NUCLEAR PHYSICS

Introduction to Nuclear Physics

We have learnt that all matter, right from a tiny speck of dust to a gigantic cosmic entity consists of atoms. Does an atom have a structure? An atom consists of a central part called nucleus around which electrons will revolve. Another question comes to our mind is that whether a nucleus too have a structure like an atom? If so, what is the nature of its constituents and how are they held together in the nucleus? In unfolding such series of questions, a separate branch in physics called Nuclear physics has evolved.

The year 1896, marks the beginning of nuclear physics. It is in this year, the French physicist Henri Becquerel discovered the phenomenon of radioactivity in one of the Uranium compounds, quite accidentally. The phenomenon of radioactivity refers to a particular type of invisible radiation emerging from certain specific substances. At first sight, this radiation was quite puzzling for scientists. Later on the experiments conducted by Ernst Rutherford and others proved that this radiation consists of alpha, beta and gamma rays. These rays were found to be originating in the nucleus. The experiments conducted by Geiger and Ernst Marsden, at the suggestion of Rutherford in 1911, involving the scattering of alpha particles have revealed that there exists a positively charged nucleus at the centre of each atom. It was James Chadwick’s discovery of neutron in 1932 that clinched the issue of nuclear structure. Soon after the discovery of neutron Werner Heisenberg proposed that the nucleus consists of neutrons and protons. The discovery of artificial radioactivity in 1933 and nuclear fission in 1938, development of first controlled fission reactor in 1942 are some of the important milestones in the field of nuclear physics. More recently, the scientists are focusing on the nature of nuclear forces and are trying to integrate electroweak force (which resulted after integrating electromagnetic force and weak nuclear force), strong nuclear force and gravitational force.

What Is an Atomic Nucleus

The atomic nucleus is the small, dense, positively charged central region of an atom, around which the electrons are distributed. It contains almost the entire mass of the atom and occupies only a very small region at the centre of the atom.

The nucleus is held together by strong forces and plays a fundamental role in determining the identity and many important properties of an atom.

Composition of Nucleus

An atomic nucleus is composed of elementary particles called protons and neutrons. These two particles are collectively called nucleons. The protons are positively charged particles and neutrons are electrically neutral. The charge of proton being positive and equal to the charge of electron (-e) in magnitude can be represented as (+e). The mass of the neutron is slightly more than that of the proton.

Atomic Number

The number of protons in the nucleus is called atomic number (Z).

Mass Number

The total number of protons and neutrons is called mass number (A).

Neutron Number

Hence, (A – Z) gives the number of neutrons and is called neutron number (N).

If X is the chemical symbol of an element, then it is represented by ^A_ZX.

Isotopes

The nuclei having the same atomic number (Z), but different mass numbers (A) are called isotopes. They have same proton number e.g., ¹₁H, ²₁H, ³₁H are the isotopes of hydrogen. ¹⁶₈O, ¹⁷₈O, ¹⁸₈O are the isotopes of oxygen.

Isotones

The nuclei having the same neutron number (N) but different atomic numbers (Z) are called isotones. e.g., ¹⁹⁸₈₀Hg, ¹⁹⁷₇₉Au; ⁴⁰₂₀Ca, ³⁹₁₉K.

Isobars

The nuclei having the same mass number (A), but different atomic numbers (Z) are called isobars. They have same nucleon number e.g., ¹⁴₆C, ¹⁴₇N; ⁷⁶₃₂Ge, ⁷⁶₃₄Se.

Isomers

Nuclei having the same atomic number (Z) and mass number (A) but with different nuclear properties such as radioactive decay and magnetic moment are called isomers.

e.g., ⁸⁰₃₅Br^m, ⁸⁰₃₅Br^g. Here m denotes meta stable state and g denotes ground state.

The mass of the nucleus itself constitutes almost all the mass of the atom because the mass of electron is quite negligible when compared to either of the nucleons-proton or neutron. The mass of a proton is about 1836 times the mass of the electron whereas the neutron is slightly massive than proton and its mass is about 1839 times the mass of electron.

Atomic Mass Unit

Mass is generally expressed in kilogram. The mass of elementary particles may also be expressed in atomic mass units denoted by amu or simply u called unified atomic mass unit. One atomic mass unit is defined as ¹⁄₁₂ mass of ¹²₆C, an isotope of carbon atom. The exact value for the mass of ¹²₆C atom in atomic mass unit is 12 amu.

1 amu = 1u = 1.660565 × 10^-27 kg.

In nuclear physics the mass is also expressed as million electron volt/(speed of the light)² or simply MeV/c².

1u = 931.5 MeV/c²* and the energy equivalent of 1u is 931.5 MeV.

Masses of Elementary Particles

The masses of electron, proton and neutron in terms of various units are:

Mass of the electron = m_e = 9.1095 × 10^-31 kg = 0.000549 u = 0.511 MeV/c².

Mass of the proton = m_p = 1.6726 × 10^-27 kg = 1.007276 u = 938.28 MeV/c².

Mass of the neutron = m_n = 1.6750 × 10^-27 kg = 1.008665 u = 939.573 MeV/c².

Size of the Nucleus

The nucleus is not a solid object like a hard ball. Its surface has no clear boundary. However it is assumed that the nucleus is spherical, and hence its size can be expressed in terms of its radius (R).

A rough estimation of the size of the nucleus was obtained in Rutherford’s α scattering experiment. The radius of the nucleus is found to be of the order of 10^-15 m, whereas the atomic radius is of the order of 10^-10 m. Thus the size of the nucleus of an atom is very much smaller than the size of the atom.

The volume of the nucleus (V) is found to be proportional to its mass number (A). If R is the radius of nucleus having mass number A, we can write:

Therefore,

where R₀ is constant of proportionality and is same for all the nuclei. Its value is 1.4 × 10^-15 m.

Nuclear distances are measured in the units of “fermi” or simply fm (1 fermi = 1 fm = 10^-15 m). Hence the average size of a nucleus is of the order of 10^-15 m or fermi.

Mass Defect and Binding Energy

Mass Defect

The difference between the total mass of all the nucleons of the nucleus and the actual mass of a nucleus is called mass defect. It is denoted by Δm.

Here, Δm is the mass defect, Z is the atomic number, A is the mass number, m_p is the mass of a proton, m_n is the mass of a neutron, and M is the actual mass of the nucleus.

We know that the nucleus consists of protons and neutrons. Naturally, one expects that the mass of the nucleus of a particular element would be equal to the sum of the masses of protons and neutrons inside the nucleus. However, the measurements using mass spectrometer have revealed that the mass of a nucleus is always found to be less than the sum of the masses of separate protons and neutrons present in it.

This decrease in mass results as the nucleons combine to form a nucleus. The difference between the total mass of the individual nucleons and the actual mass of the nucleus is therefore called mass defect.

Binding Energy

Binding energy is the energy released when protons and neutrons combine to form a nucleus. It can also be defined as the energy required to break the nucleus into its constituent protons and neutrons. It is denoted by ΔE.

Here, ΔE is the binding energy, Δm is the mass defect, and c is the speed of light in vacuum.

According to Einstein’s mass-energy relation, the energy equivalent to the mass defect is released when the nucleons combine to form a nucleus. This energy is known as binding energy.

The binding energy can also be expressed in mega electron volts (MeV). Since 1 atomic mass unit (u) is equivalent to 931.5 MeV/c², the binding energy can be calculated as:

Thus, the greater the mass defect, the greater is the binding energy of the nucleus.

Relation Between Mass Defect and Binding Energy

If A and Z are the mass number and atomic number of an element, and m_e, m_p, m_n, m_N and m_a are the masses of electron, proton, neutron, nucleus and atom of the element expressed in u respectively, then the mass defect is given by:

To express the mass defect in terms of the mass of the atom (m_a) instead of the mass of the nucleus (m_N), we add and subtract Zm_e to the right-hand side of equation (1).

Here, m_H is the mass of a hydrogen atom. The relations used above are m_H = m_p + m_e and m_a = m_N + Zm_e.

Binding Energy–Mass Defect Relation

According to Einstein’s mass-energy relation, the energy equivalent of the mass defect is given by:

Since 1u × c² = 931.5 MeV, equation (3) gives the binding energy directly in MeV when the mass defect is expressed in atomic mass units.

The above expression represents the relation between mass defect and binding energy.

In terms of the mass of the atom (m_a), the binding energy can be written as:

Binding Energy Per Nucleon

Nuclear binding energy is an indication of the stability of the nucleus. However, in comparing the stability of any two nuclei, we must consider the fact that they have different numbers of nucleons. For this reason, it is more meaningful to use the nuclear binding energy per nucleon.

If ΔE is the total binding energy of a nucleus of mass number A, then:

The following graph depicts how the binding energy per nucleon varies with the mass number A.

It can be observed from the graph that the binding energy per nucleon is highest in the range 28 < A < 138. The binding energy of these nuclei is very close to 8.7 MeV. With further increase in the mass number, the binding energy per nucleon decreases and consequently for the heavy nuclei like uranium it is 7.6 MeV.

In the region of smaller mass numbers, the binding energy per nucleon curve shows the characteristic minima and maxima. Minima are associated with nuclei containing an odd number of protons and neutrons such as ⁶₃Li, ¹⁰₅B and ¹⁴₇N, and the maxima are associated with nuclei having an even number of protons and neutrons such as ⁴₂He, ¹²₆C and ¹⁶₈O.

Let us consider the nuclei of uranium, helium and iron as examples so as to explain the relationship between binding energy per nucleon and stability of the nuclei. Uranium has a relatively low binding energy per nucleon as 7.6 MeV. Hence to attain greater stability uranium breaks up into intermediate mass nuclei resulting in a phenomenon called fission.

On the other hand light nuclei such as hydrogen combine to form heavy nucleus to form helium for greater stability, resulting in a phenomenon called fusion.

Iron whose binding energy per nucleon stands maximum at 8.7 MeV is the most stable and will undergo neither fission nor fusion.

Natural Radioactivity

The spontaneous disintegration of the nuclei of certain elements by emitting alpha (α), beta (β) and gamma (γ) rays is called natural radioactivity.

The emission of these rays takes place because of the instability of the nucleus. In the process of emitting these rays, a nucleus tries to attain greater stability.

In general, natural radioactivity is displayed by heavy nuclei, beyond lead in the periodic table. There are also naturally radioactive light nuclei, such as potassium isotope ⁴⁰₁₉K, the carbon isotope ¹⁴₆C and the rubidium isotope ⁸⁷₃₇Rb, to name a few.

The three kinds of rays produced by naturally radioactive substances are α-rays, β-rays and γ-rays. The decay of a radioactive nucleus is characterised by decay constant (λ) and half-life (T).

Alpha Radiation and α-Decay

When a nucleus disintegrates by radiating α-rays, it is said to undergo α-decay.

Experimental evidence shows that α-rays are nothing but a stream of helium nuclei. Thus, when a nucleus emits an alpha particle, its atomic number Z decreases by two units and its mass number A decreases by four units. The resultant nucleus therefore corresponds to a different element.

The original nucleus is called the parent nucleus and the resultant nucleus after disintegration is called the daughter nucleus.

Example for α-Decay

In the above α-decay, uranium-238 emits an alpha particle, which is a helium nucleus, and changes into thorium-234.

Both electric charge and nucleon number are conserved in the process of α-decay.

General Form of α-Decay

The general form of α-decay can be written as:

Here, P represents the parent nucleus and D represents the daughter nucleus. During α-decay, the mass number decreases by 4 and the atomic number decreases by 2.

Properties of Alpha Rays

1. α-rays are a stream of particles, each of which consists of two protons and two neutrons. It is identical to a doubly ionised helium atom. In other words, it is nothing but a helium nucleus.

2. A beam of α-particles can be deflected by an electric field as well as a magnetic field.

3. The speed of α-particles is of the order of 10⁶ m/s.

4. α-particles produce intense ionisation of the medium through which they pass.

5. α-particles can penetrate only small distances in matter and can be stopped after travelling a few centimetres in air. Due to their large mass, the penetrating power of α-particles is lower than that of β-rays and γ-rays.

6. α-particles produce scintillations when they strike certain fluorescent materials such as zinc sulphide.

7. α-particles affect photographic plates.

8. α-particles carry a positive charge of +2e, where e is the magnitude of the charge of an electron.

Beta Radiation and β-Decay

When a nucleus disintegrates by radiating β-rays, it is said to undergo β-decay.

β-particles are nothing but electrons. Hence, when a nucleus emits a β-particle, the atomic number of the nucleus increases by one unit, but the mass number does not change.

Example for β-Decay

General Form of β-Decay

The general form of β-decay can be written as:

Here, P represents the parent nucleus and D represents the daughter nucleus. During β-decay, the mass number remains unchanged, while the atomic number increases by one.

Both electric charge and nucleon number are conserved in β-decay also.

Properties of Beta Rays

1. β-rays are a stream of electrons. They originate in the nucleus.

2. β-particles are deflected by electric as well as magnetic fields.

3. The speed of β-particles is of the order of ¹⁄₁₀ of the speed of light.

4. β-particles ionise the medium through which they pass, but their ionising power is only ¹⁄₁₀₀ of α-particles.

5. β-particles penetrate through matter. The penetrating power of β-particles is 100 times greater than that of α-rays but 100 times less than that of γ-rays.

6. β-rays produce scintillations in fluorescent materials, but these scintillations are weak.

7. β-rays affect photographic plates.

Gamma Radiation and γ-Decay

Gamma radiation is a form of electromagnetic radiation emitted by an excited atomic nucleus when it changes from a higher energy state to a lower energy state.

When a nucleus disintegrates by radiating γ-rays, it is said to undergo γ-decay. Gamma rays are electromagnetic radiations of extremely short wavelength and very high frequency. Their wavelength is generally less than about 10⁻¹⁰ m.

Unlike α-decay and β-decay, the emission of γ-rays does not change either the atomic number Z or the mass number A of the nucleus. It only results in a decrease in the energy of the nucleus.

A nucleus may be left in an excited state after undergoing α-decay or β-decay. Such an excited nucleus eventually returns to a lower energy state or to its ground state by emitting one or more γ-ray photons. Thus, γ-radiation is often associated with α-decay and β-decay.

If an excited nucleus is represented by ^A_ZX^*, its transition to a lower energy state can be represented as

^A_ZX^*  →  ^A_ZX  +  γ

Here, γ represents the emitted gamma-ray photon. Since the values of A and Z remain unchanged, the nucleus remains the same element after γ-emission; only its energy state changes.

Gamma rays have no electric charge and no rest mass. Therefore, they are not deflected by electric or magnetic fields. They travel through vacuum with the speed of light.

Gamma rays have very high penetrating power because they interact relatively weakly with matter. However, they can interact with matter through processes such as the photoelectric effect, Compton scattering and pair production.

The energy of a gamma-ray photon is related to its frequency and wavelength by

E = hν = hc/λ

where E is the energy of the photon, h is Planck’s constant, ν is its frequency, c is the speed of light and λ is its wavelength.

Properties of Gamma Rays

1. γ-rays are electromagnetic radiations of wavelengths less than 1 Å.

2. γ-rays are not deflected either by electric or magnetic fields because they do not possess any electric charge.

3. γ-rays travel with the speed of light in vacuum, approximately 3 × 10⁸ m/s.

4. The ionising power of γ-radiations is small when compared to α- and β-rays.

5. The penetrating power of γ-rays is the largest when compared to α- and β-rays.

6. γ-rays also produce scintillations when they strike suitable fluorescent materials.

7. γ-rays affect photographic plates more than α- or β-particles.

8. γ-rays have no rest mass and carry no electric charge because they consist of electromagnetic radiation.

9. In a uniform medium, γ-rays travel in straight-line paths and are not bent by electric or magnetic fields.

10. When γ-rays pass through matter, they interact with atoms mainly through processes such as the photoelectric effect, Compton scattering and pair production.

Law of Radioactive Decay

The radioactive decay law states that the number of radioactive nuclei in a radioactive sample decreases exponentially with time.

A macroscopic sample of any radioactive isotope consists of a vast number of radioactive nuclei. These nuclei do not decay all at a time. Rather, they decay one by one over a period of time. This decay is a random and statistical process, i.e., each and every nucleus has an equal chance of disintegration at any time. We cannot predict exactly which nucleus in a sample will decay, but we can determine statistically how many nuclei in a sample will decay over a period of time.

Consider a sample of radioactive substance. Let the number of radioactive nuclei present in the sample initially at t = 0 be N₀, and let N radioactive nuclei remain at an instant t.

The rate of radioactive decay,

\[ -\frac{dN}{dt} \]

that is, the number of nuclei decaying per unit time at any instant, is directly proportional to the number of nuclei N present at that instant and is independent of external physical conditions such as temperature, pressure, etc.

\[ -\frac{dN}{dt}\propto N \tag{1} \]

\[ dN=-\lambda N\,dt \tag{2} \]

Here, \(\lambda\) is the proportionality constant and is called the decay constant or disintegration constant. The negative sign indicates the decrease in the number of radioactive nuclei as time passes.

Derivation of the Radioactive Decay Law

From Equation (2), we can write

\[ \frac{dN}{N}=-\lambda\,dt \tag{3} \]

Integrating both sides,

\[ \int\frac{dN}{N}=-\lambda\int dt \tag{4} \]

\[ \ln N=-\lambda t+C \tag{5} \]

Here, C is the integration constant.

At t = 0, N = N₀. Substituting these values into Equation (5), we get

\[ \ln N_0=C \tag{6} \]

Therefore,

\[ \ln N=-\lambda t+\ln N_0 \tag{7} \]

Rearranging,

\[ \ln N-\ln N_0=-\lambda t \tag{8} \]

\[ \ln\left(\frac{N}{N_0}\right)=-\lambda t \tag{9} \]

Taking the exponential of both sides,

\[ \boxed{N=N_0e^{-\lambda t}} \tag{10} \]

This equation represents the radioactive decay law.

Activity of a Radioactive Sample

From Equation (3),

\[ -\frac{dN}{dt}=\lambda N \tag{11} \]

The absolute value of the quantity

\[ \left|-\frac{dN}{dt}\right| \]

gives the number of nuclei that decay per unit time and is called the activity of the sample.

\[ \boxed{\text{Activity of a radioactive sample}=\lambda N} \tag{12} \]

The SI unit of activity of a radioactive substance is the becquerel (Bq).

\[ 1\ \text{Bq}=1\ \text{disintegration per second} \]

Another commonly used unit of activity is the curie (Ci). The curie was originally chosen as a unit because it is approximately equal to the activity of one gram of pure radium.

\[ 1\ \text{Ci}=3.7\times10^{10}\ \text{disintegrations/s} \]

\[ 1\ \text{Ci}=3.7\times10^{10}\ \text{Bq} \]

Half Life of a Radioactive Substance

Half-life of a radioactive substance is defined as the time required for the number of radioactive nuclei of the substance to disintegrate to half of its original number of nuclei. It is denoted by T.

Radioactive disintegration is an exponential process. While a radioactive sample decays exponentially, the initial amount of the sample will take infinite time to decay completely. Hence, half-life is a convenient measure of the time required for the number of radioactive nuclei in a sample to reduce to half of its initial value.

The half-life gives an idea about the life of a radioactive sample and the relative amount of the radioactive substance present after a given time compared with its original amount.

If the initial number of radioactive nuclei present in a sample is N₀, then after one half-life T, only N₀/2 nuclei remain. After two half-lives, only N₀/4 nuclei remain, and after three half-lives, only N₀/8 nuclei remain.

It can be noticed that the number of radioactive nuclei present at t = 0 is N₀. After time T, only N₀/2 nuclei are left. After time 2T, only N₀/4 remain, and after time 3T, only N₀/8 remain.

Thus, after every half-life, the number of radioactive nuclei present becomes half of the number present at the beginning of that interval. As the decay continues, the number of radioactive nuclei approaches zero, but the sample does not become completely zero in any finite time.

Relation Between Half-Life and Decay Constant

From the radioactive decay law, the number of radioactive nuclei remaining after time t is given by

N = N₀e^−λt

At the end of one half-life, t = T and the number of radioactive nuclei remaining is N = N₀/2. Therefore,

N₀/2 = N₀e^−λT

1/2 = e^−λT

2 = e^λT

λT = ln 2

T = ln 2 / λ

T = 2.303 log₁₀ 2 / λ

T = 0.693 / λ

Therefore, the half-life of a radioactive substance is inversely proportional to its decay constant.

The half-life T depends only on the decay constant λ of the radioactive substance.

Different radioactive substances have different values of the decay constant λ. Therefore, the half-lives of different radioactive substances vary considerably.

Examples of Half-Life

For example, uranium-238 ²³⁸₉₂U has a half-life of approximately 4.47 × 10⁹ years, whereas krypton-89 ⁸⁹₃₆Kr has a half-life of approximately 3.16 minutes.

The large difference in half-lives shows that different radioactive substances decay at very different rates, depending on their respective decay constants.

Average Life of a Radioactive Substance

Average life of a radioactive substance is the average time for which the radioactive nuclei initially present in a sample survive before disintegrating. It is equal to the total lifetime of all the initially present radioactive nuclei divided by their total number, and is denoted by τ (tau).

The time measure of radioactive disintegration can also be described in terms of average life. Let N₀ be the number of radioactive nuclei present at t = 0 in a radioactive sample.

Consider a small number of radioactive nuclei, −dN, which decay between time t and t + dt. These nuclei must have survived for a time t before undergoing disintegration. Therefore, the total lifetime contributed by these nuclei is

t(−dN)

The total lifetime of all the nuclei initially present in the sample can be obtained by adding the lifetimes of all the nuclei that eventually decay. Since the sample contains N₀ radioactive nuclei at t = 0 and decays completely only as t → ∞, the total lifetime is obtained by integrating t(−dN) between the limits t = 0 and t = ∞.

Therefore, the average life τ is given by the total lifetime of all the initially present nuclei divided by the total number of original nuclei N₀.

τ = ∫₀^∞ t(−dN) N₀

Here, τ represents the average life of the radioactive substance, whereas t represents the lifetime of the nuclei that decay at time t.

Derivation of Average Life

From the radioactive decay law, the rate of disintegration is given by

− dN dt = λN

Therefore,

−dN = λNdt

From the radioactive decay law,

N = N₀e^−λt

Substituting this value of N in the relation −dN = λNdt, we get

−dN = −λN₀e^−λtdt

Since −dN represents the positive number of nuclei disintegrating during the small time interval dt, we use

−dN = λN₀e^−λtdt

Substituting this expression for −dN in the expression for average life,

τ = ∫₀^∞ tλN₀e^−λtdt N₀

Cancelling N₀, we obtain

τ = λ∫₀^∞te^−λtdt

On evaluating the integral, we get

τ = 1/λ

Thus, the reciprocal of the decay constant gives the average life of a radioactive sample.

The average life of a radioactive substance is inversely proportional to its decay constant.

Relation Between Average Life and Half-Life

We know that the relation between the half-life T and the decay constant λ is

T = 0.693/λ

Since

τ = 1/λ

Therefore, the relation between average life and half-life of a radioactive substance is

τ = T 0.693

Hence, the average life of a radioactive substance is greater than its half-life.

τ = 1.443T

Therefore, the average life and half-life are related by τ ≈ 1.443T.

Nuclear Forces

The force that holds the nucleons together in the nucleus is called the nuclear force.

The nucleus consists of positively charged protons and electrically neutral neutrons, collectively called nucleons. These nucleons are confined within an extremely small region of space, with the radius of a nucleus being of the order of 10⁻¹⁵ m.

Since protons are positively charged, they repel one another due to the electrostatic force. However, the protons and neutrons remain bound together inside the nucleus. Therefore, there must be a strong attractive force acting between the nucleons that overcomes the electrostatic repulsion between the protons and holds the nucleus together.

Nuclear forces act between proton-proton, neutron-neutron, and proton-neutron pairs. They are extremely strong at very small distances and have a very short range. At distances comparable to the size of a nucleus, nuclear forces are much stronger than gravitational and electrostatic forces.

Nuclear force is understood as the residual strong interaction between nucleons. It is responsible for the stability and binding of atomic nuclei and plays a fundamental role in nuclear structure and nuclear reactions.

Properties of Nuclear Forces

1. Nuclear force is attractive in nature and is one of the strongest of the basic forces.

Nuclear forces are strong attractive forces that exist between proton and neutron (p-n), proton and proton (p-p), and neutron and neutron (n-n). The relative strengths of gravitational, Coulomb and nuclear forces are approximately in the ratio

F_g : F_c : F_n = 1 : 10³⁶ : 10³⁸

This shows that the nuclear force is enormously stronger than the gravitational force and is also much stronger than the electrostatic force at nuclear distances.

2. Nuclear force is a short-range force.

The nuclear force becomes significant when the separation between nucleons is of the order of 1 fm or less, where

1 fm = 10⁻¹⁵ m

The nuclear force decreases rapidly as the separation between two nucleons increases and becomes negligible when the separation is greater than about 2 fm.

At very small separations, of the order of 0.4 fm or less, the nuclear force becomes strongly repulsive. This short-range repulsive behaviour prevents the nucleons from collapsing into one another.

3. Nuclear force is independent of the electric charge of the nucleons.

It is observed that the nuclear forces acting between two protons, between two neutrons, and between a proton and a neutron are approximately the same when the electromagnetic effects are excluded.

Hence, nuclear force is essentially independent of the electric charge of the nucleons. In this respect, protons and neutrons can be regarded as equivalent particles as far as the nuclear force is concerned.

4. Nuclear force is spin dependent.

Nuclear force depends on the orientation of the spins of the interacting nucleons. The strength of the nuclear interaction can change depending on the relative orientation of their spins.

In simplified terms, the nuclear force can be stronger for certain relative spin orientations and weaker for others. This spin dependence plays an important role in determining the structure and energy levels of nuclei.

5. Nuclear force is not completely central.

A force that depends only on the magnitude of the separation between two particles is called a central force. The nuclear force between two nucleons does not depend solely on the distance between them.

It also depends on the orientation of the nuclear spins relative to the line joining the two nucleons. Therefore, the nuclear force is not completely central.

In a more detailed description, the nuclear interaction contains a tensor component, which is responsible for part of its non-central character.

6. Nuclear force has the property of saturation.

Each nucleon interacts strongly only with a limited number of its nearest neighbouring nucleons and not with all the nucleons present in the nucleus.

This property is known as saturation of nuclear force. It is one of the reasons why the average binding energy per nucleon remains approximately constant for medium and heavy nuclei.

The saturation property also explains why the nuclear density is approximately constant for nuclei of different mass numbers.

7. Nuclear force is an exchange force.

The nuclear force between two nucleons can be described in terms of the exchange of particles between them. At the nuclear scale, the residual strong interaction is effectively described through the exchange of mesons, particularly π mesons in the traditional nuclear-force picture.

The exchange-particle picture also helps explain why the nuclear force has a very short range: a massive exchange particle can mediate an interaction only over a limited distance.

In summary, nuclear forces are very strong, short-range attractive forces between nucleons. They are approximately independent of electric charge, depend on spin and the relative orientation of nucleons, are not completely central, possess saturation, and can be described as exchange interactions.