11. Baryons, Mesons and Particle Accelerators Flashcards
What spin do quarks have?
1/2
How many quarks do baryons have?
3
What spin does a quark pair have?
0 or 1
What is the spin of a baryon?
1/2 or 3/2
Give two examples of baryons with spin 1/2
- Proton
- Neutron
What are the allowed spin-3/2 baryons?
S = strangeness
What are the allowed spin-1/2 baryons?
S = strangeness
Why aren’t ddd, uuu, sss spin-1/2 baryons observed in nature?
The Pauli Exclusion Principle forbids more than one fermion from occupying the same quantum state.
What is the ket notation for a symmetric 2-particle wavefunction?
What is the ket notation for an antisymmetric 2-particle wavefunction?
Give the equation for the overall wavefunction of baryons
ψ = wavefunction
The 4 terms of the baryon wavefunction equation are _________.
Seperable
How can an antisymmetric total wavefunction of baryons be found based on the overall wavefunction equation?
By multiplying 3 symmetric wavefunctions by an anti-symmetric wavefunction.
Are spin wave functions symmetric or anti-symmetric on particle exchange?
Symmetric
Are spatial wave functions symmetric or anti-symmetric on particle exchange?
Symmetric
Are flavour wave functions symmetric or anti-symmetric on particle exchange?
Symmetric
Are colour wave functions symmetric or anti-symmetric on particle exchange?
Anti-symmetric
Give the equation for the flavour wavefunction of a baryon
Give the equation for the colour wavefunction of a baryon
Why is the colour wavefunction for baryons known as the colour singlet?
Because there is only one possible state. All known baryons have colour wavefunctions of this form.
State the normalised spin wavefunction for the singlet (s = 0) state
Is the singlet state wavefunction symmetric or anti-symmetric?
Anti-symmetric
State the normalised spin wavefunction for a triplet (s = 1) state
Is the triplet state wavefunction symmetric or anti-symmetric?
Symmetric
How are quarks combined to form spin-3/2 baryons with a symmetric spin wavefunction?
A quark is added to the 2 quark s = 1 triplet state, making it symmetric.
State the 4 spin wavefunctions of spin-3/2 baryons
Why are there spin-3/2 baryons with the same quark structure as protons and neutrons?
They are higher energy excited states of protons and neutrons.
How are quarks combined to form spin-1/2 baryons?
Either by adding a third quark to the 2-quark s = 1 triplet state or to the 2-quark s = 0 singlet state
State the 2 spin wavefunctions of spin-1/2 baryon from a s = 0 starting state
State the 2 spin wavefunctions of spin-1/2 baryon from a s = 1 starting state
What type of symmetry to spin-1/2 baryons have?
Partial symmetry (symmetrical on 2 out of 3 of the quarks)
Give the equation for the de Broglie wavelength
λ = de Broglie wavelength
h = Planck’s constant
p = momentum
The more energy particles have the _______ their de Broglie wavelength.
Shorter
What is the value of the speed of light?
Give the equation for the relativistic energy
E = energy
m0 = rest mass
γ = Lorenz factor
c = speed of light
Give the equation for the Lorenz factor
γ = Lorenz factor
β = v / c
v = particle velocity
c = speed of light
Give the equation for the relativistic momentum
p = relativistic momentum
m0 = rest mass
γ = Lorenz factor
β = v / c
v = velocity
c = speed of light
Give the equation for the relationship between energy and momentum
E = energy
p = momentum
c = speed of light
m0 = rest mass
What is the approximate value of β for highly relativistic particles?
β ~ 1
What is the approximate value of E for highly relativistic particles?
E ~ pc
Give the equation for kinetic energy at relativistic speeds
T = kinetic energy
E = total energy
m0 = rest mass
c = speed of light
γ = Lorenz factor
Give the equation for the Lorentz force of particles
F = Lorentz force
p = change in momentum
t = time
q = charge
E = electric field
v = particle velocity
B = magnetic field
What is 1 electron volt in joules?
What is the rest mass energy of an electron?
What is the rest mass energy of a proton?
What is the rest mass energy of a neutron
How can rest mass energies be used to see if relativistic effects are important?
The accelerator energy can be compared to the rest mass.
What does the Lorentz force describe?
The motion of a single particle with no radiation losses.
What conditions have to be true for a particle to carry out circular motion in a magnetic field?
E = 0
B ⊥ v
What can be used to determine the direction of the Lorentz force?
The left hand rule
Give the equation for the relativistic centripetal force
F = centripetal force
p = momentum
v = particle velocity
r = radius of orbit
Give the equation that relates the Lorentz force to the relativistic centripetal force
p = momentum
q = particle charge
B = magnetic field
r = radius of orbit
Give the equation for the radius of a particle’s orbit in a uniform, constant magnetic field
r = radius
p = momentum
q = particle charge
B = magnetic field
Give the equation for the time period of a particle’s orbit in a uniform, constant magnetic field
T = time period
r = radius of orbit
v = particle velocity
p = momentum
q = particle charge
B = magnetic field
m = particle mass
Give the equation for the frequency of a particle’s orbit in a uniform, constant magnetic field
f = frequency
T = time period
q = particle charge
B = magnetic field
m = particle mass
What is the problem with accelerating particles to high energies?
A large potential difference is required to generate the electric field. This can cause voltage breakdown and is dangerous.
How are higher energy electric fields produced for LINACs without using dangerous (~ MeV) voltages?
An oscillating voltage is applied to electrodes of increasing length. Every other electrode has the same voltage.
What are the advantages of a LINAC?
- No expensive magnetics needed
- No energy loss from synchrotron radiation
What are the disadvantages of a LINAC?
- Requires many structures and voltage breakdown is still an issue
- Large energy requires a long accelerator which is impractical
How does a cyclotron work?
A constant magnetic field is applied so particles orbit in a circular path. There orbit inside two semi-circular “dee’s” that an alternating electric field is applied to. When the charged particle reaches the gap, the electric field accelerates the particle. After crossing the gap the polarity of the field is reversed.
In a cyclotron, frequency is independent of _______.
Radius
What type of electric field is used in a cyclotron?
A constant frequency alternating electric field
Why does a particle spiral out to a larger radius in a cyclotron?
It gains energy (and hence momentum) which cause the radius and velocity to increase.
Give the equation for the maximum velocity in a cyclotron
v_max = maximum velocity
q = particle charge
B = magnetic field
R = maximum radius
m = particle mass
Give the equation for the maximum kinetic energy of a particle in a cyclotron at non-relativistic energies
KE_max = maximum kinetic energy
q = particle charge
B = magnetic field
R = maximum radius
m = mass
What is needed for a cyclotron to reach higher energies?
A larger radius
How do particles change at relativistic speeds?
The mass increases (m₀γ), hence, the orbital frequency changes.
How can the energy of a circularly accelerating particle be increased without increasing the radius of orbit?
- Modulating the frequency
- Increasing the magnetic field
What is a synchrotron?
A particle accelerator in which particles orbit at a constant radius. This is achieved by allowing both the magnetic field and the frequency to vary with time.
Give the equation for the relativistic energy of a particle in a synchrotron
E = energy
q = charge
r = radius
B = magnetic field
c = speed of light
m0 = rest mass
Give the equation for the frequency of a particle in a synchrotron
f = frequency
q = particle charge
B = magnetic field
m = mass
c = speed of light
r = radius
m0 = rest mass
The equation for the frequency of a particle in a synchrotron defines the relation between B and f required to __________ _____________.
Maintain synchronisation
What is the main problem with the synchrotron?
There are energy losses due to synchrotron radiation.
What type of accelerators were the first accelerators?
Fixed target accelerators
What was the main problem with the first accelerators?
Lots of the available energy was wasted in the kinetic energy of the products (in order to conserve momentum).
What type of accelerators are modern accelerators?
Colliding beam photons
What is the main problem with modern accelerators?
The beam density is typically small resulting in few collisions. This is solved by storing accelerator pulses in storage rings.
Why is particle accelerator progress slowing?
Due to the cost of making particle accelerators
