NN_{A}M2.699gcm^{3}6.022 x 10^{23}^{atoms}mole26.9815gmole6.024 x 10^{22}^{atoms}cm^{3}DOE-HDBK-1019/1-93Reactor Theory (Neutron Characteristics)NUCLEAR CROSS SECTIONS AND NEUTRON FLUXRev. 0Page 7NP-02Example:A block of aluminum has a density of 2.699 g/cm . If the gram atomic weight of3aluminum is 26.9815 g, calculate the atom density of the aluminum.Solution:CrossSectionsThe probability of a neutron interacting with a nucleus for a particular reaction is dependentupon not only the kind of nucleus involved, but also the energy of the neutron. Accordingly,the absorption of a thermal neutron in most materials is much more probable than the absorptionof a fast neutron. Also, the probability of interaction will vary depending upon the type ofreaction involved.The probability of a particular reaction occurring between a neutron and a nucleus is called themicroscopic cross section( ) of the nucleus for the particular reaction. This cross section willvary with the energy of the neutron. The microscopic cross section may also be regarded as theeffective area the nucleus presents to the neutron for the particular reaction. The larger theeffective area, the greater the probability for reaction.Because the microscopic cross section is an area, it is expressed in units of area, or squarecentimeters. A square centimeter is tremendously large in comparison to the effective area ofa nucleus, and it has been suggested that a physicist once referred to the measure of a squarecentimeter as being "as big as a barn" when applied to nuclear processes. The name haspersisted and microscopic cross sections are expressed in terms of barns. The relationshipbetween barns and cm is shown below.21 barn = 10cm-242