NP Flashcards
Cross section
effective area quantifying the intrinsic probability of a scattering event when an incident beam hits a target composed of discrete particles cross section = reaction rate/ particle flux of incident beam * area of overlap between the beam and the target
Differential cross section
quantifies the intrinsic rate at which scattered projectiles can be detected at a given angle
Rutherford cross section
conservation of momentum, energy and angular momentum relationship between scattering angle & impact parameter
Fermi’s Golden rule
probability for transition between inital state and final state
Liquid drop model and Semiempirical mass formula
r = r0 A^1/3 nuclear size scales with the number of constituents volume surface reduces binding Coulomb repulsion between protons Asymmetry energy (imbalance of p and n) Pairing correction for spin coupling effects
Explain the basic features of ultrarelativistic heavy-ion collisions and the properties of the hadron-gas to quark-gluon phase transition
energy regime where KE exceeds the rest mass energy significantly (with energies exceeding 10 GeV per nucleon); very large numbers of particles produced - typically exceeds number of initial nucleons by a factor of 10 low energy densities; quarks and gluons are confined in hadrons BUT with increasing temperature (heating) and/or increasing baryon density (compression), phase transition occur to the state where ordinary hadrons become quark gluon plasma where quarks and gluons become proper degrees of freedom and their motion is not confined to hadrons
Asymptotic freedom
interaction between particles becomes weaker at shorter distances quark-quark potential vs distance (r) at large distances, αs increases => energy becomes infinite no free quarks possible so always q and q- pairs => confinement
Color confinement
Other side of asymptotic freedom; color charged particles e.g. quarks and gluons cannot be isolated as separate objects i.e. not directly observed
What are the differences between QED and QCD in terms of interaction and screening?
QED: photon has no charge hence no self interaction at large distances, charge is screened => α = 1/137 small distances, α increases (since more charge seen) QCD: gluon has colour charge => self-interaction (split and fuse) at smaller distances (because of the gluon cloud), αs decreases so less colour charge seen => antiscreening gives rise to asymptotic freedom
Deuteron
ndicates proton and neutron spin are parallel S = 1/2 + 1/2 = 1 difficult to start from fundamental interaction => try effective model approach quantum numbers L= 0 π = (-1)L = +1 (parity) I = 1 Iz = -1, 0, +1 => deuteron is in TRIPLET state => nucleon-nucleon interaction must be spin dependent (no singlet state exists)
Shell model and magic numbers
central Coulomb potential: e-s experience attractive field of nucleus atoms with many e-s => Hartree Fock approximation (effective charge) atomic radius (nm) & ionisation energy (eV) vs Z shows smooth variations which correspond to gradual filing of an atomic shell sudden jumps show transitions to the next shell particular stabilities at particle numbers 2, 8, 20, 28, 50, 82, 126 suggests that atomic nucleus has a shell structure like the atom => try to solve using central potential (though nuclear density profile suggests this will not work)
What is spontaneous symmetry breaking?
way to keep Lagrangian gauge symmetric (all particles apparently massless), and yet add mass terms for fermions and bosons requires adding a new complex field - Higgs field (spin 0, I3W = 1/2) process where a symmetry of a theory is not realised in the lowest energy configuation (the vacuum) - ground states do not share some symmetry possessed by the dynamics
How many free parameters are there in the Standard Model?
18 (but 19 apparently) 9 fermion masses 3 CKM mixing angles + 1 phase 1 EM coupling constant 1 strong coupling constant 1 weak coupling constant GF = 1.16637*10-5 GeV-2 1 Z0 mass mZ = 91.187621 GeV/c2 1 Higgs mass
What is helicity?
projection of spin along direction of flight of a particle not Lorentz invariant (can always find a reference system where LH looks RH) => only L. inv. if mass = 0 helicity is commuting with H => a set of eigenstates for helicity is also a set of eigenstates for H Dirac soln in base u1, u2 (v1, v2 for anti-particle) => Diract soln in base u↑, u↓ (v↑, v↓)
How is the weak interaction unique?
only interaction changing flavour of quarks (i.e. changing one type of quark into another) sees 3 families of falvour whereas photon interacts individually interacts with each charged particle propagated by carrier particles (W, Z) that have significant masses, feature explained in Standard Model by Higgs mechanism only interaction that violates P and CP symmetry (recall experimental evidence lecture 2, p11 and 15)
