The eighth lecture

1. Neutrons (Basic Concepts) The eighth lecture

2. Neutrons (Basic Concepts) • It is desirable to classify neutrons according to their kinetic energy into:

3. (1) Slow Neutrons • Slow neutrons are that with energies from zero to about 1000 eV. The most important kinds of slow neutrons are (i) coldneutronsthat have average energy less than thermal neutrons.,(ii) thermal neutrons that can be obtained by slowing down the fast neutrons until the average energy of the neutrons is equal to the average thermal energy of the atoms around them.,(iii) epithermal neutrons that have velocities exceed any permitted by a Maxwell distribution for the temperature of the moderator., and (iv) resonance neutrons that have energies corresponding to the resonance absorption of the nuclei to the neutrons with energies ranging from 1 to 100 eV.

4. (2) Intermediate Neutrons • Intermediate neutrons having energies in the range 1000 eV-0.5 MeV and are obtained by the deceleration of fast neutrons. We haven't enough information about intermediate neutrons than about slow neutrons due to the difficulty of finding efficient detectors. In this energy range elastic scattering process is dominant.

5. (3) Fast Neutrons • Neutrons with energies having range between 0.5 and 10 MeV are called fast neutrons. This energy region range gives the possibility of many nuclear reactions which are energetically impossible at lower ranges of which the inelastic scattering is dominant.

6. (4) Very Fast Neutrons • These are neutrons having energies in the range 10-50 MeV and is distinguished from the proceeding by the appearance of nuclear reactions involving the emission of more than one product such as the (n, 2n) reaction.

7. (5) Ultra Fast Neutrons • Neutrons with energies beyond 50 MeV are called ultra high neutrons. They are produced by p-n interactions induced in nuclei by high energy protons. The cosmic radiation is also a source of neutrons with energies well above those which are likely to be produced by accelerations. (43)

8. Interactions of Neutrons • In common with gamma rays, neutrons carry no charge and therefore cannot interact in matter by means of the Coulomb force. Neutrons can also travel through many centimeters of matter without any type of interaction and thus can be totally invisible to a detector of common size. As a result of the interaction of the neutron with the nucleus of the absorbing material, it may either totally disappear and be replaced by one or more secondary radiations, or else the energy or direction of the neutron is changed significantly. • In contrast to gamma rays, the secondary radiations resulting from neutron interaction are almost heavy charged particles. These particles may be produced either as a result of neutron-induced nuclear reactions or they may be the nuclei ofthe absorbing material itself, which have gained energy as a result of neutron collisions.

9. Slow Neutron Interactions • For slow neutrons, the significant interactions include elastic scattering with the absorber nuclei and a large set of neutron induced nuclear reactions. Because of the small kinetic energy of slow neutrons, very little energy can be transferred to the nucleus in elastic scattering. Consequently, this is not an interaction on which detectors of slow neutrons can be based. • Elastic collisions tend to be very probable, however, and often serve to bring the slow neutron into thermal equilibrium with the absorber medium before a different type of interaction takes place. Much of the population in the slow neutron energy range will therefore be found among these thermal neutrons, which, at room temperature, have an average energy of about 0.025 eV.As the result of the elastic scattering, the nucleus remains in the same state and the neutron retains its initial kinetic energy in the center of mass system.

10. The slow neutron interactions of real importance are neutron-induced reactions that can create secondary radiations of sufficient energy to be detected directly. Because the incoming neutron energy is so low, all such reactions must have a positive Q-value to be energetically possible. In most materials, the radiative capture; reaction [or (n,γ) reaction] is the most probable and plays an important role in the attenuation or shielding of neu­trons. • Radiative capture reactions can be useful in the indirect detection of neutrons using activation foils, but they are not widely applied in active neu­tron detectors because the secondary radiation takes the form of gamma rays, which are also difficult to detect. Instead, reactions such as (n,), (n,p), and (n,fission) are much more attractive because the secondary radiations are charged particles.

11. Fast Neutron Interactions • The probability of most neutron-induced reactions potentially useful in detectors decreases rapidly with increasing neutron energy. The importance of scattering becomes greater, however, because the neutron can transfer an appreciable amount of energy in one collision. These secondary radiations, in this case, are recoil nuclei which have picked up a detectable amount of energy from neutron collisions. At each scattering site the neutron loses energy and is thereby moderatedor slowed to lower energy. The most efficient moderator is hydrogen because the neutron can lose up to all of its energy in a single collision with a hydrogen nucleus. For heavier nuclei, only a partial energy transfer is possible.

12. If the energy of the fast neutron is sufficiently high, inelasticscattering with nuclei can take place in which the recoil nucleus is elevated to one of its excited states during the col­lision. The nucleus quickly de-excites, emitting a gamma ray, and the neutron loses a greater fraction of its energy than it would in an equivalent elastic collision. Inelastic scattering and the subsequent secondary gamma rays play an important role in the shielding of high-energy neutrons but are an unwanted complication in the response of most fast neutron detectors based on elastic scattering.

13. According to the collision type: • The way in which neutrons interact with matter depends to a large extent on their energies, which can range from hundreds of MeV down to fractions of an eV. Neutrons are uncharged particles and do not interact with atomic electrons in the matter through which are passing, but they do interact with the nuclei of these atoms. The nuclear force , which leads to these interactions, is very short ranged which means the neutrons have to pass close to a nucleus for an interaction to take place. Because of the small size of the nucleus in relation to the atom as a whole, the neutrons will have a low probability of interaction, and could thus travel consider- able distances in matter. • The interactions of neutrons with nuclei are divided into two categories: scattering (elastic and inelastic) and absorption.

14. Elastic Scattering: • This is analogous to a billiard ball type of collision. The neutron collides with a nucleus and rebounds in a different direction. The energy lost by the neutron is gained by the target nucleus which moves away at an increased speed (recoil nucleus). If the neutron collides with a massive nucleus it rebounds with almost the same speed and loses very little energy. On the other hand, light nuclei will gain a lot of energy from such a collision and will therefore be more effective for slowing down neutrons. Elastic scattering, illustrated in figure 1.5, is not effective in slowing down neutrons with very high energy (above 150 MeV).

15. Inelastic Scattering: • Neutron may strike a nucleus and form a compound nucleus instead of bouncing off as in elastic scattering. This nucleus is unstable and emits a neutron of lower energy together with a gamma photon which takes up the remaining energy. This process, called inelastic scattering, is most effective at high neutron energies in heavy materials, but at lower energies (few MeV) elastic scattering becomes a more important reaction for energy loss provided that there are light nuclei present. An illustration is shown in Figure

16. Absorption • In this type of interaction, the neutron disappears, but one or more other particles appear after the reaction takes place. This may lead to transmutation, radiative capture or fission. • Transmutation, when neutrons strike a nucleus and form a compound nucleus which then ejects a different particle, a transmutation is said to have occurred. This is because the target nucleus is changed from one element to another. • Radiative capture, this is one of the most common neutron reactions. The neutron is again captured by a nucleus   which emits only a gamma photon. This reaction, which occurs in most materials, is the most important one for neutrons with very low energy. The product nuclei are usually radioactive and are beta and gamma emitters. • Fission, in which a heavy nucleus splits into two heavy fragments with release of more than one neutron.

17. Neutron Reaction Cross Sections • Consider a monoenergetic parallel beam of neutron hitting a thin target of thickness t. The number of reactions per second, R, taking place in this target may be written as • R (reactions/s) = (neutrons per m2 /s hitting the target) x (targets exposed to the beam) x (probability of interactions per n/m2 per nucleus) • or • R = I [n / (m2 s)] [N (nuclei / m3)] [a (m2)] [t (m)] [σ (m2)] • Where I, a, and t are the intensity, cross section, thickness respectively (figure 1.7). The parameter σ, called the cross section, has the following physical meaning: • σ (m2) = Probability that an interaction will occur per target nucleus per neutron per m2 hitting the target. • The unit of σ is the barn (b) • 1b = 10-24 cm2 = 10-28 m2 • Since the nuclear radius is approximately 10-15 to 10-14 m, 1b is approximately equal to the cross-sectional area of a nucleus.

19. Neutron cross sections are defined separately for each type of reaction. For example, if • σs = elastic scattering cross section • σi = inelastic scattering cross section • σa = absorption cross section • σγ = capture cross section • σf = fission cross section • Then the total cross section, - i.e., the total probability that a reaction of any type will take place – is equal to the sum of all's σ 's: • σtot = σs+ σi + σγ + σf+ …. • In this notation used here, σa = σγ + σf . • Neutron cross sections depend strongly on the energy of the neutron as well as on the atomic weight and atomic number of target nucleus.

20. The cross section σ(b) is called the microscopic cross section. Another form of cross section is the macroscopic cross section, defined by the equation • and having the following physical meaning: • Σi = probability that an interaction of type i will take place per unit distance of travel, of a neutron moving in a medium that has N nuclei /m3. • If a parallel beam of monoenergetic neutrons with intensity I(0) impinges upon a material of thickness t, the number of neutrons that emerges without having interacted in the material is • Where Σt = Σs +Σi+Σa + …. = total macroscopic neutron cross section. • It is worth to mention that the scattering cross section is high for fast neutrons with light nuclei. So, such nuclei are used as moderating material in nuclear reactors to slow down the neutrons emitted in fission