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Physics 2 > Nuclear and Particle Physics > Flashcards

Nuclear and Particle Physics Flashcards

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1
Q

plum-pudding model

A

atom was uniform distribution of positive charge with negative electrons sprinkled evenly inside

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2
Q

what did Geiger and Marsden expect when firing alpha particles at gold foil

A

electron too small to deflect so expected alpha particles to pass straight through with very slight deflection

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3
Q

what did Geiger and Marsden actually find

A

alpha particles sometimes deflected by large angles

led Rutherford to hypothesise the nucleus

foundation for Bohr model

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4
Q

for a nucleus with atomic number Z, the mass is

A

not just Z times the proton mass

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5
Q

what lead to the discovery of the neutron

A

needed neutral particle to make up the mass

used to think nucleus also contained electrons but inconsistent with quantum mechanics

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6
Q

number of neutrons N=

A

A-Z
where Z is atomic number
and A is mass number

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7
Q

we can measure nuclear masses using a

A

mass spectrometer

nuclei are charged so will bend in a magnetic field

know charge so can work out mass from how much they bend

vary magnetic field strength so only one particular mass will reach detector

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8
Q

nuclear masses are measured in

A

atomic mass units, u

1u is 1/12 the mass of the carbon-12 atom

atom not nucleus so need mass of electron too

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9
Q

how to convert nuclear mass into energy

A

E=mc^2

units of MeV/c^2

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10
Q

1eV

A

the energy an electron gains if accelerated through an electromagnetic potential of 1V

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11
Q

approximately

mp =

A

mn= 1 GeV/c^2 = 1u

neutron slightly heavier than the proton

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12
Q

nuclear masses and atomic masses are not the same because

A

atomic masses include the electrons AND atomic binding energy

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13
Q

nuclear mass =

A

atomic mass - electron mass + atomic binding energy

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14
Q

if we scatter electrons off the nucleus, they form

A

a diffraction pattern and the position of the first minimum gives us the charge radius of the nucleus

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15
Q

measuring many nuclei with atomic mass A we find their radii obey the rule

A

R=R0 A^1/3 with R0=1.2fm

makes sense since volume scales like R^3 and volume will scale like mass if nuclei have a constant density

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16
Q

how does nucleus stay together

A

strong nuclear force binds the protons and neutrons together

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17
Q

mass defect

A

difference between adding up masses of the protons, neutrons and electrons, and the atomic number

this is the energy that is used to bind the protons and neutrons together in the nucleus

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18
Q

for a general nucleus with atomic number Z and atomic mass number A

A

mNc^2 = Zmpc^2 + Nmnc^2 - B

=Zmpc^2 + (A-Z)mnc^2 - B

where N is number of neutrons and B is the nuclear binding energy

can rearrange for B

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19
Q

why is atomic binding energy neglected

A

very small compared to nuclear binding energy

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20
Q

the more binding energy the nucleus has…

A

the more stable it will be

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21
Q

the nucleus needs more binding energy for

A

more nucleons

useful to consider the binding energy per nucleon B/A

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22
Q

most stable nucleus

A

Iron Fe

highest binding energy per nucleon

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23
Q

nuclei heavier than iron

A

want to break apart to become more stable

fission

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24
Q

nuclei lighter than iron

A

want to join together to become more stable

fusion

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25
Q

where is everything lighter than iron made

A

in stars

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26
Q

nuclide

A

a nucleus with a fixed number of protons and neutrons

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27
Q

heaviest stable nuclide

A

Pb

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28
Q

heaviest naturally occurring nuclide

A

uranium 238

unstable but half life of billions of years

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29
Q

neutrons feel the same strong nuclear force as protons but do not

A

feel electromagnetic repulsion

therefore as nuclides get heavier we need more and more neutrons for stability

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30
Q

isotope

A

nuclides with same no of protons but different no of neutrons

thus different atomic mass number

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31
Q

isobars

A

nuclides with the same atomic mass number but different numbers of protons and neutrons

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32
Q

isotones

A

nuclides with the same number of neutrons but different number of protons

thus different atomic mass number

(name isotone derived from isotope but n instead of p becasue Neutrons stay same)

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33
Q

if we exchange a proton for a neutron or vice versa

A

resulting nuclide will be unstable

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34
Q

if nuclide has too few protons

A

it will tend to beta - decay, turning a neutron into a proton

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35
Q

if a nuclide has too many protons

A

will beta + decay, turning a proton into a neutron instead

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36
Q

valley of beta stability

A

plot of beta - and beta + decay

parabola

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37
Q

the valley of beta stability is described by

A

the Bethe-Weizsäcker formula

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38
Q

semi-emirical

A

semi based on experiment

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39
Q

Bethe-Weizsäcker formula.
each term is inspired by

A

the liquid drop model, with each term’s coefficient fitted to data

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40
Q

first three terms of Bethe-Weizsäcker formula

A

volume R^3
surface R^2
coloumb 1/R

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41
Q

final two terms in Bethe-Weizsäcker formula

A

due to asymmetry and pairing

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42
Q

Bethe-Weizsäcker formula gives a parabola so can find

A

minimum by differentiating

setting mn=mp gives expected result - need roughly as many neutrons as protons to keep nucleus stable but more for larger nuclei

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43
Q

The nucleons are described by the Schrödinger
Equation with an appropriate potential. We can solve this to find…

A

the allowed energies of the nuclear states.

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44
Q

nuclear shell model - For the nuclear case, we need to find the

A

best potential. We want the nucleons to
be almost free but held together by the
potential boundary

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45
Q

nuclear shell model - a first try was

A

a square well potential but a
better try is the Woods-Saxon potential,
which has a smoother boundary

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46
Q

energy levels of the nucleus tend to

A

clump together into “shells”

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47
Q

nuclear magic numbers

A

shells occur at nucleon numbers 2, 8, 20, 28, 50, 82, 128, 184…. and a nuclide
with this number of protons or neutrons will be more stable than naively expected.

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48
Q

doubly magic

A

If a nucleus has a magic number of protons and neutrons, we say it is “doubly
magic”. For example, the 16O nucleus has 8 protons and 8 neutrons, so is doubly
magic and very stable. Our heaviest stable nuclide, lead-208, is also doubly magic

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49
Q

4 main types of nuclear reactions

A

α-radiation (4He nuclei)
* β-radiation (electrons and positrons)
* electromagnetic radiation (photons)
* neutron radiation

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50
Q

nuclear radiation is ionising radiation because

A

It can knock the atomic electrons out of their orbit around the
nucleus, resulting in charged ions and free electrons.

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51
Q

alpha radiation

A

helium nuclei

two protons, two neutrons

when emitted will change Z by 2 and A by 4

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52
Q

typical energy of alpha particle

A

3-7MeV

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53
Q

range of alpha particles

A

big and heavy so have a range of only a few cm in air

do not pass through paper

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54
Q

uses of alpha particles

A

smoke detectors
energy sources - satellites and space probes
radiotherapy

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55
Q

smoke detectors

A

Some smoke detectors use Americium-241 as an α-particle
source. The α-particles ionise the air between two charged plates
to create a current in the connected circuit. If smoke gets between
the plates, the α-particles are absorbed by the smoke instead
causing the current to stop and setting off the alarm.

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56
Q

energy sources for remote devices like satellites and space probes

A

. These convert the heat generated by the radioactive decay
into electricity via the thermoelectric (Seebeck) effect.

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57
Q

warnings for earthquakes

A

Thermal energy in the Earth’s core comes from radioactive decays of 232Th, 238U, 40K and 235U. 238U may
decay to Radon-222, which is radioactive with a half-life of 3.8235 days. Radon is a gas, so seeps out of
cracks if the molten core is close to the surface and is detected by its α-particle emissions

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58
Q

radiotherapy - alpha

A

α-particles can deposit targeted doses of energy in radiotherapy, by placing the α-source directly in the
tumour and using their short range to keep the damage localised.

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59
Q

beta radiation - 3 processes

A

beta + decay
beta - decay
electron capture `

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60
Q

beta + decay

A

proton –> neutron + positron + electron neutrino

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61
Q

beta - decay

A

neutron –> proton + electron + electron anti neutrino

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62
Q

electron capture

A

proton + electron –> neutron + electron neutrino

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63
Q

beta + decay can’t happen outside the nucleus because…

A

the neutron is heavier than the proton. In fact, the proton is
stable with a half-life > 1034 years!

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64
Q

beta particles can by stopped by

A

sheet of aluminium

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65
Q

uses for beta decay

A

positron emission tomography

paper manufacture

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66
Q

positron emission tomography (PET)

A

A patient is injected with a radioactive material that is taken up in
metabolic processes e.g. fluorodeoxyglucose containing unstable Fluorine-18. This is absorbed by the body
(as a sugar), entering the tissues and accumulating inside tumours. 18F decays to 18O via β+-decay emitting a
positron that annihilates an electron in the surrounding atoms to produce photons (e+e− → ϒϒ). The
photons are detected by the PET scanner, to provide a 3-d image of the body. Other examples are Sodium
Fluoride (again with active 18F), which enters the bones, and 15O, which is used to image blood flow.

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67
Q

paper manufacture

A

to adjust the width of the paper. Put a βemitter on one side and a Geiger-Müller tube on the
other. The β-particles are absorbed by the paper, so
the amount getting through measures the paper’s
thickness. This can be fed back to adjust the paper
rollers and keep a constant thickness.

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68
Q

photons can be ionising if

A

high enough energy such as gamma rays

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69
Q

EM radiation - gamma rays

A

typically MeV energies and are made when nuclei drop from one nuclear energy level to another

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70
Q

gamma rays need what to stop

A

thick block of lead

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71
Q

gamma rays applications

A

radiotherapy
neutron activation analysis

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72
Q

neutron activation analysis

A

uses ϒ-Ray emissions to determine the constituents of matter, similar to atomic
spectra. We bombard a material with neutrons to make unstable isotopes that decay, then use the emission of ϒRays to tell us what was present.

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73
Q

alpha particles have +ve charge so

A

bend in a magnetic field

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74
Q

beta - particles have -ve charge so

A

bend in a magnetic field, in opposite direction to alpha (beta + in same direction as alpha)

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75
Q

gamma rays are neutral

A

don’t bend in magnetic field

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76
Q

neutrons can be ejected when

A

a nucleus breaks up

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77
Q

neutron radiation like fission is energetically favourable because

A

lighter nuclei need fewer neutrons to keep them stable

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78
Q

alpha particles lose energy by

A

ionisation, knocking electrons out of their orbits

lose more energy by passing through dense materials and ionise more when travelling slowly

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79
Q

rate of energy lost with respect to distance travelled (alpha)

A

-dE/dx prop Z^2/v^2

where Z= atomic number, v=velocity of alpha particle

80
Q

Bragg peak

A

most of the energy loss will happen just before the alpha particle stops

81
Q

processes where beta particles lose energy

A

ionisation
bremsstrahlung
moller or bhabha scattering
positrons may annihilate with electrons

82
Q

bremsstrahlung

A

literally ‘breaking radiation’
radiation emitted by a charged particle undergoing a deceleration

83
Q

moller or bhabha scattering

A

electromagnetic scattering off the electrons in the material

84
Q

energy loss of x rays and gamma rays depends on

A

energy of the photons and the atomic number

85
Q

photoelectric effect

A

photon completely absorbed, giving up all its energy and knocking an electron out of its atomic orbit

86
Q

compton scattering

A

photon is not completely absorbed but is deflected with reduced energy

electron is ejected from the atom, ionising process

87
Q

pair production

A

in the electric field of the nucleus, gamma ray may have enough energy to split into an electron-positron pair

88
Q

becquerel
(Bq)

A

SI unit of radioactive activity

1 decay per second

89
Q

absorbed dose

A

energy that a material absorbs (SI unit gray)

90
Q

equivalent dose

A

takes into account the biological effect on living tissue

equivalent dose = absorbed dose x RBE

sieverts

91
Q

effective dose

A

also takes into account the type of tissue

also measured in Sv

92
Q

probability of an individual nucleus decaying in time dt is

A

constant

for N nuclei, dN=-lambda Ndt

where -lambda is the decay constant

93
Q

half life

A

time taken for sample to half

given by ln2/lambda

94
Q

probability of having any nuclei in the sample decay must be proportional to

A

the sample size

95
Q

mean life-time

A

t = 1/lambda see notes for derivation

96
Q

activity

A

number of decays per second

A(t)=lambdaN(t)

97
Q

one step decays

A–>B with B stable

A

NA+NB=N0

NA(0)=N0 and NB(0)=0

NA(t)=N0e^-lambdat

NB(t)=N0=NA(t)

98
Q

A to B or C with B and C stable

A

NA+NB+NC=N0

λA=λB+λC

see notes for full calculation

99
Q

A to B to C

A

NB(0)=NC(0)=0
NA(0)=N0

see notes for full calculation

100
Q

actinide alpha decay chains

A

thorium,uranium,neptunium,actinium series

chains of alpha and beta decays

101
Q

alpha decays always reduce

A

the atomic mass A by 4

102
Q

beta decay always reduce

A

unchanged atomic mass

103
Q

parent daughter relation for alpha and beta decays

A

Amod4 = A’mod4

A’ is daughter

104
Q

actinide alpha decay chains - atomic mass numbers differ by

A

4

105
Q

thorium series

A

4n

106
Q

uranium series

A

4n+1

107
Q

neptunium series

A

4n+2

108
Q

actinium series

A

4n+3

109
Q

thorium decays are useful for

A

determining the age of the Earth

has a very long half life and then a relatively fast decay chain to stable lead

can work out age of the rocks formed

110
Q

Q value

A

difference in kinetic energy between initial and final states

111
Q

positive Q value

A

exothermic - energy released

112
Q

negative Q value

A

endothermic - energy absorbed

113
Q

kinetic energy threshold

A

added energy must be the kinetic energy

minimum kinetic energy the particle needs to make reaction happen is the kinetic energy threshold.

114
Q

daughter nuclei particle can be produced at rest only if

A

in the centre of mass frame of the nuclei where all the momentum sum to zero

115
Q

how to work out kinetic energy threshold

A

calculate Q in the CM frame and translate to lab frame

116
Q

fission

A

breaking apart of heavy nuclei to make more stable, lighter nuclei

often triggered by hitting the nucleus with neutron or proton creating an unstable isoptope which breaks apart

117
Q

nuclear fission power plants

A

generate power via controlled fission chain reaction

energetic neutrons provide heat to boil water to make steam which turns turbine and produces electricity

118
Q

thermal neutrons

A

energies comparable to the material

want to slow down the neutrons using their extra energy to provide heat energy

do this with a moderator

control rods also used to prevent runaway reaction

119
Q

nuclear fusion

A

fuse together light nuclei to form heavier, more stable nuclei

energy source for stars

mechanism for making elements lighter than iron

120
Q

creating fusion in lab extremely difficult because

A

need to overcome electromagnetic repulsion of the nuclei to get close enough to fuse

121
Q

inertial frame of reference

A

viewpoint for taking measurements that is not accelerating

122
Q

event

A

happens at a particular point and time

123
Q

observers in s and s’ will witness the same events but

A

assign them different coordinates

124
Q

event on x-axis
coordinates in s’ will be

A

x’=x-ut
t’=t

125
Q

galilean relativity

A

differentiating terms for x’ and t’ shows acceleration same in both frames

newton’s laws of motion are the same

126
Q

postulates of SR

A
  1. laws of physics the same in all inertial reference frames
  2. speed of light the same in all inertial reference frames
127
Q

deriving time dilation

A

bouncing light off a mirror and measure time taken to come back

t=2d/c

for moving, mirror has moved ut’ so t’=2l/c= 2/c sqrt(d^2+(ut’/2)^2)

rearrange and simplify for equation

128
Q

proper time

A

time between two events in the reference frame where they happen at the same place

129
Q

proper length

A

length of object at rest

130
Q

whether events are simultaneous depends on

A

reference frame

131
Q

four vector

A

(ct,x,y,z)

132
Q

momentum four vector

A

mV=(gamma mc, gamma mv)

133
Q

standard model

A

a relativistic quantum field theory built around the symmetry

SU(3)xSU(2)xU(1)

SU(3) is strong nuclear force or quantum chromodynamics

SU(2) is weak
U(1) is EM or quantum electrodynamics

134
Q

fermions

A

quarks and leptons

135
Q

quarks

A

up, down
charm, strange
top, bottom

136
Q

leptons

A

electron, muon, tau and their neutrinos

137
Q

bosons

A

photon
gluon
w boson
z boson
higgs

138
Q

bosons are

A

force mediators exchanges between particles to transfer momentum

139
Q

h bar for bosons

A

integer multiple

W,Z, photon and gluon have spin 1
H has 0

140
Q

h bar for fermions

A

half-integer multiples

all SM fermions have spin 1/2

141
Q

helicity

A

component of spin in its direction of motion

142
Q

right handed particle

A

spin vector in its direction of motion

143
Q

left handed particle

A

spin vector against its direction of motion

144
Q

proton

A

uud

145
Q

neturon

A

udd

146
Q

charge of up quark

A

+2/3

147
Q

charge of down quark

A

-1/3

148
Q

each fermion comes with

A

antimatter partner

same pass but opposite quantum numbers

149
Q

if an electron and positron come into contact

A

they annihilate, turning all their mass into photons

150
Q

noether’s theorm

A

any symmetry in physics gives a conservation law

151
Q

strong force

A

SU(3)
gluon
conserved colour

152
Q

electromagnetism

A

U(1)
photon
conserves electric charge

153
Q

weak force

A

SU(2)
W,Z bosons
conserves isospin

154
Q

gravity

A

graviton
conserves energy/momentum

not included in SM

155
Q

quantum gravity

A

quantum mechanics version of GR where mediator is a spin-2 particle called the graviton

156
Q

the strong force binds

A

quarks together to form protons and neutrons

residual force binds protons and neutrons into the nucleus

157
Q

quantum chromodynamics

A

red, blue, green

colourless if one of each colour

anti-quarks have anti-colour so quark, anti-quark pair is also colourless

158
Q

the gluon changes

A

the colours of the quarks

159
Q

gluon must also have colour and emit/absorb other gluons

so

A

QCD force weak at high energies and strong at low energies

160
Q

asymptotic freedom

A

quarks in bound states are almost free

161
Q

difference in W and Z bosons

A

W bosons have electric charges while Z bosons are neutral

162
Q

weak force is odd because

A

it only couples to left handed fermions

163
Q

baryons

A

bound states of three quarks, each of different colour

eg: protons

164
Q

mesons

A

bound states of quark and antiquark

eg: pion

165
Q

total spin

A

J=L+S

angular momentum + quark spin

166
Q

for lightest states, take L=0 so J=S

two possible configurations of spin:

A

spins all in the same direction to give J=3/2
one spin in the opposite direction to give J=1/2

167
Q

J=3/2 baryon decuplet

A

more u to the right
more s as you go down

upside down trianlge - point is sss

168
Q

J=1/2 baryon octet

A

corner states uuu,ddd,sss missing

the uds has two separate states

169
Q

fermion states must have

A

an antisymmetric wavefunction under the exchange of quarks

170
Q

for J=3/2, all the spins

A

point in the same direction so spin is symmetric in interchange of quarks

(states like sss are also symmetric in flavour so allowed)

171
Q

for J=1/2 one spin

A

points the wrong way so spins are not symmetric and symmetric flavour combinations like sss are not allowed

172
Q

mesons must be

A

the same colour

eg red and anti-red

173
Q

pseudoscalar mesons

A

J=0

174
Q

vector mesons

A

J=1

175
Q

charge conjugation

A

exchange particles and antiparticles

swaps all charges too eg Q to -Q and red to anti-red

conserved by QED and QCD but violated by the weak interaction

176
Q

parity

A

change the sign of all space-coordinates

this will also invert all velocities/momenta

conserved by QED and QCD but violated by the weak interaction

177
Q

Wu experiment

A

parity violation in the weak interaction was demonstrated using beta decay of cobalt

magnetic field generated by solenoid to align nuclear spin

if parity conserved, particles emitted in direction of nuclear spin and in opposite direction should be same

178
Q

time reversal

A

change the sign on the time coordinate

also changes direction of motion (since v=dx/dt)

conserved by QED and QCD but violated by the weak interaction

179
Q

CP

A

weak interaction also violates this combinations

180
Q

CPT

A

could be conserved

Luders-Pauli theorem

181
Q

feynman diagram rules

A

time flows from left to right

fermions=solid line, photons/bosons=wavy line, gluon=curly, higgs=dashed

fermions have arrow in direction of particle flow, antiparticles have arrow pointing against their direction of motion

if vertical, considering emission and absorption

182
Q

steps to draw feynman diagram

A

draw initial particles on left, final particles on right and connect them using only lines and vertices in legal ways

183
Q

the QED vertex

A

cannot change the flavour or charge of the fermion

184
Q

QCD vertex

A

like QED, cannot change flavour/electric charge

185
Q

weak interaction vertex

A

W bosons can change fermion flavour
z bosons cannot change flavour or charge

186
Q

spectators

A

when before=after

187
Q

if fermions are massless, they

A

travel at c and cannot be overtaken - their helicity becomes fixed and there is no ambiguity

188
Q

above around 250GeV

A

gauge symmetries are exact and all particle are massless

189
Q

below around 250GeV

A

electroweak symmetry breaks, giving mass to the W/Z bosons and fermions

190
Q

the higgs mechanism

A

usually energy in field increases with square of field

system wants to be at minimum energy

particle is an oscillation of the field about this minimum

191
Q

the second derivative wrt the field at the minimum gives

A

the mass-squared for a boson or the mass for a fermion

192
Q

the higgs field has

A

isospon and hypercharge

193
Q

the higgs field permeates the

A

entire universe so everywhere W and B go, will be forced to interact with background higgs field which slows them down

194
Q

higgs field analogy

A

higgs field is like universe being filled with treacle

objects move through the treacle will be slowed down depending on how much they stick to the treacle

195
Q

higgs boson

A

height of valley Q

if E>Q, particle doesn’t ‘see’ bump and is still symmetric about 0

once particle E<Q, particle falls to minimum and breaks symmetry

196
Q

LHC

A

magnets used to accelerate protons

collide at 4 points and 4 experiments used to analyse the collision data

197
Q

Yukawa couplings

A

the coupling of the Higgs to fermions needs to be put in by hand

Physics 2 (8 decks)

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