{"id":13047,"date":"2016-11-15T07:54:02","date_gmt":"2016-11-15T07:54:02","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=13047"},"modified":"2024-02-07T11:50:03","modified_gmt":"2024-02-07T11:50:03","slug":"neutron-elastic-scattering","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-elastic-scattering\/","title":{"rendered":"Neutron Elastic Scattering"},"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\">Generally, <strong>a neutron scattering reaction<\/strong> occurs when a target nucleus emits a single <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutron<\/a> after a <strong>neutron-nucleus interaction<\/strong>. There is no energy transferred into nuclear excitation in an <strong>elastic<\/strong> scattering reaction between a neutron and a target nucleus.<\/div><\/div>\n<p>The elastic scattering conserves both <strong>momentum<\/strong> and <strong>kinetic energy<\/strong> of the &#8220;system&#8221;. It may be modeled as <strong>a billiard ball collision<\/strong> between a neutron and a nucleus.<\/p>\n<p>There is usually some <strong>transfer of kinetic energy<\/strong> from the incident neutron to the target nucleus. The target nucleus gains the exact amount of kinetic energy that the neutron loses. This interaction can occur via <a title=\"Compound Nucleus Reactions\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/compound-nucleus-reactions\/\">compound nucleus formation<\/a>, but in the case of elastic scattering, a neutron emission returns the compound nucleus to the ground state of the original nucleus. Therefore the initial and final neutrons do not need to be necessarily the same.<\/p>\n<p><a href=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2023\/02\/elastic-scattering-reaction.png\"><img loading=\"lazy\" class=\"aligncenter size-large wp-image-40080\" src=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2023\/02\/elastic-scattering-reaction-1024x577.png\" alt=\"elastic scattering - reaction\" width=\"1024\" height=\"577\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2023\/02\/elastic-scattering-reaction-1024x577.png 1024w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2023\/02\/elastic-scattering-reaction-300x169.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2023\/02\/elastic-scattering-reaction-768x433.png 768w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2023\/02\/elastic-scattering-reaction-1536x866.png 1536w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2023\/02\/elastic-scattering-reaction.png 1870w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/a><\/p>\n<p>The elastic scattering can occur by way of two interaction mechanisms:<\/p>\n<ul>\n<li><strong>Potential scattering<\/strong>. In potential scattering, the neutron and the nucleus interact<strong> without neutron absorption<\/strong> and <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\/\">a compound nucleus<\/a>. In fact, the incident neutron does not necessarily have to &#8220;touch&#8221; the nucleus, and the neutron is scattered by the short-range <strong>nuclear forces<\/strong> when it approaches close enough to the nucleus. Potential scattering occurs with incident neutrons that have an energy of up to about 1 MeV. It may be modeled as a billiard ball collision between a neutron and a nucleus.<\/li>\n<li><strong>Compound-elastic scattering<\/strong>. In some cases, if the kinetic energy of an incident neutron is just right to form <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\/\">a resonance<\/a>, the neutron may be absorbed, and a <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> may be formed. This interaction is more unusual and is also known as <strong>resonance elastic scattering<\/strong>. Due to the formation of the compound nucleus, the initial and final neutron are not the same.<\/li>\n<\/ul>\n<div   id="8n9s8rpp6h"    class=\"collapsible-container\">\n<h2>Conservation of momentum and kinetic energy<\/h2>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/conservation-of-momentum-and-energy.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13042\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/conservation-of-momentum-and-energy.png\" alt=\"conservation of momentum and energy\" width=\"682\" height=\"119\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/conservation-of-momentum-and-energy.png 682w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/conservation-of-momentum-and-energy-300x52.png 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/a><\/p>\n<p>where:<\/p>\n<p>m<sub>n<\/sub> = mass of the neutron<br \/>\nm<sub>T<\/sub> = mass of the target nucleus T<br \/>\nv<sub>n,i<\/sub> = initial neutron speed<br \/>\nv<sub>n,f<\/sub> = final neutron speed<br \/>\nv<sub>T,i<\/sub> = initial target speed<br \/>\nv<sub>T,f<\/sub> = final target speed<\/p>\n<h2>Key Characteristics of Elastic Scattering<\/h2>\n<ul>\n<li><strong>Elastic scattering<\/strong> is the most important process for slowing down neutrons.<\/li>\n<\/ul>\n<ul>\n<li><strong>The total kinetic energy<\/strong> of the system <strong>is conserved<\/strong> in the elastic scattering.<\/li>\n<\/ul>\n<ul>\n<li>In this process, energy lost by the <a title=\"Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/\">neutron<\/a> is transferred to the recoiling nucleus.<\/li>\n<\/ul>\n<ul>\n<li>Maximum energy transfer occurs with a head-on collision.<\/li>\n<\/ul>\n<ul>\n<li>The kinetic energy of the recoiled nucleus <strong>depends on the recoiled angle \u03c6<\/strong> of the nucleus.<\/li>\n<\/ul>\n<ul>\n<li>Elastic scattering <a title=\"Neutron cross-section\" href=\"http:\/\/sitepourvtc.com\/neutron-cross-section\/\">cross-sections<\/a> for light elements are more or less independent of neutron energy up to 1 MeV.<\/li>\n<\/ul>\n<ul>\n<li>For intermediate and heavy elements, the elastic cross-section is constant at low energy with some specifics at higher energy.<\/li>\n<\/ul>\n<ul>\n<li>A good approximation is, <strong>\u03c3<sub>s<\/sub> = const<\/strong>, for all elements that are of importance.<\/li>\n<\/ul>\n<ul>\n<li>At low energy, <strong>\u03c3<sub>s<\/sub><\/strong>\u00a0can be described by the one-level <strong>Breit-Wigner formula<\/strong>.<\/li>\n<\/ul>\n<ul>\n<li>Nearly all elements have scattering cross-sections in the range of <strong>2 to 20 barns<\/strong>.<\/li>\n<\/ul>\n<ul>\n<li>The important exception is for water and heavy water.<\/li>\n<\/ul>\n<ul>\n<li>If the kinetic energy of an incident neutron is large compared with the chemical binding energy of the atoms in a molecule, the chemical bound can be ignored.<\/li>\n<\/ul>\n<ul>\n<li>If the kinetic energy of an incident neutron is of the order or less than the chemical binding energy, the cross-section of the molecule is not equal to the sum of cross-sections of its individual nuclei.<\/li>\n<\/ul>\n<ul>\n<li>The scattering of slow neutrons by molecules <strong>is greater than by free nuclei<\/strong>.<\/li>\n<\/ul>\n<ul>\n<li>Therefore one nucleus microscopic cross-section does not describe the process correctly, while the macroscopic cross-section (\u03a3s) has a precise meaning.<\/li>\n<\/ul>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scaterring-on-Molecule-min.png\"><img loading=\"lazy\" class=\"aligncenter size-medium wp-image-13044\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scaterring-on-Molecule-min-300x155.png\" alt=\"Scattering of slow neutrons by molecules is greater than by free nuclei.\" width=\"300\" height=\"155\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scaterring-on-Molecule-min-300x155.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scaterring-on-Molecule-min-1024x531.png 1024w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scaterring-on-Molecule-min.png 1067w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a>The scattering of slow neutrons by molecules is greater than by free nuclei.<\/p>\n<figure id=\"attachment_13043\" aria-describedby=\"caption-attachment-13043\" style=\"width: 290px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scaterring-on-Water-min.png\"><img loading=\"lazy\" class=\"size-medium wp-image-13043\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scaterring-on-Water-min-300x172.png\" alt=\"Scattering of slow neutrons by molecules is greater than by free nuclei.\" width=\"300\" height=\"172\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scaterring-on-Water-min-300x172.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scaterring-on-Water-min.png 816w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-13043\" class=\"wp-caption-text\">If the kinetic energy of an incident neutron is large compared with the chemical binding energy of the atoms in a molecule, the chemical bound can be ignored.<br \/>If the kinetic energy of an incident neutron is of the order or less than the chemical binding energy, the cross-section of the molecule is not equal to the sum of cross-sections of its individual nuclei.<\/figcaption><\/figure>\n<h2>Elastic Scattering Cross-section<\/h2>\n<p>To be <strong>an effective <a title=\"Neutron moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">moderator<\/a><\/strong>, the probability of elastic reaction between neutron and the nucleus must be high. In terms of cross-sections, the elastic scattering cross-section of a moderator\u2019s nucleus must be high.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scattering-Cross-section-light-elements-min.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13045\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scattering-Cross-section-light-elements-min.png\" alt=\"Elastic scattering cross-sections for light elements\" width=\"845\" height=\"651\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scattering-Cross-section-light-elements-min.png 845w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scattering-Cross-section-light-elements-min-300x231.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scattering-Cross-section-light-elements-min-180x138.png 180w\" sizes=\"(max-width: 845px) 100vw, 845px\" \/><\/a><\/p>\n<p>Elastic scattering cross-sections for light elements are more or less independent of neutron energy up to 1 MeV.<\/p>\n<p>Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scattering-Cross-section-heavy-elements-min.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-13046\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scattering-Cross-section-heavy-elements-min.png\" alt=\"Elastic scattering cross-sections for heavy elements\" width=\"846\" height=\"665\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scattering-Cross-section-heavy-elements-min.png 846w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2015\/11\/Elastic-Scattering-Cross-section-heavy-elements-min-300x236.png 300w\" sizes=\"(max-width: 846px) 100vw, 846px\" \/><\/a><\/p>\n<p>For intermediate and heavy elements, the elastic cross-section is constant at low energy with some specifics at higher energy.<\/p>\n<p>Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library<\/p>\n<h2>Elastic Scattering and Neutron Moderators<\/h2>\n<p>As can be seen, a <strong>high elastic scattering cross-section<\/strong> is important but does not comprehensively describe moderators&#8217; capabilities. To describe the capabilities of a material to slow down neutrons, three new material variables must be defined:<\/p>\n<ul>\n<li><strong>The Average Logarithmic Energy Decrement (\u03be)<\/strong><\/li>\n<li><strong>The Macroscopic Slowing Down Power (MSDP)<\/strong><\/li>\n<li><strong>The Moderating Ratio (MR)<\/strong><\/li>\n<\/ul>\n<p>Key properties of <a title=\"Neutron moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">neutron moderators<\/a>:<\/p>\n<ul>\n<li>the high cross-section for neutron scattering<\/li>\n<li>high energy loss per collision<\/li>\n<li>the 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   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), the 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>).<\/p>\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 the 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 the scattered neutron is taken as the average of energies with scattering angles 0 and 180\u00b0.<\/p>\n<p>Moreover, it is useful to work <strong>with logarithmic quantities<\/strong>. Therefore\u00a0one 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 the 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 neutrons 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><\/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\u00a0have 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>.<\/p>\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. Still, 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 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 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, the moderator will absorb most of the neutrons, 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>.<\/p>\n<p>Therefore a higher ratio of MSDP to absorption 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 comparing 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. Still, 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. Even though graphite has <strong>much lower \u03be and \u03c3<sub>s<\/sub><\/strong>, it is a <strong>better moderator than light water<\/strong> due to its lower absorption cross-section than 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>\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 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>The elastic scattering conserves both momentum and kinetic energy of the &#8220;system&#8221;. It may be modeled as a billiard ball collision between a neutron and a nucleus. There is usually some transfer of kinetic energy from the incident neutron to the target nucleus. The target nucleus gains the exact amount of kinetic energy that the &#8230; <a title=\"Neutron Elastic Scattering\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-elastic-scattering\/\" aria-label=\"More on Neutron Elastic Scattering\">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\/13047"}],"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=13047"}],"version-history":[{"count":9,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/13047\/revisions"}],"predecessor-version":[{"id":40085,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/13047\/revisions\/40085"}],"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=13047"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}