Neutron Slowing Down and Thermalization

N ln E_high ln E_low ln E_high E_low N ln E_high E_low ln 2 x 10⁶ eV 0.025 eV 0.948 19.2 collisions Reactor Theory (Neutron Characteristics) DOE-HDBK-1019/1-93 NEUTRON MODERATION Rev. 0 Page 25 NP-02 Since represents the average logarithmic energy loss per collision, the total number of collisions necessary for a neutron to lose a given amount of energy may be determined by dividing into the difference of the natural logarithms of the energy range in question. The number of collisions (N) to travel from any energy, E , to any lower energy, E , can be calculated as shown below. high low Example: How many collisions are required to slow a neutron from an energy of 2 MeV to a thermal energy of 0.025 eV, using water as the moderator? Water has a value of 0.948 for . Solution: Sometimes it is convenient, based upon information known, to work with an average fractional energy loss per collision as opposed to an average logarithmic fraction. If the initial neutron energy level and the average fractional energy loss per collision are known, the final energy level for a given number of collisions may be computed using the following formula.