Über die Autorin bzw. den Autor

Carlos A. Bertulani is Research Professor of Physics at the University of Tennessee and the Oak Ridge National Laboratory. He is the author of Physics of Radioactive Nuclear Beams, Introduction to Nuclear Physics, and Introduction to Nuclear Reactions.

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"The particular attraction of this book is the detail with which it provides, in one place, all of the essential physics required for an understanding of the field. An excellent piece of scholarship, it will come to be regarded as an essential text for beginning graduate physics study. Indeed, I know of no other modern treatment other than this that goes to such lengths, and within this context it is indeed a tour de force."--David A. Bradley, University of Surrey

"This book does a fine job of developing three topics--hadrons, nuclei, and stars--that are often covered separately, and bringing them together in an appealing way in the context of real physical systems. Remarkably self-contained, with helpful, unobtrusive appendices, it develops most physical concepts from start to finish. It can be used for a course on stellar physics, nuclear physics, or advanced quantum mechanics."--Savas Dimopoulos, Stanford University

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"The particular attraction of this book is the detail with which it provides, in one place, all of the essential physics required for an understanding of the field. An excellent piece of scholarship, it will come to be regarded as an essential text for beginning graduate physics study. Indeed, I know of no other modern treatment other than this that goes to such lengths, and within this context it is indeed a tour de force."--David A. Bradley, University of Surrey

"This book does a fine job of developing three topics--hadrons, nuclei, and stars--that are often covered separately, and bringing them together in an appealing way in the context of real physical systems. Remarkably self-contained, with helpful, unobtrusive appendices, it develops most physical concepts from start to finish. It can be used for a course on stellar physics, nuclear physics, or advanced quantum mechanics."--Savas Dimopoulos, Stanford University

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Nuclear Physics in a Nutshell

PRINCETON UNIVERSITY PRESS

Contents

Introduction...........................................................11 Hadrons..............................................................42 The Two-Nucleon System...............................................313 The Nucleon-Nucleon Interaction......................................714 General Properties of Nuclei.........................................985 Nuclear Models.......................................................1196 Radioactivity........................................................1707 Alpha-Decay..........................................................1858 Beta-Decay...........................................................1959 Gamma-Decay..........................................................21810 Nuclear Reactions—I...........................................25811 Nuclear Reactions—II..........................................29812 Nuclear Astrophysics................................................33413 Rare Nuclear Isotopes...............................................385Appendix A Angular Momentum............................................401Appendix B Angular Momentum Coupling...................................419Appendix C Symmetries..................................................432Appendix D Relativistic Quantum Mechanics..............................440Appendix E Useful Constants and Conversion Factors.....................459References.............................................................461Index..................................................................469

Chapter One

1.1 Nucleons

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 the nucleus. 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

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detect the positive charge particles that compose the nucleus called protons. The proton, with symbol p, is the nucleus of the hydrogen atom; it has charge +e of the same absolute value as that of the electron, and mass

m_p = 938.271998(38) MeV/c², (1.2)

where the values in parentheses are the errors in the last two digits.

From study of the hydrogen molecule one can infer that the protons in the molecule can be aligned in two different ways. The spins of the two protons can be parallel, as in orthohydrogen, or antiparallel, as in parahydrogen. Each proton has two possible orientations relative to the spin of the other proton, and like the electron the proton has spin 1&frac;2.

In orthohydrogen the wavefunction is symmetric with respect to the interchange of the spins of the two protons, since they have the same direction, and experiments show that the wavefunction is antisymmetric with respect to the interchange of the spatial coordinates of the protons. This justifies the wavefunction being antisymmetric with respect to the complete interchange of the protons. In parahydrogen the wavefunction is also antisymmetric with respect to the complete interchange of the two protons, being antisymmetric with respect to the interchange of the spins of the protons and symmetric with respect to the interchange of their spatial coordinates. This shows that the protons obey Fermi-Dirac statistics; they are fermions and the Pauli exclusion principle is applicable to them. At most one proton can exist in a given quantum state.

The neutron, with symbol n, has charge zero, spin 1&frac;2, and mass

m_n = 939.565330(38) MeV/c². (1.3)

In 1930, Bothe and Becker [BB30] discovered that a very penetrating radiation was released when boron, beryllium, or lithium was bombarded with α-particles. At that time it was thought that this penetrating radiation was γ-rays (high-energy photons). In 1932, Curie and Joliot [CJ32] figured out that the radiation was able to pull out protons from a hydrogen-rich material. They suggested that this was due to Compton scattering, that is, the protons recoiled after scattering the γ-rays. This hypothesis, however, meant that the radiation consisted of extremely energetic ? -rays, and no explanation could be given for the origin of such high energies. Also in 1932, Chadwick [Ch32] showed, by means of an experiment conducted at the Cavendish laboratory in Cambridge, that the protons ejected from the hydrogen-rich material had collided with neutral particles with mass close to the mass of the proton. These were neutrons, the neutral particles that composed the penetrating radiation discovered by Bothe and Becker. The reaction that occurred when beryllium was bombarded with a-particles was

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.4)

The existence of the neutron was also necessary to explain some features of the molecular spectrum showing that the wavefunctions of nitrogen molecules were symmetric with respect to interchange of the two ¹⁴N nuclei. As a consequence, the ¹⁴N nuclei were bosons. This could not be explained if the 14N nucleus were composed only of protons and electrons, since 14 protons and 7 electrons are needed for that, which means an odd number of fermions. A system made up of an odd number of fermions is a fermion, since the interchange of two systems of this type can be made by the interchange of each of their fermions, and each change of two fermions changes the sign of the total wavefunction. In the same way, we can say that a system composed of an even number of fermions is a boson. This shows that if the ¹⁴N nucleus is formed by 7 protons and 7 neutrons it is a boson, assuming that the neutron is a fermion. In this way, the study of the N2 molecule led Heitler and Hertzberg [HH29] to conclude that atomic nuclei are composed of protons and neutrons and not of protons and electrons.

Several other studies established that neutrons obey the Pauli principle and thus are fermions, having spin 1&frac;2. We recall that particles with fractional spin (2n + 1)/2 are fermions, and that particles with integer spin are bosons. Protons and neutrons have similar properties in several aspects, and it is convenient to utilize the generic name nucleon for both.

1.2 Nuclear Forces

The origin of the Coulomb force between charged particles is the exchange of photons between them. This is represented by the Feynman diagram (a) of figure 1.1. In this diagram lines oriented up represent the direction in which time increases. At some instant of time the particles exchange a photon, which gives rise to attraction or repulsion between them. The photon has zero mass and the Coulomb force is a long-range force.

The force that keeps the nucleus bound is the nuclear force. It acts between two nucleons of any type and, in contrast to the Coulomb force, it is of short range. In 1935 Yukawa [Yu35] suggested that the nuclear force has its origin in the exchange of particles with finite rest mass between the nucleons. These particles are called mesons, and this situation is described by the Feynman diagram of figure 1.1(b). In the emission of a meson with rest...