Average logarithmic energy decrement

The mean logarithmic energy decrement or the mean logarithmic energy loss is a calculation variable used in reactor physics . It gives the logarithm of the mean energy loss of a neutron when it collides with an atomic nucleus of the moderator substance: ${\displaystyle \xi }$

${\displaystyle \xi =\ln {\overline {\frac {E_{1}}{E_{2}}}}.}$

It is the energy of the neutron before and the energy after the collision. ${\displaystyle E_{1}}$ ${\displaystyle E_{2}}$

${\displaystyle \xi }$is a material constant of the moderator. If A denotes the mass number of the moderator, it can be written using the abbreviation as ${\displaystyle \xi }$ ${\displaystyle \alpha ={\frac {(A-1)^{2}}{(A+1)^{2}}}}$

${\displaystyle \xi =1+{\frac {\alpha }{1-\alpha }}\ln \alpha .}$

For pure hydrogen is . A neutron, the kinetic energy of which is large compared to that of a moderator atom , therefore reduces its energy on average to one e- th of the original energy when it collides with it . ${\displaystyle \xi =1}$

${\displaystyle \xi }$decreases with increasing mass number. This explains the increasing number of impacts that are required in heavier moderator materials to achieve thermal energy . Taking into account a certain probability of absorption per impact, it is therefore more advantageous to choose a light element as the moderator substance.

The following table shows the mean logarithmic energy decrement of various materials and thus information about the average number of collisions that are necessary to decelerate a neutron produced by nuclear fission to thermal energy.

	hydrogen	deuterium	beryllium	carbon	oxygen	uranium
Mass of the core in u	1	2	9	12	16	238
Energy decrement ${\displaystyle \xi }$	1	0.7261	0.2078	0.1589	0.1209	0.0084
Number of shocks	18th	25th	86	114	150	2172

Individual evidence

1. ↑ D. Emendörfer, KH Höcker: Theory of nuclear reactors, Volume 1: The stationary reactor . Bibliographisches Institut AG, Zurich 1982, ISBN 3-411-01599-3