc-grid-50 lgc-tablet-grid-50 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><div   id="8n9s8rpp6h"    class=\"su-spacer\" style=\"height:10px\"><\/div>\n<h2>Elastic Scattering and Neutron Moderators<\/h2>\n<p>To be <strong>an effective <a title=\"Neutron moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">moderator<\/a><\/strong>, the probability of <a title=\"Neutron Elastic Scattering\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-elastic-scattering\/\">elastic reaction<\/a> between neutron and the nucleus must be high. In terms of cross-sections,<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\/\"> the elastic scattering cross section<\/a> of a moderator\u2019s nucleus must be high. Therefore, a <strong>high elastic scattering cross-section<\/strong> is important, but does not describe comprehensively capabilities of moderators. In order to describe capabilities of a material to slow down neutrons, three new material variables\u00a0must be defined:<\/p>\n<ul>\n<li><a title=\"Average Logarithmic Energy Decrement\" href=\"http:\/\/sitepourvtc.com\/glossary\/neutron-moderatoraverage-logarithmic-energy-decrement\/\"><strong>The Average Logarithmic Energy Decrement (\u03be)<\/strong><\/a><\/li>\n<li><a title=\"Macroscopic Slowing Down Power \u2013 MSDP\" href=\"http:\/\/sitepourvtc.com\/glossary\/macroscopic-slowing-down-power-msdp\/\"><strong>The Macroscopic Slowing Down Power (MSDP)<\/strong><\/a><\/li>\n<li><a title=\"Moderating Ratio \u2013 MR\" href=\"http:\/\/sitepourvtc.com\/glossary\/moderating-ratio-mr\/\"><strong>The Moderating Ratio (MR)<\/strong><\/a><\/li>\n<\/ul>\n<\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-50 lgc-tablet-grid-50 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">Key properties of <a title=\"Neutron moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">neutron moderators<\/a>:\n<ul>\n<li>high cross-section for neutron scattering<\/li>\n<li>high energy loss per collision<\/li>\n<li>low cross-section for absorption<\/li>\n<li>high melting and boiling point<\/li>\n<li>high thermal conductivity<\/li>\n<li>high specific heat capacity<\/li>\n<li>low viscosity<\/li>\n<li>low activity<\/li>\n<li>low corrosive<\/li>\n<li>cheap<\/li>\n<\/ul>\n<\/div><\/div><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>Average Logarithmic Energy Decrement<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">During the scattering reaction, a fraction of the neutron\u2019s kinetic energy <strong>is transferred to the nucleus<\/strong>. Using the laws of <strong>conservation of momentum and energy<\/strong> and the analogy of collisions of billiard balls for elastic scattering, it is possible to derive the following equation for the mass of target or <a title=\"Neutron moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">moderator<\/a> nucleus (M), energy of incident <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutron<\/a> (E<sub>i<\/sub>) and the energy of scattered neutron (E<sub>s<\/sub>).\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/equation-momentum-energy.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13057\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/equation-momentum-energy.png\" alt=\"equation momentum energy\" width=\"493\" height=\"98\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/equation-momentum-energy.png 493w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/equation-momentum-energy-300x60.png 300w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><\/a><\/p>\n<p>where A is the atomic mass number.<\/p>\n<p>In case of the <strong>hydrogen (A = 1)<\/strong> as the target nucleus, the incident neutron <strong>can be completely stopped<\/strong>. But this works when the direction of the neutron is completely reversed (i.e., scattered at 180\u00b0). In reality, the direction of scattering ranges from 0 to 180 \u00b0 and the energy transferred also ranges from 0% to maximum. Therefore, the average energy of scattered neutron is taken as the average of energies with scattering angle 0 and 180\u00b0.<\/p>\n<p>Moreover, it is useful to work <strong>with logarithmic quantities<\/strong> and therefore one defines <strong>the logarithmic energy decrement per collision (\u03be)<\/strong> as a key material constant describing energy transfers during a neutron slowing down. \u03be is not dependent on energy, only on A and is defined as follows:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/logarithmic-energy-decrement-equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13059\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/logarithmic-energy-decrement-equation.png\" alt=\"logarithmic energy decrement - equation\" width=\"742\" height=\"272\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/logarithmic-energy-decrement-equation.png 742w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/logarithmic-energy-decrement-equation-300x110.png 300w\" sizes=\"(max-width: 742px) 100vw, 742px\" \/><\/a><\/p>\n<p>For heavy target nuclei,<strong> \u03be<\/strong> may be approximated by following formula:<br \/>\n<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/logarithmic-energy-decrement-heavy-nuclei.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13060\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/logarithmic-energy-decrement-heavy-nuclei.png\" alt=\"the logarithmic energy decrement per collision\" width=\"684\" height=\"663\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/logarithmic-energy-decrement-heavy-nuclei.png 684w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/logarithmic-energy-decrement-heavy-nuclei-300x291.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/logarithmic-energy-decrement-heavy-nuclei-52x50.png 52w\" sizes=\"(max-width: 684px) 100vw, 684px\" \/><\/a><\/p>\n<p>From these equations it is easy to determine the number of collisions required to slow down a neutron from, for example from <strong>2 MeV to 1 eV<\/strong>.<\/p>\n<p>Example:<br \/>\nDetermine the number of collisions required for thermalization for the 2 MeV neutron in the carbon.<br \/>\n\u03be<sub>CARBON<\/sub> = 0.158<br \/>\nN(<strong>2MeV \u2192 1eV<\/strong>) = ln 2\u22c510<sup>6<\/sup>\/\u03be =14.5\/0.158 = <strong>92<\/strong><\/p>\n<figure id=\"attachment_13062\" aria-describedby=\"caption-attachment-13062\" style=\"width: 630px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/logarithmic-energy-decrement-table.png\"><img loading=\"lazy\" class=\"wp-image-13062 size-full\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/logarithmic-energy-decrement-table.png\" alt=\"Table of average logarithmic energy decrement for some elements\" width=\"640\" height=\"538\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/logarithmic-energy-decrement-table.png 640w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/logarithmic-energy-decrement-table-300x252.png 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/><\/a><figcaption id=\"caption-attachment-13062\" class=\"wp-caption-text\">Table of average logarithmic energy decrement for some elements.<\/figcaption><\/figure>\n<p>For a mixture of isotopes:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/logarithmic-energy-decrement-mixtures.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13061\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/logarithmic-energy-decrement-mixtures.png\" alt=\"the logarithmic energy decrement for mixtures\" width=\"230\" height=\"94\" \/><\/a><\/p><\/div><\/div><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>Macroscopic Slowing Down Power<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">We have defined the <strong>probability of elastic scattering reaction<\/strong>, we have defined <strong>the average energy loss<\/strong> during the reaction. The product of these variables (the logarithmic energy decrement and the macroscopic cross section for scattering in the material) is <strong>the macroscopic slowing down power (MSDP)<\/strong>.\n<p style=\"text-align: center;\"><strong>MSDP = \u03be . \u03a3<sub>s<\/sub><\/strong><\/p>\n<p>The MSDP describes<strong> the ability of a given material to slow down neutrons<\/strong> and indicates how rapidly a <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutron<\/a> will slow down in the material, but it does not fully reflect the effectiveness of the material as a <a title=\"Neutron moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">moderator<\/a>. In fact, the material with high <strong>MSDP<\/strong> can slow down neutrons with high efficiency, but it can be a poor moderator because of its high probability of\u00a0absorbing neutrons. It is typical, for example, for <a title=\"Boron 10\" href=\"http:\/\/sitepourvtc.com\/glossary\/boron-10\/\">boron<\/a>, which has a high slowing down power but is <strong>absolutely inappropriate<\/strong> as a moderator.<\/p>\n<p><span style=\"font-weight: 400;\">The most complete measure of the effectiveness of a moderator is <strong>the Moderating Ratio (MR)<\/strong>, where:<\/span><\/p>\n<p style=\"text-align: center;\"><b>MR \u00a0= \u03be . <strong>\u03a3<sub>s<\/sub><\/strong><\/b><b>\/<strong>\u03a3<sub>a<\/sub><\/strong><\/b><\/p>\n<figure id=\"attachment_13063\" aria-describedby=\"caption-attachment-13063\" style=\"width: 829px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/macroscopic-slowing-down-power-table.png\"><img loading=\"lazy\" class=\"size-full wp-image-13063\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/macroscopic-slowing-down-power-table.png\" alt=\"Table of macroscopic slowing down power MSDP for some materials.\" width=\"839\" height=\"232\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/macroscopic-slowing-down-power-table.png 839w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/macroscopic-slowing-down-power-table-300x83.png 300w\" sizes=\"(max-width: 839px) 100vw, 839px\" \/><\/a><figcaption id=\"caption-attachment-13063\" class=\"wp-caption-text\">Table of macroscopic slowing down power MSDP for some materials.<\/figcaption><\/figure>\n<\/div><\/div><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>Moderating Ratio<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>The moderating ratio<\/strong> or moderator quality is the most complete measure of the effectiveness of <a title=\"Neutron moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">a moderator<\/a> because it takes into account also the absorption effects. When absorption effects are high, most of the <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutrons <\/a>will be absorbed by moderator, leading to lower moderation or lower availability of <a title=\"Thermal Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/thermal-neutron\/\">thermal neutrons<\/a>.\n<p>Therefore a higher ratio of MSDP to absorbtion cross sections <b>\u03be . <strong>\u03a3<sub>s<\/sub><\/strong><\/b><b>\/<strong>\u03a3<sub>a<\/sub><\/strong><\/b>\u00a0is desirable for effective moderation. This ratio is called <strong>the moderating ratio<\/strong>\u00a0&#8211; <strong>MR\u00a0<\/strong>and can be used as a criterion for comparison of different moderators.<\/p>\n<p>Examples:<\/p>\n<ul>\n<li><strong>Light water<\/strong> has the <strong>highest \u03be and \u03c3<\/strong><sub><strong>s<\/strong>\u00a0<\/sub>among the moderators (resulting in the highest MSDP) shown in the table, but its moderating ratio is low due to its relatively <strong>higher absorption cross section<\/strong>.<\/li>\n<\/ul>\n<ul>\n<li>On the other hand, <strong>heavy water<\/strong> has <strong>lower \u03be and \u03c3s<\/strong>, but it has the <strong>highest moderating ratio<\/strong> owing to its <strong>lowest neutron absorption cross-section<\/strong>.<\/li>\n<\/ul>\n<ul>\n<li><strong>Graphite<\/strong> has much heavier nuclei than hydrogen in water, despite the fact graphite has <strong>much lower \u03be and \u03c3<sub>s<\/sub><\/strong>, it is <strong>better moderator than light water<\/strong> due to its lower absorption cross-section compared to that of light water.<\/li>\n<\/ul>\n<figure id=\"attachment_13064\" aria-describedby=\"caption-attachment-13064\" style=\"width: 630px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/moderation-ratio-table.png\"><img loading=\"lazy\" class=\"size-full wp-image-13064\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/moderation-ratio-table.png\" alt=\"Table of moderating ratios MR for some materials.\" width=\"640\" height=\"274\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/moderation-ratio-table.png 640w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/moderation-ratio-table-300x128.png 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/><\/a><figcaption id=\"caption-attachment-13064\" class=\"wp-caption-text\">Table of moderating ratios for some materials.<\/figcaption><\/figure>\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 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":"","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"generate_page_header":""},"categories":[6],"tags":[7],"_links":{"self":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/posts\/83"}],"collection":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/types\/post"}],"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=83"}],"version-history":[{"count":3,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/posts\/83\/revisions"}],"predecessor-version":[{"id":30941,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/posts\/83\/revisions\/30941"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=83"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/categories?post=83"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/tags?post=83"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}