Transcript The eighth lecture

Neutrons (Basic Concepts)
Neutrons (Basic Concepts)
It is desirable to classify neutrons 
according to their kinetic energy into:
(1) Slow Neutrons

Slow neutrons are that with energies from zero
to about 1000 eV. The most important kinds of
slow neutrons are (i) cold neutrons that 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.
(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.
(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.
(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.
(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)
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 of the absorbing material
itself, which have gained energy as a result of neutron
collisions.
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.


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.
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 moderated or 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.

If the energy of the fast neutron is sufficiently
high, inelastic scattering 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.
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.
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).
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
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.
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.



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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.

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


i (m )  N (nuclei/ m )[ i (m )]
1
3
2

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

I (t )  I (0)ett

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