Nln E_{high}ln E_{low}lnE_{high}E_{low}NlnE_{high}E_{low}ln2 x 10^{6} eV0.025 eV0.94819.2 collisionsReactor Theory (Neutron Characteristics)DOE-HDBK-1019/1-93NEUTRON MODERATIONRev. 0Page 25NP-02Since represents the average logarithmic energy loss per collision, the total number of collisionsnecessary for a neutron to lose a given amount of energy may be determined by dividing intothe 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.highlowExample:How many collisions are required to slow a neutron from an energy of 2 MeV to athermal energy of 0.025 eV, using water as the moderator? Water has a value of 0.948for .Solution:Sometimes it is convenient, based upon information known, to work with an average fractionalenergy loss per collision as opposed to an average logarithmic fraction. If the initial neutronenergy level and the average fractional energy loss per collision are known, the final energy levelfor a given number of collisions may be computed using the following formula.