N
ln Ehigh
ln Elow
ln
Ehigh
Elow
N
ln
Ehigh
Elow
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.
