Pair production and annihilation

18 Pages·2016·0.76 MB·English

by  Corinna Graham

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Book page 288 - 490 ©cgrahamphysics.com 2016
Pair production and annihilation
• All particles have anti particles of
1
Identical mass and spin
2
Opposite charge
• Antiparticles have
opposite charge, lepton number,
baryon number and strangeness
• Electrical neutral bosons
and mesons are their
own antiparticles
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History
• 1928: Paul Dirac

• 1932: Carl Anderson

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

• 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
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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
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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
2
mass is 𝐸 = 2𝑚𝑐
• m = rest mass of particle /
antiparticle
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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) Use RHR to show A is an antiproton
b) No, they have different radii
 they have different speeds

and different KE
c) 𝐸 = 2𝑚 𝑐2
𝑚𝑖𝑛 0
= 2𝑥1.673 × 10;27 × 9 × 1016
3.01 × 10;10
= = 1.9𝐺𝑒𝑉
1.6 × 10;19

• (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.
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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
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Orbital electrons
• Pair production can also occur • Pair production near atomic
near orbital electrons electron
 photon is non ionizing, leaves
•  more energy is needed
no trace
•  electron itself gains
• Newly formed electron and
momentum and KE
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
2
for this pair production 𝐸 = 4𝑚 𝑐 = 2.04MeV
𝑚𝑖𝑛 0
• Equation for this interaction:
; ; ©cgrah;amphysics.:com 2016
𝛾 + 𝑒 → 𝑒 + 𝑒 + 𝑒
Annihilation
• Matter collides with its corresponding antimatter
• Both particles are annihilated
• Two gamma rays with same energy but with a
0
direction at 180 to each other are produced
• Pair annihilation
• Momentum is conserved
• Energy – positron
annihilation gives energy
2
equal to 𝐸 = 𝑚𝑐
• The energy is released in form of gamma rays
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• 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
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