An introduction to Nuclear Physics.

Ronaldo V. Lobato
Department of Physics and Astronomy,
Texas A&M University - Commerce, Texas, USA.

Some history and basic concepts


1896 - Henri Becquerel discovers the radioactivity.

From: Wikipedia

1897 - J.J. Thomson discovers the electron, indicating that the atom has internal structure.

From: Wikipedia

1900 - William Thomson (Lord Kelvin) proposes the first theoretical description of the atom.

Radioactivity was extensively studied by Marie, Pierre Curie, Ernest Rutherford and others

From: Wikipedia

Physicists discovered three types of radiation.

Alpha, beta and gamma. From: Wikipedia

1903 - Nobel prize to Becquerel and to Marie and Pierre. Rutherford won the 1908 Nobel Prize in Chemistry.
1903 - Einstein formulated the ideia of mass-energy equivalence.

From: Reddit.

1906 - Rutherford did more experiments and in 1911 went before the Royal Society to explain the experiments propound the atomic nucleus.

From: Wikipedia.

1920 - Arthur Eddington proposes the mechanism of nuclear fusion process in stars.

From: Wikipedia.

1925 - By this time, it was known that protons and electrons each had spin 1/2. Franco Rasetti perfomed studies of nuclear spin, discored that nitrogen-14 had spin 1.

From: Wikipedia.

1932 - Chadwick discovers the neutron. Dimitri Ivanenko suggests that there were no electrons in the nucleus/neutrons were spin 1/2. This solve the nitrogen-14 spin problem.

From: Wikipedia.

1935 - Hideki Yukawa proposes the theory of strong force - how the nucleus holds together.

From: Wikipedia.

In the Yukawa interaction a virtual particle, meson, mediates the force between all the nucleons.

\[ V \approx g \bar{\psi} \phi \psi \qquad \rightarrow \qquad V(r)=-\frac{g^{2}}{4 \pi} \frac{1}{r} e^{-\mu r} \]

The discovery of the pi meson, showed the properties of the interaction.

The modern model of the atom was complet. The atom's center contains a tight `ball` of neutrons and protons, held together by the strong force.


A given atom is specified by the number of

  • Neutrons: \(N\)
  • Proton: \(Z\)
  • Electrons: There are \(Z\) electron in neutral atoms

Atoms of the same element have same atomic number \(Z\). But they can be different. Isotopes of the same element have different # of neutrons \(N\).

Conventionally it can be represented as


The mass number \(A\) is the total number of nucleons, i.e., \(A=N+Z\). For instance, \(^4\)He is the helium-4 nucleus, \(N=Z=2\), also called \(\alpha\).

Representation of a atom.

The nucleus diameter is \(\sim 10^{-15}\) while the atom is \(\sim 10^{-10}\) m, i.e., 1/100,000 of the size of the whole atom. A good comparisson would be a baseball ball in the middle of a stadium.
The nucleus contains more than 99.9% of the mass of the atom.

Modern Nuclear physics

Liquid-drop model

Heavy nucleus contain hundreds of nucleons. Sometimes is treated as a classical system.

Credit. C.A. Bertulani.

\(E_{\rm {B}}=a_{\rm {V}}A-a_{\rm {S}}A^{2/3}-a_{\rm {C}}{\frac {Z(Z-1)}{A^{1/3}}}-a_{\rm {A}}{\frac {(N-Z)^{2}}{A}}+\delta (N,Z)\)

\[ a_{\rm {V}} = 15.85; a_{\rm {S}} = 18.34; a_{\rm {C}} = 0.71; a_{\rm {A}} = 23.21\, {\rm MeV} \]

Nuclear shell mode

Considering quantum-mechanical effets → nuclear shell mode, developed in large part by Maria Mayer and J. Jensen (Nobel Prize 1963).

Credit. C.A. Bertulani.

Magic numbers: \(\sum _{n=0}^{k}(n+1)(n+2)={\frac {(k+1)(k+2)(k+3)}{3}}\)
This gives the following magic numbers: 2, 8, 20, 40, 70, 112, ..., which agree with experiment only in the first three entries.

Interacting boson model

- More complicated models also exist, such as the interacting boson model.

Credit. C.A. Bertulani and Wikipedia.

The model can be used to predict vibrational and rotational modes of non-spherical nuclei.

Quantum chromodynamics

- Ab initio methods try to solve the nuclear many-body problem from the ground.

\(\mathcal{L}_{\mathrm {QCD} }={\bar {\psi }}_{i}\left(i(\gamma ^{\mu }D_{\mu })_{ij}-m\,\delta _{ij}\right)\psi _{j}-{\frac {1}{4}}G_{\mu \nu }^{a}G_{a}^{\mu \nu };\quad G_{\mu \nu }^{a}=\partial _{\mu }{\mathcal {A}}_{\nu }^{a}-\partial _{\nu }{\mathcal {A}}_{\mu }^{a}+gf^{abc}{\mathcal {A}}_{\mu }^{b}{\mathcal {A}}_{\nu }^{c}\)

Credit. C.A. Bertulani.

- From QCD to nuclei.

\({\rm \scriptscriptstyle{C.A. Bertulani\ and\ J. Dobaczewski}}\)

Fundamental interactions

- Nuclear force.

From: Wikipedia.

Applications of Nuclear Physics

From: Wikipedia.
Credit. C.A. Bertulani.
Credit. C.A. Bertulani.
Credit. C.A. Bertulani.
Credit. C.A. Bertulani.
Credit. ESA.
Credit. Dani Page.