The function characterizing the energy dependence of neutron flux ф(г, E, t) is called the neutron spectrum and it varies with fuel enrichment, moderator density, void fraction, burnup, and so on. Figure 2.1 shows a neutron spectrum of a thermal reactor. The neutron spectrum of thermal reactors is divided into three distinct energy regions. In the high-energy region above 105 eV, since the prompt neutrons released by fission are dominant, the neutron spectrum is approximately

proportional to the fission spectrum x(E). In the energy region below several hundred of keV, the fast neutrons from fission lose their energies mainly through elastic scattering reaction with light moderator nuclides such as hydrogen.

According to neutron slowing-down theory [1], when fast neutron sources are in an infinite homogeneous medium which is an ideal moderator with negligible absorption, the neutron energy spectrum behaves as 1/E.

(2-6)

In the practical medium of fuel and moderator, the 1/E distribution is character­ized by the occurrence of fairly sharp depressions due to the resonance absorption of 238U, etc. as shown in Fig. 2.1. Moreover, if the resonance absorption is large, the neutron flux becomes somewhat smaller than the 1/E distribution in the low energy region.

If neutrons are moderated below several eV of kinetic energy, the kinetic energy by thermal vibration of nuclei cannot be ignored. In other words, if the kinetic energies of neutrons become appropriately small, the neutrons collide with ther­mally vibrating moderator nuclei and their kinetic energies become reversely large. This is called up-scattering against moderation (down-scattering). In this energy region, the neutron spectrum is characterized in a thermal equilibrium at a temper­ature T by a balance between down-scattering and up-scattering. Further, in the ideal infinite medium without absorption, the thermal equilibrium neutron spectrum is described by the following Maxwellian distribution function

(2.7)

where k is the Boltzmann constant. At room temperature (T = 300 K), фм is maximized at E = 0.0253 eV for which the corresponding velocity is 2,200 m/s.

On being absorbed, the thermal neutron spectrum deviates a little from фм (E) forward the high energy region because absorption cross sections are larger in lower energies. This is called absorption hardening. To compensate the Maxwellian distribution for the absorption hardening, neutron temperature, which is a little higher than moderator temperature, is used as T of Eq. (2.7).