5. The Strong Nuclear Force Flashcards
What is the strong force?
- we have already stated that there must be a strong nuclear force acting over short length scales binding the nucleus together
- this force turns out to be a force acting between individual quarks
- meaning that it is experienced by hadrons but not by leptons
How do we know that the pion exists?
- if a proton and a neutron are scattered off each other at high energy, we would expect their momenta to be largely unchanged,
- plotting likelihood of scattering at a particular angle for a range of possible angles, we would expect a high probability of small angle scattering
- in reality we observe large scattering angles are almost as common as small scattering angles
- Yukawa suggested an explanation for this is the pion
What is a pion?
- the exchange particle for the strong nuclear force
- there are three pions, positive, negative and neutral
- exchange particles must couple to a quantum property e.g. charge, in the case of pions it is baryon number
How do pions account for large angles in neutron/proton scattering?
- the explanation for the large scattering angles is that there is a proton-neutron-pion interaction
- this has the effect of turning a proton into a neutron and vice versa when a charged pion is emitted
- the small scattering angles are dues to neutral pion exchange in which the proton and neutron are unaltered
- the large scattering angles are actually the same as the small ones only the particles switch so we measure a large angle of deflection
Mass of Exchange Particle and Range of Force
-from the uncertainty principle we get:
Δx ≈ ℏ/mc
-so the heavier an exchange particle is, the shorter the range of the force it carries
Pion Mass and Lifetime
-unlike a photon, the pion has mass so requires energy to create
-the pion effectively borrows energy in order to exist
-as long as it does so in accordance with the uncertainty principle, this is an allowed effect:
ΔE Δt ≥ ℏ
-living on borrowed energy also means living on borrowed time, since the pion is likely to travel at around c we can calculate an approximate distance it is capable of travelling:
mc² Δt ≈ ℏ
mc² Δx/c ≈ ℏ
=> Δx ≈ ℏ/mc
-subbing in the nuclear reaction range ~1fm, we can estimate its mass
Discovery of the Pion
-in 1947, a strongly interacting charged particle of mass 140Mev/c² was discovered and Yukawa’s theory confirmed
Pion Exchange and Quark Exchange
- we now know that the force between hadrons due to pion exchange is a residual effect of a more fundamental strong nuclear force
- if we re-draw proton neutron scattering in terms of quarks we see that only one quark in each particle under goes change
- pion exchange is just quark exchange
How do we know that there is a more fundamental force binding quarks?
- consider the Δ- hadron, it is composed of three down quarks and has spin 3/2
- this implies that each quark has a spin of +1/2 and we assume that there is no orbital angular momentum associated with the quarks in the lightest hadrons so all three quarks appear to be in the same state, which is not allowed by the Pauli exclusion principle
- there must be another property possessed by the quarks for which they each have a different value which puts them all in a different quantum state
Colour
-three distinct types, red r, green g, blue b
-there is an exchange boson that couples different quark colours such that different colours attract and like colours repel
-this is why in baryons, quarks bind in threes:
red + blue + green = neutral colour
-there are also anticolours antired, antigreen and antiblulle
-this is why a quark and an antiquark bind together in a meson:
red + antired = neutral
Gluon-Gluon Interactions
- gluons themselves carry colour - the strong force equivalent of charge
- this means that gluons can interact with other gluons
Gluons Compared With Photons
- the quantum property coupled with photons is charge but the photon itself doesn’t have charge so photons do not interact directly with other photons
- whereas gluons themselves carry colour and mediate colour change so gluon-gluon interactions can occur
Confinement
- self interaction of gluons combined with the very high strength of the strong force leads to the property confinement
- whereas the force between two charges drops off as the inverse square of the distance between them, the force between two colour charges remains constant
- the potential energy in separating two attracted colours grows with separation until eventually new particles are produced
- this means that we can never separate the quarks in a hadron, they are confined
Asymptotic Freedom
- the potential energy in separating two attracted colours grows with separation until eventually new particles are produced
- this means that we can never separate the quarks in a hadron, they are confined
- on the other hand, at very short length scales, the strength of the gluon interaction falls away so that within a hadron, the quarks are essentially non-interacting
- this is known as asymptotic freedom
Mass of Hadrons vs Mass of Constituent Quarks
- the mass of hadrons is far greater than the masses of the quarks that make them up
- this is because they are also filled with a sea of virtual gluons and quark antipairs popping in and out of existence
- at any given moment, however, there will be a net imbalance of a particular set of quark flavours and spins that is conserved and determines the nature of the hadron
