Fundamentals of Nuclear Physics

PREFACE

This textbook clears the cavity between the elementary and the highly progressive volumes that are commonly accessible on the subject. It offers a brief but widespread outline of a number of topics, like fundamental ideas and characteristics of the nucleus, fission and fusion, general relativity, and radioactivity which are otherwise only accessible with much more detail. Providing a general introduction to the underlying concepts allows individuals who read to improve their knowledge of what these two research fields actually encompass. The book uses real-world examples to make the subject more attractive and inspire the use of mathematical formulations. Anticipated essentially for students of scientific disciplines such as physics and chemistry who want to learn about the subject and/or the associated techniques, it is also useful to high school teachers wanting to rejuvenate or modernize their understanding and to fascinated non-experts. This textbook gives an elementary understanding of nuclear and particle physics, offering an overview of theoretical as well as the experimental grounds, providing students with a profound understanding of the ideas about the nucleus, particle detectors, accelerators, radioactivity, and elementary particles, fundamental forces and recent applications of radioactivity. Each chapter provides the fundamental theoretical and experimental knowledge for students to strengthen their concepts regarding nuclear physics.

It is an appropriate textbook for undergraduate courses in nuclear and particle physics as well as more innovative courses; the book includes sophisticated and newly constructed figures as well as thoroughly solved equations that create the interest amongst undergraduate students to renovate the content of their course. It could be a vital textbook for students framing their future study or a profession in the field who needs a concrete understanding of nuclear and particle physics together. It provides a concise, thorough, and accessible treatment of the fundamental aspects of nuclear physics. Reorganized figures, resolved equations, rearranged contents and appendices make it easier to use for entire users. Indeed this book is unique because it makes important connections to other fields such as elementary particle physics and astrophysics. Moreover, its presentation is student-friendly and bridges nuclear physics as an essential part of modern physics with a comprehensive scientific and historical context. We trust that it may be advantageous for graduate students, or more commonly scientists, in various fields. In the first three chapters, we present the extract, i.e., we give the basic concepts essential to improve the rest. Chapter 1 deals with the introduction to nuclei and basic concepts in nuclear physics. In chapter 2, we describe nuclear fission and fusion. Chapter 3 is dedicated to the nuclear structure and properties of nuclei. Chapter 4 goes a step further. It deals with particle detectors. We shall see that it is conceivable to give a reasonably modest but comprehensive explanation of the major development in particle physics and fundamental dealings made since the late 1960s. In chapters 5 and 6, we turn to the important practical applications of nuclear physics, i.e., particle accelerators and nuclear reactors. In chapters 7 and 8, we intend to understand the origin and applications of radioactivity with some contemporary illustrations of how radioactivity originated and was used, be it in medicine, in the food industry or in engineering. Chapters 9 and 10 are subjected to nuclear astrophysics, stellar structure and evolution and nuclear cosmology and elementary particles. To conclude, we present an introduction to present ideas about nuclear astrophysics in chapter 10.

We want to extend our sincere thanks to all our collogues who constantly provided us with ideas before initiating this project. We are obliged to our co-workers for their irreplaceable help and recommendation throughout the years. We are also grateful to all who directly or indirectly contributed to illuminating discussions on various aspects of nuclear physics.

This book has been kept on track and seen through to completion with the support and encouragement of numerous people, including our well-wishers, our friends, as well as various institutions and laboratories. At the end of this book, it is a pleasant task to express our thanks to all those who contributed in many ways to the success of this study and made it an unforgettable experience for us to write this book.

ACKNOWLEDGEMENTS

Authors express their sincere thanks to Dr. Subhash Chaudhari, Vice Chancellor , Rashtrasant Tukadoji Maharaj Nagpur University, MH, India for his kind co-operation and we owe a great deal of appreciation and gratitude towards Dr.Sanjay Dudhe, Pro-Vice Chancellor, Rashtrasant Tukadoji Maharaj Nagpur University, MH, India for all the help extended by them during the completion of this book. At this moment of accomplishment we would like to express our cordial and honest gratitude to Dr.Arti Moglewar, Principal, Sant Gadge Maharaj Mahavidyalaya, Hingna, MH, India for her guidance, support and constant encouragement. We are also thankful to Dr. Rajesh Kumar, Principal, AV College, Amritsar, India for his valuable advice, constructive criticism and his extensive discussions around this work.

We extend our sincere thanks to all of them who directly and indirectly supported willingly and selflessly for our experiments and all of them who also stayed with us in the process. We are indebted to our many young and dynamic friends for always providing a stimulating and fun filled environment whenever we go into this process.

We can see the good shape of present book because of the enough size of our research group. We remember our communication and coordination with each other, we had interesting and cheerful discussions started from search to research. We enjoyed the same with tea and snacks during the entire process of this book project.

Ritesh Kohale

Department of Physics,

Sant Gadge Maharaj Mahavidyalaya,

India

Sanjay J. Dhoble

Department of Physics,

Rashtrasant Tukadoji Maharaj Nagpur University,

India

&

Vibha Chopra

P.G. Department of Physics and Electronics,

D.A.V. College,

India

Fundamentals of Nuclear Physics

Ritesh Kohale, Sanjay J. Dhoble, Vibha Chopra

Abstract

The present chapter is an introduction to various scientific and technological fields. It is a beginning step to trail further study in this book. The first chapter specifies the contemporary idea and fundamental understandings of nuclear physics, which is necessary to develop the rest of the studies in this domain. The present chapter deals with an introduction to nuclei, constituents of the nucleus and its properties, mass defects and binding energy, nuclear reactions, the Q-value of nuclear reactions, and the discovery of the neutron and nuclear chain reactions.

Keywords: Chain Reaction, Mass Defect, Neutron, Proton.

1. INTRODUCTION TO NUCLEI

Nuclear physics aims to improve the knowledge of all nuclei and understand astrophysical nucleosynthesis. There are similarities between the electronic structure of atoms and nuclear structure. In nuclei, protons and neutrons are two groups of similar particles [1].

1.1. Constituents of the Nucleus and its Properties

1.1.1. Proton

It is one of the major and significant constituents of the nucleus. Its positive charge and mass are 1.673 x 10-27 kg ≈ 1u.

1.1.2. Neutron

Zero charge

Mass 1.675 x 10-27 kg ≈ 1u

Mass of neutron ≈ mass of proton + mass of an electron

1.1.3. Nucleon

In chemistry and physics, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. (e.g., neutron or proton).

1.1.4. Nomenclature

A - Number of nucleons (atomic mass number)

Z - Number of protons

N - Number of neutrons

A = Z + N

The symbol for the nucleus of chemical element X.

1.1.5. Atomic Mass Unit, (U)

A convenient unit for measuring nuclear mass. Usually, nuclear mass is expressed in terms of a unit known as the atomic mass unit, denoted by the letter u. One atomic mass unit is defined as one-twelfth the mass of a carbon atom (i.e., the most abundant isotope of Carbon),

viz., ¹²C, If Mass of ¹²C = 12 u, then,

In terms of the above units,

Mass of a proton, mp = 1.00727 u

Mass of a neutron, mn = 1.00866 u

1.1.6. Nuclear Size and Density

It has Close-packed structure

Constant density

Volume proportional to atomic number (A)

Since V = 4/3 πr³, A proportional to r³

r is proportional A¹/³

r ≈ (1.2 x 10-15 m) A¹/³ = 1.2 fm A¹/³

Density of neutron star = 100 million tons/cm³

1.1.7. Nuclei

Nuclei are composed of protons and neutrons. The number of protons is atomic number Z, the number of neutrons is N, and the mass number A is approximately the total number of nucleons (i.e., protons and neutrons, A = (Z + N,)

Therefore the number of neutrons is N = A-Z

1.2. Mass Defect and Binding Energy

1.2.1. Mass Defect

The constituents of a nucleus are neutrons and protons, collectively known as nucleons. The mass of a nucleus is always less than the sum of the masses of its constituent nucleons (i.e., protons and neutrons); the difference between the total mass of nucleons and the actual mass of the nucleus is called the mass defect denoted by Δm and given by [2].

Where,

Δm = Mass Defect

Z = no of protons inside the nucleus

(A-Z) = N = no of neutrons

mp = mass of a single proton

mn = mass of a single neutron

M = total actual mass of a nucleus

The missing mass appears in the form of energy holding the nucleus together,

This energy equivalent to mass defect is called the binding energy of the nucleus [3, 4].

Example: The atomic mass of helium (⁴He) atom is 4.002602 u. Determine its mass defect.

Solution:

The actual atomic mass of helium (⁴He) atom is 4.002602 u, which is not equal to the combined mass of its constituent, i.e.4.032979 u.

Mass Defect Δm is given by equation 1.1,

Δm = [(2 x 1.007276) + (2 x 1.008665) + (2 x 0.0005486)] u – 4.002602 u

Δm = 4.032979 u – 4.002602 u

Δm = 0.030366 u

This difference between the mass of an atom and the sum of the masses of its protons, neutrons, and electrons is 0.030366 u, which is less than the combined mass called the mass defect (Fig. 1.1).

Fig. (1.1))

The schematic shows the actual atomic mass of the Helium atom and the combined mass of its constituents.

1.2.2. Binding Energy

As the mass of a nucleus is always less than the sum of the masses of its constituent nucleons, the difference between the two is called the mass defect. This loss of mass is equivalent to the energy given by Einstein’s Mass-Energy correlation: E=Δm.c² and is called the binding energy of the nucleus.

Thus, the binding energy of a nucleus can be defined as the total amount of energy released when nucleons combine to form stable nuclei or the amount of external energy required to separate the nucleus into its constituent nucleons.

From special relativity, adding energy increases mass which is a measure of binding energy and can be given as:

Δm is a mass defect, and binding energy in terms of atomic number Z and atomic mass number A is,

From equations (1.1) and (1.2)

Where, M is the mass of the combined nucleus, mp is the mass of the proton, mn is the mass of the neutron, and c is the velocity of light.

Average Binding Energy: It is defined as binding energy (B.E.) per nucleon (A) and given by,

The term in equation (1.5) is known as the packing fraction.

i.e., Binding Energy (B.E.) per nucleon = c²×Packing Fraction.

The nuclei with the greatest binding energy per nucleon are the most stable. For a given number of nucleons, if the total mass defect increases, then BE per nucleon also increases, and energy can be released. Nuclear binding energy is more or less independent of the nuclei's size and is roughly about 8.5 MeV/nucleon. Most stable nuclides, from the lightest to the most massive, have binding energies of 7 to 9 MeV/nucleon. It may be noted that the nucleus Fe is the most tightly bound nucleus with a binding energy of about 8.8 MeV per nucleon. This is why the iron group of nuclei is the most stable. A graph of binding energy per nucleon as a function of mass number A is shown in Fig. (1.2) below [5].

Fig. (1.2))

Binding energy per nucleon curve.

1. From Fig. (1.2), the maximum value of B.E.ave is for ⁵⁶Fe. The large binding energy suggests that the nucleons in a nucleus are very tightly bound.

2. For 0 ≤ A ≤ 30,

The binding energy per nucleon B.E.ave increases as the mass number ‘A’ increases. At some particular values of A, the value of B.E.ave is apparently larger than neighboring A’s.

3. For 30 ≤ A ≤ 240,

The value of B.E.ave varies slowly and is around 7.5 ~ 8.5 MeV.

4. For ≈ 56 (viz. 56Fe)

The value of B.E.ave reaches its maximum value.

5. For A>60

The value of B.E.ave decreases as the mass number ‘A’ increases. This is due to the Coulomb repulsion.

6. The binding energy per nucleon for light nuclei such as ¹H, ²H and ³H is approximately low, but it is about 8 MeV for all other nuclei.

1.3. Nuclear Reaction

A nuclear reaction is a process in which the target nucleus of an atom is bombarded by fast-moving particles that split apart or are joined with the nucleus of another atom.

In general, the nuclear reaction can be written as:

Where,

a- Is incident particle(Projectile)

X - Is the target nucleus

Y - Is the product nucleus (as X changes into Y)

b - Is the product particle

Q = energy absorbed/released in the nuclear reaction.

If Q is positive, energy is released and

Q is negative energy is absorbed

The above nuclear reaction can be written as: X (a, b) Y

An example of a nuclear reaction is firing α-particles at beryllium:

And this can be equivalently written as:

1.3.1. Q-value of Nuclear Reaction

The Q-value of a nuclear reaction is defined as the total energy released or absorbed during the nuclear reaction.

It is equivalent to the total change in the system's kinetic energy (KE). Depending upon the type of reaction, the Q-value may be positive or negative.

In a generic reaction:

Hence according to the law of conservation of energy,

From the above reaction, we can calculate the Q-value or the energy released or absorbed during the nuclear reaction as shown below:

Hence,

Hence, the Q-value of nuclear reaction is defined as the difference between the kinetic energies of the products and that of the incident particle.

1. If

Then Q-value is positive, and the reaction is exothermic.

i.e., Energy is released in the reaction.

2. If

Then the Q-value is negative, and the reaction is endothermic.

i.e., Energy is absorbed in the reaction.

3. If

Then the Q-value is zero, and the reaction is a kind of elastic collision.

i.e., Energy is neither released nor absorbed in the reaction.

1.4. Discovery of Neutron

One of the famous experiments performed by Rutherford was the bombarding of lighter elements by α - particles, e.g., When nitrogen was bombarded by -particles, the following reaction occurred.

This was one of the first man-made nuclear reactions. Rutherford and his associate James Chadwick performed experiments with many light nuclei where bombardment of light nuclei by cc-particles resulted in the ejection of protons. However, it was soon found that some light elements like boron and beryllium did not give out protons under α-particle bombardment. In 1930, W-Bothe and H. Becker found that when Beryllium or Boron was bombarded with -particles (of Polonium), highly penetrating radiation was emitted. This radiation was assumed to be γ-rays since γ-rays have a high penetrating power. Further, in 1932), Irene-Curie-Joloit (daughter of Madame Curie) and her husband, F. Joliot, found that these penetrating radiations could knock out energetic protons from Paraffin wax. They thought these penetrating radiations in the town of γ-rays knocked out protons in the same manner as X-rays knocked out electrons in Compton Effect. Further calculations show that to knock out protons of energy 4.7 MeV from paraffin wax, the γ-rays must have an energy of about 47 MeV. This much energy is unusually high for γ-rays, and so this situation is confusing. Soon afterward, in 1932, Chadwick repeated the experiment with paraffin wax, helium and nitrogen. Chadwick resolved the anomaly of energy of penetrating radiations by assuming that the unknown radiation produced by the impact of α -particles with 4Be⁹ nuclei was not γ-ray but a new type of particle of the same mass as the proton and was electrically neutral [6]. This new particle was named ‘neutron.’ The reaction proposed by Chadwick could be written as:

Since a neutron has no charge, it can have great penetrating power. Chadwick was awarded Nobel Prize in 1935 for this great discovery.

In 1930, Rutherford, in his gold foil experiment, bombarded a beam of alpha particles on an ultrathin gold foil, which explained the overall electrical neutrality of an atom and gave a clear picture of the structure of an atom (which consists of protons (inside the nucleus) and the same number of electrons outside of the nucleus).

But scientists soon realized that Rutherford's atomic model was incomplete. Various experiments showed that the nucleus's mass is approximately twice the number of protons. Then what is the origin of this additional mass? Rutherford postulated the existence of some neutral particles having mass similar to protons, but there was no direct experimental evidence.

Several theories and experimental observations eventually led to the discovery of neutrons [7]. We can summarize some of the scientific observations behind the discovery of neutrons.

In 1930, W. Bothe and H. Becker found electrically neutral radiation when they bombarded beryllium with an alpha particle. They thought it was photons with high energy (gamma rays).

In 1932, Irene and Frederic Joliot-Curie showed that this ray could eject protons when it hits paraffin or H-containing compounds.

The question arose about how massless photons could eject protons 1836 times heavier than electrons. So the ejected rays in the bombardment of beryllium with alpha particles cannot be photons.

In 1932, James Chadwick performed the same experiments as Irene and Frederic Joliot-Curie but used many different targets of bombardment besides paraffin (Fig 1.3).

By analysing the energies of different targets after bombardment, he discovered the existence of a new particle that is charged less and has a similar mass to a proton [8]. This particle is called a neutron.

Fig. (1.3))

Schematic diagram for the experiment that led to the discovery of neutrons by Chadwick.

Example: Beryllium undergoes the following reaction when bombarded with an alpha particle.

1.5. Nuclear Chain Reaction

When fission takes place for heavy atoms, it releases a number of multiplying neutrons which can be absorbed by other heavy atoms to induce further fissions; this is called a chain reaction.

Notice that in each of the reactions, neutrons are produced. If each neutron releases two more neutrons from fission, then the number of neutrons doubles in each fission generation (Fig 1.4); in that case, in 10 generations, there are 1,024 fissions, and in 80 generations, about 6 x 10²³ (a mole) fissions [9].