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Book page 288 - 490

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©cgrahamphysics.com 2016

Pair production and annihilation • All particles have anti particles of

Identical mass and 1

2 spin

Opposite charge

• Antiparticles have opposite charge, lepton number, baryon number and strangeness

• Electrical neutral bosons and mesons are their own antiparticles


History • 1928: Paul Dirac

• 1932: Carl Anderson

• Cosmic radiation traveling through a bubble chamber during pair production split up into electron path and path with same mass as electron but opposite direction

• Positron was discovered • In 1959 antiproton was discovered

Particle with same mass but opposite charge might exist in the Universe


Pair production • In the strong field close to the nucleus a

photon of the right energy can turn into a particle and its antiparticle

• I.e. a proton and antiproton

• They always come in pairs to conserve charge, L and B and strangeness


Feynman diagram

• Since particle and antiparticle have the same mass:

photon must have enough energy to create both masses

• The minimum energy needed to create the mass is 𝐸 = 2𝑚𝑐2

• m = rest mass of particle / antiparticle


Example • The following figure is a sketch of the path of the pair

production of an proton and antiproton. There is a magnetic field pointing out of the page.

• (a) Explain which of the tracks is due to the antiproton, A or B.

• (b) Deduce whether the particles have the same energy.

• (c) Calculate the minimum energy required for the pair production in GeV.

a) Use RHR to show A is an antiproton b) No, they have different radii

they have different speeds and different KE

c) 𝐸𝑚𝑖𝑛 = 2𝑚0𝑐2

= 2𝑥1.673 × 10;27 × 9 × 1016

=3.01 × 10;10

1.6 × 10;19 = 1.9𝐺𝑒𝑉


Feynmann diagram

• In this case gamma photon must at least have energy of 1.02MeV, which is twice the rest energy of an electron

• Photon energy in excess is converted to KE of 𝑒: 𝑎𝑛𝑑 𝑒; pair and the original electron


Orbital electrons • Pair production can also occur

near orbital electrons

• more energy is needed

• electron itself gains momentum and KE

• Pair production near atomic electron photon is non ionizing, leaves no trace

• Newly formed electron and positron are spiraling in opposite directions in a magnetic field

• Recoiling electron gains large amount of KE hardly bends in magnetic field bends slightly in same direction as new electron

• Threshold energy needed for this pair production 𝐸𝑚𝑖𝑛 = 4𝑚0𝑐

2 = 2.04MeV • Equation for this interaction:

𝛾 + 𝑒; → 𝑒; + 𝑒; + 𝑒: ©cgrahamphysics.com 2016

Annihilation

• Matter collides with its corresponding antimatter

• Both particles are annihilated

• Two gamma rays with same energy but with a direction at 1800 to each other are produced

• Pair annihilation

• Momentum is conserved

• Energy – positron annihilation gives energy equal to 𝐸 = 𝑚𝑐2

• The energy is released in form of gamma rays ©cgrahamphysics.com 2016

• Energy released is higher if particles annihilate in a collision

• One or both particles contribute KE

• Sometimes a pair of particles annihilate, but then one of the photons produces another pair of particles

• The new photon has a “clean slate” – it does not have any charge, baryon or lepton number, etc

• Any pair of particles can emerge

• 𝑒; + 𝑒: → 𝛾 → 𝑒; + 𝑒:

• 𝑒; + 𝑒: → 𝛾 → 𝜇; + 𝜇:

• 𝑒; + 𝑒: → 𝛾 → 𝜏; + 𝜏:

• 𝑒; + 𝑒: → 𝛾 → 𝑞 + 𝑞


Interactions • Not always is EM radiation produced

• Quarks interact with each other more readily via the strong force

• If quark and antiquark annihilate, a burst of strong force energy is produced in form of strong force exchange particles

• 𝑞𝑎 + 𝑞𝑎 → 𝑔𝑙𝑢𝑜𝑛 → 𝑞𝑏 + 𝑞𝑏

• Gluon will convert back into quarks

• This does not have to be the same quark


Feynman diagrams for pair production and annihilation

• Backward arrow is antiparticle

• Time progressing upward

• If enough energy available, other particles than photons can be produced


Review the Bohr model for hydrogen

• Postulate

1. electrons travel in certain allowed orbits. As long as they stay in these orbits, they will not radiate energy

2. Allowed orbits have radii 𝑟𝑛. For Hydrogen 𝑟𝑛 = 0.53 × 10;10 𝑛2, where n = 1, 2, 3…..

3. Allowable orbits have angular momentum (mvr)

given by 𝐿 = 𝑚𝑣𝑟𝑛 =𝑛ℎ

2𝜋

m = mass of electron 𝑟𝑛 = 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑜𝑟𝑏𝑖𝑡 v = velocity n = 1, 2, 3… ©cgrahamphysics.com 2016

Postulates continued

4. Allowable orbits have energy 𝐸 =𝑘

𝑛2 .

For 𝐻2 k = - 2.18× 10;18𝐽 𝑜𝑟 − 13.6𝑒𝑉 Negative because energy of electron at rest outside an

atom is taken to be zero When electron ‘falls’ into an atom, energy is lost as EM

radiation Electrons passing from higher to lower energy level, the

lower the energy level, the larger the negative energy value Ionization energy: amount of energy required to remove an

electron from an energy level to infinity Maximum ionization energy to remove electron from

ground state to infinity is given by 𝐸 =

13.6𝑒𝑉

𝑛2 ©cgrahamphysics.com 2016

Postulate 5 • Electrons fall between energy levels lose energy as

photons

Energy of photon is equal to energy difference between orbits

∆𝐸 = 𝐸1 − 𝐸2 (E upper – E lower)

E = hf

Frequency corresponds to lines in emission spectrum


Pair production and Heissenberg’s uncertainty principle

∆𝐸∆𝑡 ≥𝑕

4𝜋

Threshold energy for 𝑒: − 𝑒; production is 1.02MeV in the presence of a heavy nucleus Suppose • 10eV photon in vicinity

of heavy nucleus • Electron – positron

pair produced • Short time later they

collide and annihilate, producing two photons of 5eV • Is this a violation of the mass – energy conservation?


Uncertainty principle

• It allows the positron – electron production

• During the life time of 𝑒: − 𝑒; there is uncertainty of total energy

• If uncertainty was equal to 1.02MeV, what would be the limit of the life time of the pair?

• ∆𝑡 can be calculated

• ∆𝑡 =ℎ

∆𝐸4𝜋=

6.63×10−34

1.02×106×1.6×10−19×4𝜋= 3.2 × 10;22𝑠

• This life time is so short that a measurement of the energy of the pair would have an uncertainty of at least 1.02MeV

• The experiment would not be able to detect the violation of the conservation law


Consequence

• If we cannot perform an experiment to detect a violation of a conservation law then quantum mechanics says:

There is some probability of the process occurring

Nature will cheat if it can get away with it


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