observed.

Some of these reactions are:

These reactions induced by g-rays are also known as photodisintegrations or

photonuclear reactions.
Nuclear Decay and Nuclear Reactions
Dominant differences between nuclear decay (Chapter 3) and nuclear
reactions are shown in Table 4.1
TABLE 4.1 Difference between nuclear decay and nuclear reactions
Nuclear decay Nuclear reaction
It is a spontaneous process (i.e. no external aid is It is not a spontaneous process (i.e. external aid is needed to start a
needed) reaction)

Only a-, b- and g-emissions are possible In nuclear reactions all possible particles like p, n, 2H, 3He, 4He, 6Li,
etc. can be emitted
Mass of the daughter nucleus either remains
Mass of the product nucleus can also increase
same or decreases
Energy of the emitted particles or g-rays is
Energy of the emitted particles or g-rays can be very high
generally low

4.3 NUCLEAR REACTION CROSS-

SECTION
A question often arises that when some projectiles are bombarded on a target, an
interaction or reaction between these two takes place, then how many nuclei are
taking part in this reaction? Is this number small or large? Depending upon the
numbers, the probability of a particular reaction becomes small or large. There
must be a quantitative measure of this probability. This quantity should be easily
measurable and also theoretically calculable, so that we can compare the
experimental results with the theoretical calculations.
The quantity, which defines the probability of a given reaction, is called the
nuclear reaction cross-section and it is denoted as s.
The reaction cross-section can be visualized as an effective area around the
nucleus such that if the incident particles cross that area, a nuclear reaction takes
place, otherwise not. This area is also known as effective area. It is not exactly
same as the geometrical area (pr2), where r is the radius of the nucleus. This
effective area could be larger, smaller or equal to the geometrical area of the
nucleus. Thus, nuclear cross-section is a measure of the probability that
bombarding particles at a particular energy would interact with the target.

4.3.1 Measurement of Cross-Section

Consider a beam of particles of flux I (number of particles passing a unit area
per unit time) incident on a thin sheet of a material having thickness dx and face
area A as shown in Figure 4.1. Further assume that thickness is so small that
none of the nuclei of the thin sheet overlap each other. Thus, each nucleus has an
equal probability to cause a nuclear reaction with the incident beam. Let s be the
effective area of the target nucleus. As stated earlier, this area is such that when
the incident particle crosses this area the reaction always takes place. Let n be
the number of target nuclei per cc in this thin sheet.
Number of nuclei in the sheet per unit face area = n dx Total number of nuclei
in the sheet = A n dx Since each nucleus has an effective area s, so the total
effective area available for the reaction = A n s dx

Figure 4.1 A beam of particles incident on a thin foil of face area A and thickness dx.

When a projectile takes part in a nuclear reaction, it is absorbed by the target

nucleus, so the flux of incident particles decreases. If the fractional effective area
(f) is large, then the corresponding decrease in the flux (I) is large and vice versa.
Thus, the change in the intensity dI is given by dI = –fI substituting for f dI =
–Isndx or
–ve sign has been introduced because as dx increases the flux I decreases.
Assuming that at x = 0, I = I0, integrating equation with respect to x, we get
Thus, the flux of the incident beam exponentially decreases as the thickness of
the sheet increases.

4.3.2 Units of Cross-Section

Units of reaction cross-sections are the units of area. These cross-sections are
normally very small ~10–27 to 10–28 m2. Since this value is small so it is
convenient to use a unit called barn.

4.3.3 Different Types of Cross—Sections In nuclear reactions we come across

different types of reaction cross-sections. They are:

1. Partial reaction cross-section.

2. Total reaction cross-section.
3. Differential reaction cross-section.

Partial Reaction Cross—Section For a given energy and target projectile

combination, several nuclear reactions such as elastic scattering, inelastic
scattering, capture reaction, disintegration reactions, etc. are possible
simultaneously. There is a definite reaction cross-section for each such reaction
denoted by s1, s2, s3 ,…, etc. These cross-sections are known as partial reaction
cross-sections.
Total Reaction Cross—Section As stated earlier, for a given energy and target
projectile combination, many partial cross-sections may exist simultaneously.
Sum of all such partial cross-sections is known as total reaction cross-section s.
s = s1 + s2 + s3 + …
Differential Reaction Cross—Section When the incoming particles interact with
the target nuclei nuclear reaction or scattering takes place. Very often the
outgoing particles have an anisotropic distribution. This means that the number
of outgoing particles at different angles will be different. Also in most of the
cases, the energy of the outgoing particles may be different at different angles.
We measure the number of outgoing particles per second into a solid angle d
making an angle q with the incident direction. For measuring this quantity,
another type of cross-section is introduced. This cross-section depends upon the
angle and is called differential cross-section. This cross-section is defined as the
cross-section per unit solid angle and is denoted by s(q, f).

4.4 CONSERVATION LAWS IN NUCLEAR

REACTIONS
In nuclear reactions certain physical quantities never change during and after the
reaction. We say that these quantities are always conserved in nuclear reactions.
Some of the conservation laws are as under.
4.4.1 Conservation of Mass-Energy In a nuclear reaction total energy of
reactants (rest mass plus kinetic energy for a non-relativistic case) is always
equal to the total energy of the products (rest mass plus kinetic energy). Consider
a reaction a + X Y + b If Ka, Kb and KY are kinetic energies of a, b and Y
respectively, then

assuming target nucleus X is at rest initially. However, for relativistic case, we

have Ea + mXc2 = EY + Eb where

where i = a, y or b 4.4.2 Conservation of Linear Momentum In a nuclear reaction