# Nuclear Physics in a Nutshell

Carlos A. Bertulani
Series: In a Nutshell
Edition: STU - Student edition
Pages: 488
https://www.jstor.org/stable/j.ctt7shsk

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1. Front Matter
(pp. i-vi)
(pp. vii-xiv)
3. Introduction
(pp. 1-3)

The most accepted theory for the origin of the universe assumes that it resulted from a great explosion, soon after which the primordial matter was extremely dense, compressed and hot. This matter was mainly composed of elementary particles, such as quarks and electrons. As it expanded and cooled down, the quarks united to form heavier particles, called hadrons, which contain 3 quarks (baryons) or 2 quarks (mesons). The protons and neutrons (which are baryons) formed nuclei, and the electrons were captured in orbits around the nuclei forming atoms.

The larger and heavier nuclei were created inside stars, which were formed...

(pp. 4-30)

The scattering experiments made by Rutherford in 1911 [Ru11] led him to propose an atomic model in which almost all the mass of the atom was contained in a small region around its center called thenucleus. The nucleus should contain all the positive charge of the atom, the rest of the atomic space being filled by the negative electron charges.

Rutherford could, in 1919 [Ru19], by means of the nuclear reaction

${}_2^4{\rm{He + }}{}_7^{14}{\rm{N }}\ \to\ {\rm{ }}{}_8^{17}{\rm{O + p,}}$(1.1)

detect the positive charge particles that compose the nucleus calledprotons. The proton, with symbol$p$, is the nucleus of the hydrogen atom; it has charge...

5. 2 The Two-Nucleon System
(pp. 31-70)

The study of the hydrogen atom is relatively simple due the fact that the Coulomb force between the proton and the electron is very well known. The solution of this quantum problem resulted in the determination of a group of states of energy allowed for the system, permitting direct comparison with the measured values of the electromagnetic transitions between those states. Ever since, there has been great progress in understanding the hydrogen atom and atoms with many electrons. Nowadays, there are only small discrepancies between quantum theory and experimental data.

Nuclear systems are much more complex than atomic ones. Already...

6. 3 The Nucleon-Nucleon Interaction
(pp. 71-97)

The starting point for any dynamical description of a physical system is knowledge of the relevant degrees of freedom and of the interaction. In the previous chapters we have seen that nucleons are the basic components of nuclei. Their degrees of freedom are determined by the position ri, momentum pi, spin siand isospin τiof theith nucleon. For the interaction one first takes the simplest assumption that it is a two-body interaction that can be described by a potential. A further extension of the model introduces three- and many-body interactions for a deeper understanding of the many-body system....

7. 4 General Properties of Nuclei
(pp. 98-118)

The basic properties of nucleons were presented in chapters 1, 2, and 3, together with the development of the deuteron theory. Our purpose in this and the following chapters is to study the physics of nuclei with any number A of nucleons, to establish the systematics of their properties, and to present the theories that aim to explain them. However, the approach we have followed for the deuteron is not applicable here. The Schrödinger equation is already not exactly soluble for a three-nucleon system, and to establish the properties of a heavy nucleus starting from the interaction of all its...

8. 5 Nuclear Models
(pp. 119-169)

In the previous chapters we have talked about the impossibility of obtaining the properties of a system of A nucleons starting from its constituents and their underlying interactions, and it was clearly evidenced that there is a need to use models that represent some aspects of the real problem.

The models are essentially of two classes. The first class of models assume that the nucleons interact strongly in the interior of the nucleus and that their mean free path is small. This is a situation identical to that of molecules of a liquid, and the liquid drop model belongs to...

(pp. 170-184)

The stable isotopes are located in a narrow band of the nuclear chart called the$\beta$-stability line, alongside of which nuclei unstable by${\beta ^ + }$or${\beta ^ - }$emission are located. For A > 150 the emission of an$\alpha$-particle is energetically favorable, and in this region one finds several$\alpha$-emitters. Heavy nuclei also release energy if divided in two nearly equal parts and can, for this reason, fission spontaneously. Aradioactive substance, which contains some unstable isotope, is in permanent transformation by the action of one or more of these processes. The physics of each of them will be studied later....

10. 7 Alpha-Decay
(pp. 185-194)

The emission of an$\alpha$-particle is a possible nuclear disintegration process in situations in which (5.12) is satisfied. In contrast with the restricted existence of emitters of light fragments,$\alpha$-emitter nuclei are largely due to the large binding energy of the$\alpha$-particle. In turn, the$\alpha$-emitting process is energetically advantageous in practically all nuclei with A ≳ 150. Figure 7.1, based on the balance of masses, exhibits the energy available by emission of several nuclei for ²³⁹Pu. We see that$\alpha$-emission is the only energetically possible process.

Very rarely one detects emission of heavier fragments, with A > 4. Examples are...

11. 8 Beta-Decay
(pp. 195-217)

The most common form of radioactive disintegration is${\rm{\beta }}$-decay, detected in isotopes of practically all elements, with the exception, up to now, of the very heavy ones at the extreme of the chart of nuclides. It consists in the emission of an electron and an antineutrino (${\beta ^ - }$-decay) or in the emission of a positron and a neutrino (${\beta ^ + }$-decay), keeping the nucleus, in both cases, with the same number of nucleons according to the equations

$_{\rm{Z}}^{\rm{A}}{{\rm{X}}_N} \to _{{\rm{Z + 1}}}^{\rm{A}}{{\rm{Y}}_{N - 1}} + {e^ - } + v$(8.1)

and

$_{\rm{Z}}^{\rm{A}}{{\rm{X}}_N} \to _{{\rm{Z}} - {\rm{1}}}^{\rm{A}}{{\rm{Y}}_{N + 1}} + {e^ + } + v.$(8.2)

The mechanisms of$\alpha$- and$\beta$-emission differ in an essential aspect: whereas the nucleons that form the$\alpha$-particle already reside in...

12. 9 Gamma-Decay
(pp. 218-257)

The quantum system of A nucleons that form the nucleus has, above its state of lowest energy (ground state), a large number of possible excited states that can be accessed if enough energy is given to the system. The transitions among these states, either through excitation or through de-excitation, are accomplished mainly through$\gamma$-radiation, which embraces a high energy region of the electromagnetic spectrum. This region is located basically between 0.1 MeV and 10 MeV, being a 1 MeV$\gamma$-ray of order 3 × 10⁵ times more energetic than violet light.

Besides the energy released, another characteristic parameter is the...

13. 10 Nuclear Reactions—I
(pp. 258-297)

The collision of two nuclei can give place to a nuclear reaction where, similarly to a chemical reaction, the final products can be different from the initial ones. This process happens when a target is bombarded by particles coming from an accelerator or from a radioactive substance. It was in the latter way that Rutherford observed, in 1919, the first nuclear reaction produced in the laboratory,

$\alpha {\rm{ + }}_7^{14}{\rm{N}}\; \to \;_8^{17}{\rm{O + p}},$(10.1)

using$\alpha$-particles coming from a ²¹²Bi sample and using as the target nitrogen contained in a reservoir.

As in (10.1), other reactions were induced using$\alpha$-particles, the only projectile available initially. With...

14. 11 Nuclear Reactions—II
(pp. 298-333)

We have already mentioned the existence of reactions that occur within a short duration of the projectile-target interaction. Several of these mechanisms of direct reaction are known. This reaction type becomes more probable as one increases the energy of the incident particle: the wavelength associated with the particle decreases and localized areas of the nucleus can be “probed” by the projectile. In this context, importance in placed on peripheral reactions, where only a few nucleons of the surface participate. These direct reactions happen during a time of the order of 10-22s; reactions in which the formation of a compound nucleus...

15. 12 Nuclear Astrophysics
(pp. 334-384)

The hydrogen, deuterium, and most of the helium atoms in the universe are believed to have been created some 20 billion years ago in a primary formation process referred to as the Big Bang, while all other elements have been formed—and are still being formed—in nuclear reactions in the stars. These reaction processes can only be understood in an astrophysical context, as briefly outlined in this chapter, which also describes how nuclear science has provided much understanding about the universe, our solar system and our planets.

The evolution of the universe is the object of study of cosmology...

16. 13 Rare Nuclear Isotopes
(pp. 385-400)

The study of nuclear physics demands beams of energetic particles to induce nuclear reactions on the nuclei of target atoms. It was from this need that accelerators were born. Over the years nuclear physicists have devised many ways of accelerating charged particles to ever increasing energies. Today we have beams of all nuclei from protons to uranium ions available at energies well beyond those needed for the study of atomic nuclei. This basic research activity, driven by the desire to understand the forces that dictate the properties of nuclei, has spawned a large number of beneficial applications. Among its many...

17. Appendix A Angular Momentum
(pp. 401-418)
18. Appendix B Angular Momentum Coupling
(pp. 419-431)
19. Appendix C Symmetries
(pp. 432-439)
20. Appendix D Relativistic Quantum Mechanics
(pp. 440-458)
21. Appendix E Useful Constants and Conversion Factors
(pp. 459-460)
22. References
(pp. 461-468)
23. Index
(pp. 469-473)