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143 Cards in this Set
- Front
- Back
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What is an isotope?
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Two atoms with the same atomic number Z but different masses A
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What is an isobar?
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Two atoms with the same mass number A but different atomic numbers Z
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In the SEMF, what is the characteristic of a stable isobar?
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The mass does not change with atomic number Z for a given value of A
dM/dZ |A = 0 |
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What is the binding energy of a nucleus B?
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The energy required to separate the nucleons to infinity.
It is the total internal energy of the nucleus due to the strong nuclear force, the coulomb force and the kinetic energy of the nucleons. It is given by - Δmc^2 - the difference in mass of the bound and unbound states ΔM(Z,A) = M(Z, A) - Zmp - Nmn; -ΔMc^2 is the binding energy |
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What is the meaning of B/A?
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The binding energy divided by the total number of nucleons
. Dominated by surface tension for small nuclei and coulombic repulsion for large. Derived by considering the difference in energy between M(Z, A) = Zmp + Nmn - B (Z,A) and the equivalent for M(Z, A-1) |
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What does a graph of B/A vs A for stable nuclei look like?
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A steep upward curve to Fe56 at the peak, with a shallower fall off after this.
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What is the relationship between surface/volume and binding energy?
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Larger nucleus => larger volume => larger coulombic repulsion BUT further distance apart
Smaller nucleus => larger relative surface area => smaller strong force between neighbours |
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What is a magic/double magic nucleus?
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Magic: The number of protons or neutrons forms fulls shells.
Doubly magic: Both protons and neutrons form full shells. |
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Why are even-even nuclei are stable against β-decay?
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They have an additional pairing compared to odd-odd nuclei.
Thus they are unlikely to β-decay into an odd-odd at lower binding energy. even-even parabola lies lower than odd-odd and stable nuclei won't make upward jumps. |
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What is the difference between fissile and non fissile materials?
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Fissile materials are able to sustain a chain reaction from low energy neutrons.
Non-fissile materials cannot sustain a chain reaction even though they may be fissionable. |
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What is the critical value for a chain reaction?
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k = f-l =1 where f = number of neutrons produced in a fission event and l = number of neutrons lost through non-fission events.
OR k = no. of neutrons in (n+1)th fission stage/no. of neutrons in nth fission stage = 1 |
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Give two ways that a chain reaction can be induced in natural uranium.
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Enrichment or use of a moderator to thermalise neutrons (deuterium or graphite)
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Explain the idea of a fast breeder reactor.
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The fuel is a mixture of 20% fissile Pu-239 and non-fissile U-238.
Fission is induced using fast neutrons. Neutron capture produces Pu-239 from the U-238. The reactor produces more fuel than it uses. |
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Why is the decay of a free proton forbidden?
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A decay must conserve baryon number, since the proton is the lightest baryon it cannot decay into a heavier baryon without the addition of energy.
In a nucleus, the proton can decay into a neutron in β+ decay when the mother nucleus has less energy than the daughter nucleus. |
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What is the av term in the SEMF?
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It is the volume term, described by the liquid drop model.
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What is the as term in the SEMF?
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It is the surface term, a correction to the volume term av since outside nucleons only have half as many neighbours.
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What is the ac term in the SEMF?
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It is the coulombic repulsion term between protons, described by the liquid drop model.
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What is the aa term in the SEMF?
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It is the asymmetry term, an energy penalty from having uneven protons or neutrons, described by the fermi gas model and related to the Pauli Exclusion Principle.
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What is the δap term in the SEMF?
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It is the pairing term due to the spin-coupling, maximised for Z/N even, and is described by the shell model.
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What does the SEMF describe?
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It calculates B/A through a number of corrections to the simple binding energy calculation.
odd mass and even mass nuclei of the same A lie on different parabolas. |
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What is critical mass?
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The smallest mass of a fissile material needed for a sustained chain reaction.
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Why is spontaneous fission possible for A>100
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For A>100 the coloumb repulsion can overcome the surface tension to produce two daughters with binding energies smaller than the parent nucleus.
This is energetically allowed from binding energy alone and little quantum tunnelling is required. Smaller than A=100, the daughter nuclei will be at the other side of the Fe56 barrier with no energy advantage. |
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What is the cross section σ and differential cross-section?
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Cross-section is the area perpendicular to the beam direction.
Differential cross-section takes into account the solid angle subtended. dΩ = d(cosθ)dϕ |
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What is the range of a gluon?
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Infinite in principle, small in practice due to quark confinement.
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What are the couplings for a gluon?
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Any strong interaction OR itself, since it carries colour current.
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What interaction are neutrinos involved in?
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WEAK interaction only
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Why were neutrinos predicted?
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Mass deficit/energy conservation in positron decay spectrum.
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How is ʋ mass measured?
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Oscillation experiments which measure mass differences between the ʋ
End point of tritium β-decay spectrum 0ʋ double-β decay Cosmology (indirect) |
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What is lepton universality?
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Interactions of all 3 generations of leptons ar the same if mass difference are taken into account.
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What is the evidence for quarks?
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Hadron spectroscopy (variability and properties of hadrons)
Lepton scattering (Lepton/nucleon scattering appears to be from smaller point sources) Hadron jet production (new hadrons formed in high energy collisions as quarks recombine) |
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Which quark numbers are conserved in strong interactions?
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Individual quark number is conserved in strong interactions.
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Which quark numbers are conserved in EM interactions?
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Individual quark number is conserved in EM interactions.
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Which quark numbers are conserved in weak interactions?
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Total quark number is conserved in weak interactions.
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What quark combinations can be produced in EM interactions?
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Only quark/anti-quark pairs.
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What quark combination can be produced in strong interactions?
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Only quark/anti-quark pairs.
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What quark combinations can be produced in weak interactions?
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Any quark combinations as long as baryon number is conserved.
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How are higher state mesons generated?
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Ground state mesons have spin = 0
By changing spin and parity higher mass states or resonances are produced Resonances decay through strong interaction with very short lifetime. |
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What are the decay modes for hadrons?
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In order of lifetime, shorter to longer:
strong interaction with short lifetimes EM interaction with longer lifetimes weak interaction with much longer lifetimes. Decay type can be determined by inspecting quark number. |
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What is flavour independence in quarks?
What effect does it have? |
Strong force between quarks is independent of quark flavour (after accounting for charge and mass differences).
Creates charge multiplets: familes of particles with similar mass, spin-parity, B, S, C and ~B but different charge. e.g. Pion triplet π+ π0 π-; Nucleon doublet p/n |
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What are the advantages and disadvantages of fixed target experiments?
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+ Big targets, high rates, range of different materials
- Lower Ecm ~ √Eb |
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What are the advantages and disadvantages of colliding beam experiments?
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+ High energy Ecm = 2 Eb
- Need: stable beam particles, lower beam densities and highly focused beams. |
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What are the types of accelerator and types of accelerating field?
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In order of energy: cathode ray tube, LINAC, synchrotron
fields are always EM, they may be steady or radio frequency (RF) |
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What is a secondary beam experiment?
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Magnetic focusing of the products of a fixed-target experiment and then detecting the decay of these secondary beams.
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What types and range of particle interactions are used in detectors?
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SHORT RANGE: strong nuclear interactions (hadrons) and weak interactions (neutrinos)
LONG RANGE: ionisation and radiation energies - both EM interactions. |
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What interactions do hadrons undergo with detector materials?
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Short range interactions.
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What weak reactions occur in colliding beam experiment?
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Charge current and neutral current weak interactions, both involving leptons and producing hadronic showers.
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Which particles undergo ionisation energy loss?
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Ionisation energy loss dominates over radiation losses for all charged particles except e+ and e- at most energies.
Radiative losses may dominate at very high energy. |
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What does the Bethe-Bloch formula show?
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The ionisation energy loss per unit distance for a particle interacting with a medium.
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What is z in the Bethe-Bloch formula?
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Is is the charge of the incident particle in units of e
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What is I in the Bethe-Bloch formula?
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It is the ionization potential of the material.
It may be approximated by I (H).Z where I(H) is the ionisation potential of hydrogen. |
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What is ne in the Bethe-Bloch formula?
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Is is the electron density in the material.
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What is K in the Bethe-Bloch formula?
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It is a constant of proportionality and includes a number of constants characterising the coulombic interaction.
It varies according to how the formula is arranged. |
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What is δ in the Bethe-Bloch formula?
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It is a correction term related to the density of the material and characterising the screening effect of atomic electrons.
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How can the Bethe-Bloch formula be used in particle identification?
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Measurement of ionisation energy loss can be used to determn the particle velocity. Its momentum and charge polarity can be derived from curvature in a magnetic field. Hence the mass of a particle can be deduced.
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How and why can ionisation energy loss dE/dx be found in units of MeV/cm from MeVg^-1cm^2?
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Multiply by the material density. Almost all materials lie along the same -dE/dx vs βɣ (p/Mc) curve.
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What is Bremsstrahlung?
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Radiation of photons from a charged particle due to acceleration/deceleration in the vicinity of a nucleus.
It is particularly important for e +/- |
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By what mechanisms do photons interact with matter?
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Photoelectric effect (electron ejected from a material)
Compton scattering (scattered photon and recoil electron) Pair production (ɣ => e+ + e-) |
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What are the main interactions of e-?
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Bremsstrahlung, ionisation, annihilation.
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What are the main interactions of e+?
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Bremsstrahlung, ionisation, annihilation
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What are the main interactions of ɣ?
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Photoelectric effect, Compton scattering, pair production (ɣ => e+ + e-)
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What is the main interactions of μ?
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Ionisation, Bremsstrahlung (>>1GeV)
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What are the main interactions of ʋ?
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Weak interaction (NC, CC)
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What are the main interactions of a hadron?
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Strong force
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What are the 6 ideal qualities of a detector?
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Spatial resolution
Time resolution Energy resoluton Particle ID Large dynamic range Radiation Hardness |
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What are the two broad kinds of detector?
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Tracking and Particle ID
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What is the broad mechanism of Particle ID?
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Measure the energy (momentum) then measure the velocity to determine the mass and hence ID the particle.
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How does a scintillation detector work?
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Energy absorbed from charged particles then emitted as fluorescence
Photomultiplier tube then detector. |
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What is the mechanism of a drift chamber?
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Gas filled anode
Ionisation causes electrons to drift to an anode where they induce and electrical signal drift time measures distance from hit to the wire Signal strength measures ionisation amount => Particle ID |
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How does a time-of-flight detector work?
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Particle is detected at two scintillator paddles with known separation
For a given momentum the speed and hence the time of flight is a function of mass. ToF detectors work for momenta up to ~4GeV |
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What is Cerenkov radiation?
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The light emitted when a charged particle traverses a medium of refractive index n and v>c/n.
Cerenkov light is emitted at and angle θc o the direction of motion. |
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How is Cerenkov radiation used in detectors?
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Threshold detectors record the presence of Cerenkov radiation in a given volume.
Ring-imaging detectors reconstruct the Cerenkov cone. |
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What Cerenkov rings are produced by Cerenkov detectors?
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ʋμ produces a μ which has a sharp ring as they are no very ionising and have a clean path
ʋe produces an e- and a fuzzy ring due to Bremsstrahlung energy loss. |
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What are the available particle ID detectors in order of relativistic velocity?
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ToF
Threshold Cerenkov Ring-imaging Cerenkov Relativistic rise in dE/dx Transition radiation detectors. |
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What do calorimeters measure?
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Energy and position of particles by total absorption
They detect EM and hadronic showers. |
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What is an electromagnetic shower?
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At high energies e+/- Bremsstrahlung and photon pair-production dominate
The radiation length for both processes is similar Hence Bremsstralung produces photons which cause pair production etc. |
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What is the distance scale for hadronic showers?
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The nuclear interaction length - generally much larger than the radiation length.
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What are the layers of a layered detector (inside-outside)?
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Tracking chamber
Magnet coil EM calorimeter Hadronic calorimeter Μuon chambers |
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What is isospin and hypercharge?
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A property of colour ONLY, analagous to spin and charge and involved in strong interactions only.
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What QCD terms are conserved at a strong interaction vertex?
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Colour, isospin and hypercharge are conserved at a strong interaction vertex.
The strong interaction is flavour independent. |
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What is a gluon made of?
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colour anti-colour pairs
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How many types of gluon are there?
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8 - one for each colour/anti-colour combination for different colours/anti-colours (6 in total), and two further composite states made of linear combinations of colour-anticolour pairs with the same colours.
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What is the evidence for colour?
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The calculated and measured cross section ratio for electron-positron hadron production/electron-positron muon production.
Colour factor in π0 decay rate Colour factor in W-decay branching ratios All include a factor of 3 indicating 3 colours. |
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What is the deviation from the cross-section ratio due to?
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Higher order corrections due to eg three-jet events
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What effects can be described by gluon-gluon coupling?
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Quark confinement and asymptotic freedom.
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What are the characteristics of the force between two quarks?
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At short distance it is dominated by one-gluon exchange V(r) = - αs ħ c/r (coulombic potential)
At r>0.1 it becomes approximately CONSTANT V(r) ~ λr thus total potential is the addition of these - it is confining and does not die away. |
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What are the effects of the force between two quarks?
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As the potential does not decrease with distance, at some separation there is enough energy to create a new quark-antiquark pair, which will combine to form a new hadron. Hence single quarks are not observed.
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How are hadron jets produced?
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Two stage process: e+e-=> q-antiq q-antiq=> hadrons
the sum of the hadron momenta is the momenta of the parent quarks. |
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How are 3-jet hadron jets produced?
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Two stage process: e+e-=> q-antiq q-antiq=> hadrons + a gluon
the gluon can fragment to produce hadrons also. |
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What is the consequence of the 3-jet/2-jet event ratio for hadron jets?
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Confirms QCD predictions, confirms that the gluon has spin +1
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What is deep inelastic scattering?
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The scattering of a lepton from a nucleon at scales << the size of the nucleon.
The nucleon will break up to produce hadrons. final invariant mass > nucleon mass. |
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What is the physical meaning of x in deep inelastic scattering?
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x is the fraction of the incoming proton's momentum carried by the struck quark.
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What does the e-p cross-section in deep inelastic scattering tell us about quarks?
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It is only consistent with particles of spin -1/2 with fractional charges.
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What are scaling violations and why do they arise?
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The number of quarks inside a photon does not depend on the momentum of the e in an e-p collision.
However there are deviations from the predicted structure of a proton for different incident e momentum The nucleon is actually a complicated sea of quarks and gluons combining and recombing, rather than single set particles. The apparent number of quarks therefore can change with incident e momentum. |
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What is a charged current?
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The interaction of charged subatomic particles through the weak force and exchange of a W+/- boson.
eg. ʋμ + N => μ- + X |
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What is a neutral current?
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The interaction of neutral subatomic particles through the weak force and exchange of a Z boson.
ʋμ + N => ʋμ + X |
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When are the EM and weak interactions unified in the electroweak force?
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At high energies which overcome the much greater mass of the W/Z bosons.
E is comparable to Mw/z |
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What is the parity operator?
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It creates a 'mirror image' of the wavefunction. Odd parity wavefunctions are 'flipped' by the parity operato and have parity -1, Even parity wavefunctions are unchanged by the parity operator and have parity +1.
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What is the charge conjugation operator?
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It changes the sign of the electric charge and any electric/magnetic fields, thus it changes a particle into an anti-particle.
Particles which are their own anti-particle (eg π0) are unchanged and have a C of +1. Others have C -1. |
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Which interactions conserve parity?
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Strong interactions and EM interactions conserve parity, weak interactions don't.
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What is the CP operator and CP symmetry?
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CP is the combined action of the charge conjugation and parity operators.
CP symmetry is a conservation law that states that a reaction should occur at the same rate in both some 'original' and CP-transformed states. |
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What is CP violation and when does it occur?
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CP violation is when only one CP state is favoured for an interaction, in violation of the conservation law. It occurs in weak interactions.
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How was parity violation observed?
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β-decay in Co-60 was observed to be preferentially in the direction opposite the nuclear spin, in violation of conservaton of parity.
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What is the consequence of CP-violation?
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Weak interactions are spin-dependent.
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What is helicity?
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Spin is quantised along the direction of motion. Helicity can be left handed or right handed. Left handed is when the projection of spin is away from the direction of motion, right-handed is vice versa.
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What is the helicity of a ʋ?
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Neutrinos have left-handed helicity.
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What is the helicity of an anti-ʋ?
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Anti-neutrinos have right-handed helicity.
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Why do ʋs always have left-handed helicity?
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As neutrinos are massless according to the standard model, it is not possible to choose a reference frame faster than the neutrino in which the direction of motion is changed and hence flip the helicity.
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Do particles other than neutrinos have fixed helicity?
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Only in ultra-relativistic limits. In this case the contribution of the forbidden helicity states are supressed by factors ~ m^2c^4/E^2
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What is chirality?
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It is a property whereby a particle does not have the same properties as its mirror image. The parity operator will transform between chiralities.
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What is the difference between chirality and helicity?
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For massless particles there is no difference. For massive particles, it is possible to move in a faster reference frame such that the direction of motion and thus the helicity appears to change.
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How is the spin dependence of weak interactions represented?
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V-A interaction: V is a linear vector, A is an axial vector whose direction in unchanged by parity transformation. Only V-A is observed in weak interactions.
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How was ʋ helicity established?
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Goldhaber experiment (1958): measured helicity of photon by applying conservation of AM. Only LH neutrinos and RH anti-neutrinos were observed.
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What is K-mixing?
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Since strangeness is not conserved in weak interactions, K and anti-K states can be converted into each other. Thus the observed particles are in fact linear combinations of the two.
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Why can't p - antip mixing occur?
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Baryon number must be conserved in a weak interaction. Hence, conversion of a p to an anti-p would violate baryon conservation.
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What is strangeness oscillation?
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K0 antiK0 mixing means that strangeness can change as the mixed state evolves. K0 has S=+1, antiK0 has S=-1
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What can strangeness oscillation be used for?
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It enables an excellent measurement of the masses of Kl and Ks
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What does the time evolution of Kl-Ks mixing look like?
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A decrease in K0 corresponds to an increase in anti-K0. The two lines cross (more anti-K0 than K0) then converge to the same point (equal numbers of each state)
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What are the decay modes of W/Z bosons?
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Hadronic - showers created after decay into a q-antiq pair.
Leptonic - decay into a lepton and anti-lepton ʋ, with lepton number conserved. |
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Why is the weak interaction short in range?
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Because of the large mass of the W/Z bosons at most energies.
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What is the approximate range of the weak interaction at large energies?
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It is a zero-range point interaction.
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What is the mechanism of weak interactions of hadrons?
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W-bosons are emitted or absorbed by quarks which can change their flavour.
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What is lepton-quark symmetry?
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Quark couplets and lepton couplets have identical weak interactions. The quarks should convert between their own couplet.
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What is quark mixing?
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It explains 'forbidden' decays, where a quark changes to another quark outside of its own couplet. It occurs only for W bosons (charged current reactions)
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How does quark mixing work?
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The d, s and b quarks participate in weak interactions via linear combinations
The linear combinations are derived using CKM matrices involving mixing angles θ1/2/3 and a complex term δ which describes CP violations. |
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What is the unified electroweak theory?
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For higher order W+/- diagrams divergences were observed. Including diagrams involving Z0 and photons solved the divergences - when all the diagrams of a given order were added together the divergences disappeared.
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What quark numbers are conserved in neutral current reactions?
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Individual quark numbers.
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What quark numbers are conserved in charged current reactions?
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Total quark number only.
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What is the unification of Z and photon reactions?
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In and process where a photon is exchanged, a Z0 can be exchanged. Z0 contribution is not large at low energies (E<< Mzc^2).
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What are the assumptions of the Fermi gas model?
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An individual nucleon feels a potenial equal to the superpostioin of the potentials of other nucleons, with the shape of a sphere of radius RoA^1/3 fm
Nucleons move freely like gas inside the nucleus Nucleons fill energy levels in well up to the 'Fermi energy' Ef Potential wells for protons and neutrons can be different, with the neutron well deeper than the proton well (hence stability of high neutron nuclei) There are 2 protons and 2 neutrons per energy level. |
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What is the difference between the Fermi energy and the potential well energy in the Fermi gas model?
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This is the binding energy per nucleon B'.
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What is the difference between the proton potential and the neutron potential in the Fermi gas model?
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The proton potential is shallower and curves off exponentially at the top. The neutron potential is a square well.
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How is the asymmetry term in the SEMF derived?
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By considering the kinetic energies of all nucleons and noting that the term N^5/3 + Z^5/3 has a minimum if N=Z. Thus this term has a dependence on the neutron surplus.
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Where do the 'shells' in the shell model come from?
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From the spherical harmonic solutions of the solution to the infinite spherical well potential.
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What is the form of the nuclear potential in the shell model of the nucleus?
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The Woods-Saxon potential, intermediate form between the harmonic oscillator and potential well.
It is wine-bottle shaped with a large exponential tail for protons, and almost square for neutrons. |
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Where do the split j terms in the shell model come from?
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From the spin/orbit splitting.
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How are excited states predicted in the shell model?
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One of the neutrons or protons or neutrons can move up to the next level. The most likely excited state is that with the smallest energy jump.
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What is unusual about the β-decay energy spectum in the Fermi gas model?
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It was thought to have a single energy, rather than a distribution. A second particle (the ʋ) was predicted from the spectrum.
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How can the ʋ mass be predicted from a Kurie plot?
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A plot of electron density vs energy has a negative slope. At the x-intercept, the line deviates slightly from the straight line, this deviation gives the mass of the ʋ. It is the point at which a positron carries all the energy and a ʋ carries none.
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What causes fission?
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Competition between the surface and coloumb terms. The coloumb barrier must be overcome to cause fission.
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How is the fission likelihood calculated?
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Neutron mean free path - what is the probability of inducing fission on collision - how many collisions will it make before inducing fission - how far will it travel in this time? This gives a critical mass for the fissile material which corresponds to the radius of a sphere of this distance.
However, the sphere needs to be bigger than this as neutrons are lost to escape or radiative transfer. |
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How are nuclear reactions controlled?
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By delayed neutrons
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What are the candidate reactions for nuclear fusion?
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Hydrogen/hydrogen to helium
Hydrogen-hydrogen to deuterium Hydrogen/hydrogen to heavy helium |
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What are the limitations to nuclear fusion?
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Large particle density and large plasma confinement time.
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