What does this science study?
Nuclear physics is the science of the structure and properties of atomic nuclei, their mutual transformations (radioactive decay, nuclear reactions) and the forces that govern them. Particle physics studies the smallest constituents of matter — leptons, quarks, interaction carriers — and the fundamental interactions between them. More than 99.95 % of an atom's mass is concentrated in the nucleus, whose volume is $10^{14}$ times smaller than that of the atom. The radiation of stars, the origin of the chemical elements, nuclear power and nuclear medicine all rest on the laws of this science.
Let us pose a question before the lecture: why is the energy released in nuclear processes a million times larger than in chemical reactions? The answer lies in the scales of the microworld.
Main stages of development
| Stage | Key discoveries |
|---|---|
| 1896–1932: discovery of the nucleus | H. Becquerel — radioactivity of uranium (1896); P. and M. Curie — polonium and radium (1898); E. Rutherford — alpha and beta rays, the decay law; the Geiger–Marsden experiments and Rutherford's nuclear model (1911); the first artificial nuclear reaction ${}^{14}\mathrm{N}(\alpha,p){}^{17}\mathrm{O}$ (1919) |
| 1932–1950: nucleon structure and nuclear energy | J. Chadwick — the neutron (1932); D. Ivanenko and W. Heisenberg — the proton–neutron model of the nucleus; C. Anderson — the positron; the Cockcroft–Walton accelerator; I. and F. Joliot-Curie — artificial radioactivity (1934); E. Fermi — theory of beta decay; H. Yukawa — meson theory (1935); O. Hahn and F. Strassmann — fission of uranium (1938); the first nuclear reactor (1942) |
| 1950–1975: the particle “zoo” | the pion (1947), strange particles, the antiproton (1955), detection of the neutrino (Reines and Cowan, 1956), parity violation (1956–1957), the quark model (Gell-Mann and Zweig, 1964) |
| 1975–today: the Standard Model | c and b quarks, W and Z bosons (1983), the t quark (1995), neutrino oscillations (1998), the Higgs boson (LHC, 2012) |
Clearly each stage is tied to a new experimental technique: from radioactive sources to accelerators and reactors, then to giant colliders and underground detectors.
Scales of microworld phenomena
Length
An atom is $\sim 10^{-10}$ m across, a nucleus $10^{-15}$–$10^{-14}$ m. Nuclear physics therefore uses the fermi (femtometre): $1\ \text{fm} = 10^{-15}\ \text{m}$. The proton radius is $\approx 0.84$ fm, the radius of the heaviest nuclei $\approx 7$ fm. The probability of nuclear reactions is measured in barns: $1\ \text{b} = 10^{-28}\ \text{m}^2 = 100\ \text{fm}^2$.
Mass and energy
Masses are measured in atomic mass units: $1\ \text{u} = \frac{1}{12}m({}^{12}\mathrm{C}) = 1.66054\cdot10^{-27}$ kg. By Einstein's relation
$$E = mc^2,\qquad 1\ \text{u}\cdot c^2 = 931.494\ \text{MeV},$$
where $E$ is the rest energy, $m$ the mass and $c$ the speed of light. The energy unit is the electronvolt: $1\ \text{eV} = 1.602\cdot10^{-19}$ J, $1\ \text{MeV} = 10^6$ eV. The rest energy of the electron is 0.511 MeV, of the proton 938.27 MeV, of the neutron 939.57 MeV.
Energy scales: chemical bonds in molecules — a few eV; inner atomic electrons — keV; binding energy of a nucleon in a nucleus — about 8 MeV; particle physics — GeV and TeV.
Useful combinations
$$\hbar c = 197.327\ \text{MeV}\cdot\text{fm},\qquad \frac{e^2}{4\pi\varepsilon_0} = 1.440\ \text{MeV}\cdot\text{fm}.$$
For example, the Coulomb energy of two protons at $r = 2$ fm is $1.44/2 = 0.72$ MeV, whereas the binding energy of the electron in a hydrogen atom is only 13.6 eV.
Time
Light crosses a nucleus in $\tau \sim R/c \sim 10^{-23}$ s — the characteristic time of the strong interaction. Half-lives range from $10^{-20}$ s to $10^{24}$ years.
Quantum character
Microparticles have wave properties: the de Broglie wavelength is $\lambda = h/p$. To “see” inside a nucleus, the wavelength of the probe must be smaller than the nucleus; for a 200 MeV electron $\lambda \approx hc/(pc) \approx 6.2$ fm. The uncertainty relation $\Delta x\,\Delta p \gtrsim \hbar$ lets us estimate the kinetic energy of a confined particle.
Example
A nucleon is confined to a region of size $\Delta x \approx 2$ fm. Estimate its kinetic energy.
Solution. $\Delta p \approx \hbar/\Delta x$, hence $$T \approx \frac{(\Delta p)^2}{2m} = \frac{(\hbar c)^2}{2mc^2(\Delta x)^2} = \frac{197.3^2}{2\cdot 938.3\cdot 2^2}\ \text{MeV} \approx 5.2\ \text{MeV}.$$ The same estimate for an electron in an atom ($\Delta x \sim 0.1$ nm) gives a few eV. Nuclear energies are of order MeV because the particles are confined to a very small volume — this answers our opening question.
Nuclides and their classification
A nucleus consists of $Z$ protons and $N$ neutrons; $A = Z + N$ is the mass number (number of nucleons) and $Z$ the charge number. A species of atom with given $Z$ and $N$ is called a nuclide and written ${}^{A}_{Z}X$, e.g. ${}^{238}_{92}\mathrm{U}$ ($N = 146$).
- Isotopes — same $Z$, different $N$: ${}^{12}\mathrm{C}$, ${}^{13}\mathrm{C}$, ${}^{14}\mathrm{C}$.
- Isobars — same $A$: ${}^{40}\mathrm{Ar}$, ${}^{40}\mathrm{K}$, ${}^{40}\mathrm{Ca}$.
- Isotones — same $N$: ${}^{14}\mathrm{C}$, ${}^{15}\mathrm{N}$, ${}^{16}\mathrm{O}$ ($N = 8$).
- Isomers — same $Z$ and $A$, but one nucleus is in a long-lived excited state: ${}^{99m}\mathrm{Tc}$ ($T_{1/2} = 6$ h) and ${}^{99}\mathrm{Tc}$.
- Mirror nuclei — isobars with $Z$ and $N$ interchanged: ${}^{3}\mathrm{H}$ and ${}^{3}\mathrm{He}$, ${}^{13}\mathrm{C}$ and ${}^{13}\mathrm{N}$.
On the interactive timeline on the lecture page follow the discoveries in order, and in the scale model compare sizes from the proton to the Universe with the zoom.
Key concepts
- Stages: radioactivity (1896) → nucleus (1911) → neutron (1932) → fission (1938) → quarks (1964) → Standard Model.
- Scales: 1 fm = 10⁻¹⁵ m, 1 b = 10⁻²⁸ m², 1 u = 931.494 MeV/c², ħc = 197.3 MeV·fm.
- Nuclear energies (MeV) are ~10⁶ times larger than chemical ones (eV).
- Nuclide ${}^{A}_{Z}X$; isotopes, isobars, isotones, isomers, mirror nuclei.