Topic 8: Nuclear and particle physics  

1. The language of atom:

• Thermionic emission – electrons leaving a hot metal surface.
• These electrons can be accelerated by electric and magnetic fields, which enables the ratio of their charge to mass, e/m to be determined.
• The evidence for the very small positive nucleus at the centre of an atom came from experiments performed at Manchester University in 1913.
• The experiments involved alpha particles that were fired at gold foil and found to be scattered in a special manner.
• – The proton number (or atomic number) Z denotes the number of protons in an atomic nucleus of a given element (and is also the number of electrons in a neutral atom of that element), e.g. for gold Z = 79.
• – The neutron number N denotes the number of neutrons in the nucleus of an atom, e.g. for gold N = 118.
• – The nucleon number (or mass number) A denotes the total number of protons and neutrons in the nucleus of an atom, e.g. for gold A = 197.
• Atomic nuclei are represented by their symbol, with the proton number at bottom left and the nucleon number at top left, e.g.[math] _{79}^{197}\text{Au}\ \, \text{or } _{6}^{12}\text{C}\ [/math]
• 
• These symbols and numbers are also used to represent nuclides the nucleus plus its electrons.
• Most elements have at least one stable nuclide plus several unstable nuclides.
• Nuclides of the same element are called isotopes, and have different nucleon numbers A because
• A = Z + N
• For example, for the only stable isotope of gold:
• A(197) = Z(79) + N(118)
• For one of the unstable isotopes of gold:
• A(196) = Z(79) + N(117)
• Unstable isotopes decay to stable ones with characteristic half-lives on nuclear decay.
• In the process they emit alpha ( α ), beta ( β ) and gamma ( γ ) radiations.

2. Alpha particle scattering:

• The material of the nucleus is very dense – about [math] 10^{16} \text{kgm}^{-3}[/math]. When α – particles from a natural radioactive source were fired at a very thin sheet of gold.
• Most passed through undeflected from their path; other were deflected though small angles.
• A tiny fraction fewer than 0.01% of the α – particles were deflected by more than 90°, and from this unexpected scattering the physicist Ernest Rutherford was able to confirm the nuclear model of the atom with its tiny, massive, charged nucleus.
• He was further able to calculate a rough value for the diameter of the nucleus.
• Figure 1a shows a modern version of the experiment.
• The paths of three α – particles that pass just above and very close to a gold nucleus are shown in Figure 1b.
• Figure 1 α – particles  scattering; a) The apparatus b) Some α – particles paths
• Rutherford was later able to establish conclusively that α – particles, when they gain electrons, are atoms that emit a spectrum exactly like the element helium.
• In the Rutherford and Royds experiment, the wall of capsule A was only 0.01mm thick, and the compression of the gas in capsule A was only performed after six days!
• To ensure it was a ‘fair test’, capsule A was leter filled with helium gas, but no helium was found in capsule B, even after several days.

3. Thermionic emission:

• When a piece of metal is heated to a high temperature, negatively charged electrons ‘bubble’ out of its surface.
• Of course, they will be attracted back to the surface by the positively charged protons they leave behind.
• But if a positively charged plate is placed near the piece of metal in a vacuum, the electrons accelerate towards it and can be made into a narrow beam. In this arrangement, called an electron gun, the metal is usually heated by a resistor (connected to a 6V supply) placed behind it and the narrow beam is produced by making a small hole in the positive plate (which is at a potential of about +2000V).

– Force on an electron in an electric field [math] F_E = eE [/math] parallel to the field.
– Force on an electron moving in a magnetic field [math] F_E = Bev [/math] perpendicular to the field.

Figure 2 An electron beam made visible

• In Figure 2 the electrons are projected horizontally to the right from an electron gun in a magnetic field that is directed out of the plane of the photo.
• As electrons are negatively charged, the left-hand rule shows that the Bev force is centripetal and remains so as the electrons move round part of a circle.

4. The role of electric and magnetic fields in particle accelerators and detectors:

• Applying Newton’s second law to an electron in the beam
• By using the centripetal force and electromagnetic force
• [math] \begin{gather*}
  F_c = \frac{mv^2}{r} \qquad (1) \\
  F_B = Bev \qquad (2) \\
  \text{Comparing these equations:} \\
  \frac{mv^2}{r} = Bev \\
  mv = Ber \qquad (3)
  \end{gather*} [/math]
• As [math]mv = p [/math], the momentum of the electron, then
• [math] p = Ber \\
  r = \frac{p}{Be} [/math]
• This tell us that the radius of the circle in which the electron moves is proportional to the momentum with which the electron is fired.
• By using the equation 3
• [math] \begin{gather*}
  mv = Ber \\
  \frac{v}{r} = \frac{Be}{m} \qquad (4)
  \end{gather*} [/math]
• By using the angular velocity
• [math] \begin{gather*}
  v = r \omega \\
  \omega = \frac{v}{r} \\
  \omega = 2 \pi f
  \end{gather*} [/math]
• Substitute in equation 4
• [math] \begin{gather*}
  \omega = \frac{Be}{m} \\
  2\pi f = \frac{Be}{m}
  \end{gather*} [/math]
• So, the frequency at which the electron circles does not depend on its initial momentum, and hence on its initial kinetic energy, provided its mass remains constant. This is key to the cyclotron.

• ⇒The cyclotron:

• A cyclotron is used to force charged particles into a circular path that accelerates them to very high speeds.
• Cyclotrons are often used with heavier particles like alpha particles and protons.
• Experiments using particle accelerators investigate the structures of complex molecules like proteins, as well as sub-nuclear structures.
• The cyclotron is formed from two semi-circular ‘dees’, separated by a small gap and connected to a high- frequency alternating potential difference (Figure 3).
• 

  Figure 3 Structure of a cyclotron, a proton accelerator.

• A strong magnetic field is applied perpendicular to the dees. The perpendicular magnetic field forces charged particles to move in a circular path inside the dees.
• The particles experience a potential difference when they travel across the gap, and gain energy equal to QV (where is the particle’s charge in coulombs, and V is the potential difference in volts).
• Since the particles have more kinetic energy, they move faster and accelerate to the next dee.
• The ac voltage is timed to change direction every time the particles reach the gap between the dees.
• It must alternate to accelerate the particles each time they reach a gap.
• If the voltage did not alternate, the particles would follow a cycle of accelerate-decelerate-accelerate.
• Particles spend the same time inside each dee, but the radius of their path increases after each gap and they travel further in the same time.

• ⇒Linear acceleration:

• To accelerate protons (or other charged particles) to energies beyond this, a linear accelerator or linac, of a different design detail for each particle, is used.
• In the electron linac, shown in Figure 4, the electrons are given energy as they pass between charged metal tubes.
• As in a cyclotron, the energy is delivered to the charged particles by the electric field in the small gap between the tubes.
• Figure 4 An electron linac
• The tubes are connected to a high-frequency alternating voltage supply. and the lengths of the tubes are calculated so that there is always a positive charge, as seen by the accelerating electrons, on the ‘next’ tube.
• In this way a bunch of electrons fired by the electron gun is attracted to the first tube but while it is in that tube the charge on the next tube again becomes positive, thus attracting the bunch leaving the first tube; and so on.
• The length of the tubes increases as the speed of the bunch of electrons increases so that the time the electrons spend in each tube is the same.
• In any one tube the electrons travel at a steady speed they drift – there being no electric field inside the metal tubes. This is also the case for charged particles while they are inside a Dee in the cyclotron.
• Electron linacs are now routinely used in hospitals to produce beams of high-energy electrons. When the beam hits a tungsten target the result is a beam of X-rays see Figure 4.

5. Charged particle in a magnetic field:

• The equation you’re referring to is the Lorentz force equation, which describes the motion of a charged particle in a magnetic field. The equation is:
• [math] r = \frac{P}{BQ} [/math]
• Where:
  – r is the radius of the circular path
  – P is the momentum of the particle
  – B is the magnetic field strength
  – Q is the charge of the particle
• To derive this equation, we can start with the Lorentz force equation:
• [math] F = Q \left( E + \mathbf{v} \times \mathbf{B} \right) [/math]
• Since the particle is moving in a circular path, the force is centripetal, and we can write:
• [math] F = \frac{P^2}{r} [/math]
• Equating the two expressions, we get:
• [math] \frac{P^2}{r} = Q (E + v * B) [/math]
• Since the electric field E is zero in this case (assuming a uniform magnetic field), we can simplify to:
• [math] \frac{P^2}{r} = Q (v * B) [/math]
• Using the definition of cross product, we can rewrite:
• [math] \frac{P^2}{r} = Q (vB sinθ) [/math]
• Since the particle is moving perpendicular to the magnetic field (θ = 90°), sinθ= 1, and we get:
• [math]  \frac{P^2}{r} = Q ( vB ) [/math]
• Rearranging, we finally get:
• [math] r = \frac{P}{BQv} [/math]
• This equation describes the radius of the circular path of a charged particle in a magnetic field. It’s a fundamental concept in particle physics and has numerous applications in fields like particle accelerators and plasma physics.

6. Conservation of charge, energy and momentum to interactions:

• Conservation of charge, energy, and momentum are fundamental principles in physics that apply to interactions between particles.
  1. Conservation of Charge: The total charge of a closed system remains constant before, during, and after an interaction.
  2. Conservation of Energy: The total energy of a closed system remains constant, but can be converted between different forms (e.g., kinetic energy, potential energy, thermal energy).
  3. Conservation of Momentum: The total momentum of a closed system remains constant, but can be transferred between particles or converted between different forms (e.g., linear momentum, angular momentum).
• When interpreting particle tracks, these principles help us understand the interactions and properties of particles.
• Some common particle tracks and their interpretations include:
  – Straight tracks: Indicate a stable particle (e.g., electron, muon).
  – Curved tracks: Indicate a charged particle in a magnetic field (e.g., electron, proton).
  – Vertex: Indicates an interaction point (e.g., collision, decay).
  – Decay tracks: Indicate a particle decay (e.g., beta decay, hadronic decay).
• By applying conservation principles and analyzing particle tracks, we can gain insights into the properties and behaviors of subatomic particles and forces.

7. Structure of nucleon:

• High energies are required to investigate the structure of nucleons (protons and neutrons) because:
  1. Small size: Nucleons are extremely small, on the order of [math]10^{-15} [/math] meters. To probe such small distances, high-energy particles are needed to “resolve” the nucleon’s structure.
  2. Strong nuclear force: The strong nuclear force holds quarks together inside nucleons. High energies are required to overcome this force and probe the nucleon’s internal structure.
  3. Quark confinement: Quarks are never found alone, but are always bound inside hadrons (like nucleons). High energies are needed to “break” this confinement and study quark properties.
  4. Resolution: High energies provide the necessary resolution to study the nucleon’s structure. Think of it like a microscope: higher energies = higher magnification.
  5. Particle production: High energies allow for the creation of new particles, which helps us understand the nucleon’s composition and properties.
• Figure 5 Structure of nucleon
• To achieve these high energies, particle accelerators like the Large Hadron Collider (LHC) accelerate particles to nearly the speed of light, then collide them. By analyzing the collision products, scientists can infer the properties of nucleons and their constituents.
• Remember, high energies are needed to “probe” the tiny distances and strong forces that hold nucleons together. It’s like using a powerful tool to study a tiny, intricate structure.

8. Einstein’s equation:

• The equation
• [math] ∆E = c^2 ∆m [/math]
• relates to the energy-mass equivalence, where:
• ∆E = change in energy
• c = speed of light (approximately [math] 3 \times 10^8 [/math] meters per second)
• ∆m = change in mass
• This equation shows that mass and energy are interchangeable. In situations involving the creation and annihilation of matter and antimatter particles, this equation is crucial.
  1. Particle-antiparticle creation: When a photon (light particle) with sufficient energy (∆E) interacts with a nucleus or a particle, it can create a particle-antiparticle pair (e.g., electron-positron). The mass of the created particles (∆m) is equivalent to the energy of the photon.

     [math] ∆E = c^2 ∆m [/math]

  2. Particle-antiparticle annihilation: When a particle and its antiparticle collide, they annihilate, releasing energy (∆E) equivalent to their combined mass (∆m).

     [math] ∆E = c^2 ∆m [/math]

  3. Mass-energy equivalence: In nuclear reactions or particle decays, a small amount of mass (∆m) can be converted into a large amount of energy (∆E), and vice versa.
• Figure 6 Proton-antiproton and electron-positron annihilation
• Remember, this equation shows that mass and energy are two sides of the same coin. In high-energy particle interactions, it’s essential to consider both aspects.

9. [math] \text{MeV and GeV (energy) and } \frac{\text{MeV}}{c^2}, \frac{\text{GeV}}{c^2}[/math] (mass) and convert

• MeV (Mega-electronvolts) and GeV (Giga-electronvolts) are units of energy, commonly used in particle physics.
• Energy unit:
  – 1 MeV = [math]10^6 [/math]  eV (electronvolts)
  – 1 GeV = [math]10^9 [/math] eV
• These units represent energy values in high-energy physics, such as particle collisions or decays.
• To convert between energy units:
  – 1 MeV = [math]1.602 \times 10^{-13} [/math] Joules (SI unit)
  – 1 GeV = [math]1.602 \times 10^{-10} [/math] Joules
• Mass units:
• [math] \frac{\text{MeV}}{c^2} \text{ and } \frac{\text{GeV}}{c^2} [/math] are units of mass, where c is the speed of light.
  – 1 [math] \frac{\text{MeV}}{c^2} = 1.783 \times 10^{-30} \text{ kg (SI unit) } [/math]
  – 1 [math] \frac{\text{GeV}}{c^2} = 1.783 \times 10^{-27} \text{ kg}  [/math]
• To convert between mass units:
  – 1 proton mass (mp) ≈ 938.27 [math] \frac{\text{MeV}}{c^2} [/math]
  – 1 proton mass (mp) ≈ 0.93827 [math] \frac{\text{GeV}}{c^2} [/math]
• Some examples to practice:
  – Convert 500 MeV to Joules: [math] 500 \, \text{MeV} \times \left(1.602 \times 10^{-13} \, \text{J}/ \text{MeV}\right) = 8.01 \times 10^{-11} \, \text{J}[/math]
  – Convert 2  [math]\frac{\text{GeV}}{c^2} \times \left(1.783 \times 10^{-27} \, \frac{\text{kg}}{\left(\text{GeV} / c^2\right)}\right) = 3.566 \times 10^{-27} \, \text{kg} [/math]
• These units represent mass values in high-energy physics, using the famous equation
• [math] E = mc^2 [/math]
• By dividing energy units (MeV or GeV) by [math] c^2 [/math], we can express mass in these convenient units.

10. The relativistic increase in particle lifetime is significant:

• The relativistic increase in particle lifetime is significant in situations where:

• ⇒ High-speed particles:

• “Particles moving at a significant fraction of the speed of light, such as in particle accelerators or cosmic rays”.
• When particles move at a significant fraction of the speed of light, their lifetime appears to increase due to time dilation.
• This effect becomes more pronounced as the particle’s speed approaches the speed of light.
  – A high-speed particle is like a clock ticking very fast.
  – From the particle’s perspective (its “rest frame”), the clock ticks normally.
  – But from our perspective (the “observer frame”), the clock appears to tick slower due to time dilation.
  – This means the particle’s lifetime appears longer to us than it would if it were at rest.
• In particle physics, this effect is significant for particles like:
  – Muons (which decay into electrons, neutrinos, and antineutrinos)
  – Pions (which decay into muons, neutrinos, and other particles)
  – Kaons (which decay into pions, muons, and other particles)
• These particles have relatively short lifetimes, but when moving at high speeds, their lifetime appears to increase, allowing them to travel farther and interact more before decaying.

• ⇒ Short-lived particles:

• “Particles with very short lifetimes (e.g., muons, pions) that decay quickly in their own rest frame”.
• These particles have extremely short lifetimes, often decaying into other particles in a matter of nanoseconds or even faster.
• Due to their brief existence, short-lived particles are often difficult to study, but their properties and behaviors provide valuable insights into the fundamental forces and interactions of nature.
• Some examples of short-lived particles include:
  – Muons (lifetime: 1.5 microseconds)
  – Pions (lifetime: 26 nanoseconds)
  – Kaons (lifetime: 12 nanoseconds)
  – D mesons (lifetime: 0.4 picoseconds)
  – B mesons (lifetime: 1.5 picoseconds)
• These particles decay quickly through various channels, such as:- Weak decay (e.g., muon decaying into electron, neutrino, and antineutrino)- Strong decay (e.g., pion decaying into muon and neutrino)- Electromagnetic decay (e.g., photon decaying into electron-positron pair)

• ⇒High-energy collisions:

• “Particle collisions at high energies, where the collision products have significant kinetic energy”.
• These collisions involve particles accelerated to nearly the speed of light, then made to collide with other particles or targets.
• The resulting interactions reveal valuable information about the fundamental nature of matter and the forces that govern it.
• Figure 7 High energy collision of two protons
• High-energy collisions can:
  – Create new particles: Collision energy can convert into mass, producing new particles, such as Higgs bosons, top quarks, or even new, unknown particles.
  – Explore fundamental forces: High-energy collisions help physicists study the strong nuclear force, weak nuclear force, and electromagnetic force in extreme conditions.
  – Probe particle properties: Collisions can reveal details about particle spin, parity, and other properties.
  – Investigate the early universe: High-energy collisions recreate conditions similar to those in the universe’s first fraction of a second.
• ⇒ Particle decay in flight:
• Particles decaying while moving at relativistic speeds, leading to a longer observed lifetime.
• Particle decay in flight refers to the phenomenon where a high-energy particle decays into other particles while in motion, often over long distances.
• This occurs when a particle’s lifetime is shorter than the time it takes to travel a significant distance, leading to its decay into daughter particles.
• Particle decay in flight is important in:
  – Particle physics: Studying decay patterns and daughter particles reveals information about the original particle’s properties and interactions.
  – High-energy collisions: Decays in flight can provide insight into the collision dynamics and properties of produced particles.
  – Cosmic ray physics: Decays in flight help understand the composition and properties of high-energy cosmic rays.
  – Particle astrophysics: Decays in flight can be used to study high-energy particles from astrophysical sources.
• Some examples of particles that decay in flight include:
  – Muons: Decay into electrons, neutrinos, and antineutrinos
  – Pions: Decay into muons, neutrinos, and other particles
  – Kaons: Decay into pions, muons, and other particles
  – D mesons: Decay into kaons, pions, and other particles
  – B mesons: Decay into D mesons, pions, and other particles
• Studying particle decay in flight requires sophisticated detectors and analysis techniques to reconstruct the decay vertices and trajectories of the particles involved.
• ⇒ Cosmological scenarios:
• Particles in the early universe or in high-energy astrophysical environments.
• Cosmological scenarios involve the study of the origin, evolution, and fate of the universe on large scales. Particle decay in flight plays a crucial role in various cosmological contexts:
  – Cosmic ray physics: High-energy particles from outside the solar system interact with the atmosphere, producing secondary particles that decay in flight.
  – Particle astrophysics: Decays in flight help study high-energy particles from astrophysical sources like supernovae, active galactic nuclei, and gamma-ray bursts.
  – Early universe: Particle decays in flight during the early universe’s first fraction of a second can reveal insights into the universe’s thermal history and fundamental physics.
  – Inflationary cosmology: Particle decays in flight can be used to study the properties of particles during the inflationary epoch.
  – Dark matter: Decays in flight can be used to search for dark matter particles, which may decay into visible particles.
  – Baryogenesis: Particle decays in flight can help explain the matter-antimatter asymmetry in the universe.
  – Leptogenesis: Decays in flight can help explain the origin of the universe’s matter-antimatter asymmetry.
• In these situations, the relativistic increase in particle lifetime becomes important due to time dilation, which causes the particle’s clock to appear to run slower to an observer. This effect can lead to a significant increase in the particle’s observed lifetime.

11. Quark-lepton model particles:

• This famous experiment was performed in Manchester in 1913. In the late 1960s, a similar experiment was performed at Stanford in the USA, but this time the bombarding particles were high-energy electrons and the target was liquid hydrogen in a bubble chamber.
• At low energies, the negatively charged electrons were deflected by the protons forming the nuclei of hydrogen as if the protons’ positive charge was confined in a tiny volume (as in the a-particle scattering experiment). There was no net loss of kinetic energy, i.e. the scattering was elastic (Figure 7a).
• At high electron energies above about 6 GeV ([math] 6 \times 10^9 [/math] electron-volts) – funny things began to happen.
• Now the electron lost a lot of energy in colliding with the proton and the proton fragmented into a shower of particles rather than recoiling (Figure 7b).
• This energy-to-matter transformation meant that the collision was inelastic, hence the name ‘deep inelastic scattering’.
• The conclusion was that protons were not tiny ‘balls’ of positive charge but contained localised charge centres. The electrons were interacting with these charge centres via the electrostatic force, which is an inverse-square law force.
• Figure 8 a) Elastic and b) inelastic scattering
• The charge centres, of which there are three in the proton and also in the neutron, are called quarks. Figure 8 shows the quarks ‘inside’ a proton and a neutron. The quarks here are of two varieties:
  ‘up’ quarks with a charge [math] +\frac{2}{3} e [/math] , symbol u
  ‘down’ quarks with a charge [math] – \frac{1}{3} e [/math], symbol d
• The quarks in protons and neutrons are bound together tightly (the springs in the model shown in Figure 8 represent this), and in order to break the quarks apart very high-energy bombarding electrons are needed. However, the experimenters did not find any individual quarks in the showers of particles resulting from the inelastic collisions, and no one has yet found a ‘free’ quark. The showers of particles were mainly ‘mesons’ consisting of quark-antiquark pairs.
• Figure 9 The quarks that make up a proton and a neutron
• ⇒ Baryons:
• Baryons are composite particles made up of three quarks. The most familiar baryons are:
  – Neutrons (n): composed of two down quarks (d) and one up quark (u), denoted as (udd)
  – Protons (p): composed of two up quarks (u) and one down quark (d), denoted as (uud)
• Figure 10 Baryons of proton and neutron
• Other examples of baryons include:
  – Lambda baryons (Λ): composed of one up quark (u), one down quark (d), and one strange quark (s), denoted as (uds)
  – Xi baryons (Ξ): composed of one up quark (u), one strange quark (s), and one down quark (d) or up quark (u), denoted as (usd) or (usu)
  – Delta baryons (Δ): composed of three up quarks (u) or three down quarks (d), denoted as (uuu) or (ddd)
• Baryons are held together by the strong nuclear force, which is mediated by gluons. The strong nuclear force is what keeps the quarks inside the baryon bound together.
• ⇒Mesons:
• Mesons are composite particles made up of a quark and an antiquark. The most familiar mesons are:
  – Pions (π): composed of an up quark (u) and an antidown quark (d), or a down quark (d) and an antiup quark (u), denoted as (u-anti-d) or (d-anti-u)
  – Kaons (K): composed of an up quark (u) and an antistrange quark (s), or a strange quark (s) and an antiup quark (u), denoted as (u-anti-s) or (s-anti-u)
  – D mesons (D): composed of a charm quark (c) and an antiup quark (u) or antidown quark (d), denoted as (c-anti-u) or (c-anti-d)
  – B mesons (B): composed of a bottom quark (b) and an antiup quark (u) or antidown quark (d), denoted as (b-anti-u) or (b-anti-d)
  – Phi mesons (φ): composed of a strange quark (s) and an antistrange quark (s), denoted as (s-anti-s)
  – Rho mesons (ρ): composed of an up quark (u) and an antidown quark (d), or a down quark (d) and an antiup quark (u), denoted as (u-anti-d) or (d-anti-u).
• Figure 11 Some type of mesons
• Mesons are also held together by the strong nuclear force, which is mediated by gluons. The strong nuclear force is what keeps the quark and antiquark inside the meson bound together.
• ⇒ Leptons:
• Leptons are a class of fundamental particles that do not participate in the strong nuclear force and are not part of the quark model. They are among the most well-known particles in the Standard Model of particle physics.
• – Leptons are elementary particles, meaning they cannot be broken down into smaller particles.
  – There are six types (flavors) of leptons:
1. Electron (e-)
2. Muon (μ-)
3. Tau (τ-)
4. Electron neutrino (νe)
5. Muon neutrino (νμ)
6. Tau neutrino (ντ)
• – Leptons have no color charge, which means they do not interact with the strong nuclear force.
  – Leptons interact via the electromagnetic force (like electrons) and the weak nuclear force (like neutrinos).
  – Leptons have no internal structure; they are point-like particles.
  – Leptons are involved in various processes, such as:
  – Electromagnetic interactions (e.g., electrons and photons)
  – Weak nuclear decays (e.g., neutron decay)
  – Neutrino oscillations (flavor changes)
• Some interesting aspects of leptons include:
  – Neutrino oscillations, which show that neutrinos have mass and can change flavor
  – The electron’s antiparticle, the positron (e+), which is identical except for its opposite charge
  – The muon’s role in particle physics, serving as a “heavy electron” for studying weak interactions
  – Tau particles, which are similar to electrons but heavier and more short-lived.
• ⇒ Photon:
• Photons are massless particles that represent the quanta of electromagnetic radiation, such as light or radio waves.
• They have zero rest mass and zero electric charge, but they do have energy and momentum.
  – Photons are elementary particles, meaning they cannot be broken down into smaller particles.
  – They are the carriers of the electromagnetic force, which is one of the four fundamental forces of nature.
  – Photons have both wave-like and particle-like properties, exhibiting wave-particle duality.
  – They are created when a charged particle accelerates or decelerates, such as when an electron transitions to a lower energy level.
  – Photons are absorbed or emitted in discrete packets, called quanta, which gives rise to the concept of wave-particle duality.
  – They have a frequency (f) and wavelength (λ) related by the speed of light (c): c = fλ
  – Photons interact with matter through various processes, including:
  – Photoelectric effect: absorption by electrons
  – Compton scattering: scattering by free electrons
  – Pair production: creation of particle-antiparticle pairs

12. Every particle has a corresponding antiparticle and the properties of a particle to deduce the properties of its antiparticle:

• Every particle has a corresponding antiparticle, also known as an antimatter particle. The properties of a particle and its antiparticle are related in specific ways.
1. Charge: The antiparticle has the opposite charge. For example, the antiparticle of the electron (e-) is the positron (e+).
2. Mass: The antiparticle has the same mass as the particle.
3. Spin: The antiparticle has the same spin as the particle.
4. Lifetime: The antiparticle has the same lifetime as the particle.
5. Interactions: The antiparticle interacts with other particles in the same way as the particle, but with opposite charges and couplings.
• Using these relationships, you can deduce the properties of an antiparticle from the properties of its corresponding particle, and vice versa.
• For example, if you know the properties of the electron (e-), you can deduce the properties of its antiparticle, the positron (e+):
  – Charge: +1 (opposite of the electron’s -1 charge)
  – Mass: same as the electron’s mass
  – Spin: same as the electron’s spin ( 1/2 )
• Figure 12 Electron’s spin
• – Lifetime: same as the electron’s lifetime (stable)
  – Interactions: same as the electron’s interactions, but with opposite charges and couplings

13. Laws of conservation of charge, baryon number and lepton:

• The laws of conservation of charge, baryon number, and lepton number are fundamental principles in particle physics that help us determine whether a particle interaction is possible. Here’s how to apply them:
• Conservation of Charge: The total electric charge before and after the interaction must be the same.
• Conservation of Baryon Number: The total baryon number (number of quarks) before and after the interaction must be the same.
• Conservation of Lepton Number: The total lepton number (number of leptons) before and after the interaction must be the same.
• To determine if an interaction is possible, follow these steps:
  – Write down the initial and final particles involved in the interaction.
  – Check if the total charge, baryon number, and lepton number are conserved.
• – If any of these quantities are not conserved, the interaction is not possible.
  – If all quantities are conserved, the interaction is possible.
• Let’s practice with an example:
• Suppose we want to know if the following interaction is possible:
• [math] \text{e} + \text{(positron)} + \text{p (proton)} → \text{n (neutron)} + \text{ν (neutrino)} [/math]
• Write down the initial and final particles:
• [math] \text{Initial: e} + \text{(positron),p (proton)} \\ \text{Final: n (neutron),ν (neutrino)} [/math]
• Check conservation laws:
• – Charge: + 1 (e+) + +1 (p) = + 2 (initial) vs. 0 (n) + 0 (ν) = 0 (final) → NOT conserved
• – Baryon number: 0 (e+) + 1 (p) = 1 (initial) vs. 1 (n) + 0 (ν) = 1 (final) → Conserved
• – Lepton number:1 (e+) + 0 (p) = 1 (initial) vs. 0 (n) + 1 (ν) = 1 (final) → Conserved
• Since charge is not conserved, this interaction is NOT possible.