All reactor physics and shielding calculations need data for neutron-induced reac­tions covering the range of incident neutron energies of interest for the calculation, for all materials present in the system.

The experimental data usually come from different sources and have to be first compiled in a consistent format acceptable by the computer codes used in each particular case. Besides up-datings are often necessary to include new experimental data or because of new user’s requirements. Various sets of data have been in use at different laboratories, but in recent years there has been a great tendency to standardi­zation, based on the utilization of the evaluated nuclear data file (ENDF) which allows an easy exchange of information between various laboratories.<1_3) Two different evaluated data libraries are maintained. The first (ENDF/A) contains the data as available and may include several different evaluations for the cross-sections of each material. From this set a cross-section evaluation working group chooses periodically a recommended reference data set (ENDF/B). This second set contains at any given time only one complete evaluated data set for each material. The libraries are contained on magnetic tape or discs. An evaluated set for each material is divided into files, each of which contains data of a certain class. They are

File number Class of data

1 General information

2 Resonance parameter data

3 Neutron cross-sections

4 Angular distributions of secondary neutrons

5 Energy distributions of secondary neutrons

6 Energy-angular distributions of secondary neutrons

7 Thermal neutron scattering law data

12 Multiplicities for photons (from neutron reactions)

13 Photon production cross-sections (from neutron reactions)

14 Angular distributions of photons (from neutron reactions)

15 Energy distributions of photons (from neutron reactions)

16 Energy-angular distributions of photons (from neutron reactions)

23 Photon interaction cross-sections

24 Angular distributions of photons (from photon reactions)

25 Energy distributions of photons (from photon reactions)

26 Energy-angular distributions of photons (from photon reactions)

27 Atomic form factors (for photon interactions)

The cross-sections are represented by a series of tabulated values, plus a method of interpolating between input values. The limit on the number of energy points to be used to represent a particular cross-section is 5000.

It should not be always assumed that newer versions of ENDF/B are more accurate than older ones, before they are tested for the cases of interest. The first version appeared in 1967-8, version II in 1970 and version III in 1972. The newer cross-section evaluations have mostly been aimed at fast reactor calculations and did not involve significant changes in the thermal energy range.

The following features are being incorporated into the ENDF/B-IV Library, which is due for distribution:

1. Completely revised evaluations for the “big five” isotopes: 235U, 238U, 239Pu, 24°Pu and “Pu. In addition to the cross-section files, which have been revised by a

special task force, these evaluations will have revised values for v, fission neutron (prompt and delayed), energy spectra, and fission product yields.

2. New evaluations for fifty-two of the other materials (including materials not present in ENDF/B-III).

3. Increased number of materials with y-ray production data, and a new у-interaction file.

4. A new fission product data file, containing radioactive decay spectra for about 300 materials of interest for decay heat calculation.

5. A dosimetry file, consisting of reactions of interest to dosimetry calculations.

6. Thermal constants for fissile and fertile materials, revised by the Normalization and Standards Subcommittee.

7. Error information for the cross-sections of selected materials and for the fission product decay data.<4)

ENDF material is available to U. S. users from the National Neutron Cross Section Center (NNCSC) at BNL and to NEA countries from the Neutron Data Compilation Centre at Saclay.

The existing codes for neutron calculations require libraries which are different from one another and from ENDF/B. Therefore processing codes are needed in order to generate from ENDF/B a library usable in a reactor calculation code (see § 8.8).

It must be noted that beside the ENDF/B, other cross-section sets are being used. Although these data are usually older than ENDF/B they have been often tested against critical experiments and are sufficiently accurate for most calculations (see refs. 5 to 9). Ways of estimating unknown cross-sections from basic data or from cross-sections of other materials are described in ref. 10.

The neutron flux in heterogeneous assemblies is usually strongly space dependent and this fact complicates the calculation of resonance absorption in nuclear reactors.

It is usually possible to simplify the problem assuming a cell structure of the core, in which two regions are defined—a moderator and a fuel region. The fuel region consists in general of a mixture of resonance absorber and moderator and may have a complicated geometry (it does not need to be a single isolated body, but it may consist of a cluster of pins embedded in the moderator region, etc.). It is useful to use in this case the collision probability form of the transport equation

The index 0 refers to the fuel region, 1 to the moderator regions. P0 and P, are the escape probabilities from region 0 and 1: probability that a neutron originating in the region considered has its next collision outside of this region.

The terms P0 and Pi are in general functions of the neutron energy, and of the flux distribution in the regions considered.

The other quantities are:

Vo Vi volumes of fuel and moderator regions,

2to total cross-section of fuel region,

2s0 scattering cross-section of absorber,

2smo scattering cross-section of moderator in the fuel region 2*i scattering cross-section of moderator in the moderator region.

In practice the flat flux approximation is made for calculating the escape probabilities Pо and Pi for each region.

This assumption is made in most resonance-absorption calculations and works well.

Pо and Pi are related by the reciprocity relation (see ref. 3, p. 112):

2*i ViP, = 2t„ V0Po. Using this relation we can eliminate Pi and obtain

(7.13)

Another assumption which is ordinarily made is that of 1 IE asymptotic flux in the moderator region. Equation (7.10) becomes then

7.2. Narrow resonance approximation for heterogeneous assemblies

As in the homogeneous case a 1 IE flux is substituted in the integrals at the right-hand side of eqn. (7.13) obtaining

2,„4>o = (1 — Po) Xs0+^sm0 + Po 2,0

Using this approximation it is possible to express the resonance integral as the sum of a volume and a surface component / = /„+/* (see ref. 4) but this formulation is now seldom used.

Uranium ore contains approximately 0.15% equivalent of U308. This is processed and concentrated in a mill situated near the mine. After precipitation in the form of sodium diuranate or magnesium diuranate the product, because of its appearance, is called “yellow cake”. In order to be enriched uranium has then to be converted in UF6 which is a gaseous product. The natural uranium which contains 0.71% 235U is then enriched to 93% for use in HTRs with Th cycle, or to 5-8% for use in HTRs with low enriched U cycle.

Fuel fabrication takes place over a period of several months before loading into the reactor. The in-core residence time may vary between 3 to 6 years; after a cooling period the spent fuel is then shipped to a reprocessing plant where the fissile materials are separated from the other isotopes.

A typical fuel cycle scheme is shown in Fig. 10.1.<M) Figure 10.2<l4) shows the time sequence of a typical fuel segment. The name fuel segment is given to a fraction of the core which is loaded and discharged together (sometimes the term batch is used to indicate a segment).