DOE-HDBK-1019/1-93Reactor Theory (Neutron Characteristics)NUCLEAR CROSS SECTIONS AND NEUTRON FLUXRev. 0Page 15NP-02NeutronFluxMacroscopic cross sections for neutron reactions with materials determine the probability of oneneutron undergoing a specific reaction per centimeter of travel through that material. If onewants to determine how many reactions will actually occur, it is necessary to know how manyneutrons are traveling through the material and how many centimeters they travel each second.It is convenient to consider the number of neutrons existing in one cubic centimeter at any oneinstant and the total distance they travel each second while in that cubic centimeter. The numberof neutrons existing in a cm of material at any instant is called neutron density and is3represented by the symbol n with units of neutrons/cm . The total distance these neutrons can3travel each second will be determined by their velocity.A good way of defining neutron flux (1 ) is to consider it to be the total path length covered byall neutrons in one cubic centimeter during one second. Mathematically, this is the equationbelow.1=n v(2-5)where:1=neutron flux (neutrons/cm -sec)2n=neutron density (neutrons/cm )^{3}v=neutron velocity (cm/sec)The term neutron flux in some applications (for example, cross section measurement) is usedas parallel beams of neutrons traveling in a single direction. The intensity (I) of a neutron beamis the product of the neutron density times the average neutron velocity. The directional beamintensity is equal to the number of neutrons per unit area and time (neutrons/cm -sec) falling on2a surface perpendicular to the direction of the beam.One can think of the neutron flux in a reactor as being comprised of many neutron beamstraveling in various directions. Then, the neutron flux becomes the scalar sum of thesedirectional flux intensities (added as numbers and not vectors), that is, 1 = I + I + I +...I .1 2 3 nSince the atoms in a reactor do not interact preferentially with neutrons from any particulardirection, all of these directional beams contribute to the total rate of reaction. In reality, at agiven point within a reactor, neutrons will be traveling in all directions.