It is convenient to consider the number of neutrons existing in one cubic centimeter at any one instant and the total distance they travel each second while in that cubic centimeter. The number of neutrons existing in a cm3 of material at any instant is called neutron density and is represented by the symbol n with units of neutrons/cm3. The total distance these neutrons can travel each second will be determined by their velocity.

A good way of defining neutron flux (0) is to consider it to be the total path length covered by all neutrons in one cubic centimeter during one second. Mathematically, this is the equation below.

ф =nv (1)

where: ф = neutron flux (neutrons cm-2 s-1), n = neutron density (neutrons cm-3), and v = neutron velocity (cm s-1). The term neutron flux in some applications (for example, cross

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section measurement) is used as parallel beams of neutrons travelling in a single direction. The intensity of a neutron beam is the product of the neutron density times the average neutron velocity. The directional beam intensity is equal to the number of neutrons per unit area and time (neutrons cm-2 s-1) falling on a surface perpendicular to the direction of the beam. One can think of the neutron flux in a reactor as being comprised of many neutron beams travelling in various directions. Then, the neutron flux becomes the scalar sum of these directional flux intensities. Macroscopic cross sections for neutron reactions with materials determine the probability of one neutron undergoing a specific reaction per centimeter of travel through that material. If one wants to determine how many reactions will actually occur, it is necessary to know how many neutrons are travelling through the material and how many centimeters they travel each second. Since the atoms in a reactor do not interact preferentially with neutrons from any particular direction, all of these directional beams contribute to the total rate of reaction. In reality, at a given point within a reactor, neutrons will be travelling in all directions (DOE, 1993).