E - Beta Decay Flashcards
Why is there a distribution of energies of beta decay and discrete value for alpha decay & EC?
Must be Conserved:
• Energy
• Momentum
• Lepton Number
If solving the equation from the reference frame of the parent nuclei, momentum is zero. Hence net momentum of the products must be zero.
The daughter nuclei will have a large mass and thus, must receive an insignificant amount of (kinetic) energy. Hence the remaining energy must go to the other (very small mass) products in order for momentum to be conserved.
Therefore energy is distributed between the beta particle and neutrino (to conserve momentum and lepton number)
In Alpha and EC decay, there is only ever one other product to the daughter nuclei, hence producing discrete values of KE and momentum
What is time-dependant perturbation theory?
Used in QM to study the behaviour of a quantum system under the influence of an external perturbing potential that varies with time.
• it’s particularly useful for analysing how a quantum system evolves when subjected to time-varying perturbations.
External perturbing potential
• any external influence or force applied to a quantum system that modifies its behaviour from its original, unperturbed state.
• ex: EM field, gravitational field, or any other interaction
What is Fermi’s Golden Rule?
Key concept within Time-dependent perturbation theory.
It provides a way to calculate transition rates between quantum states due to a time-dependent perturbation.
This provides the transition probability per unit time for a system to make a transition from an initial state to a final state when perturbed.
What is phase space? What does it allow scientists to do?
Refers to a mathematical space that represents all possible states of a system.
The volume of phase space provides a measure of the number of available states that particles can occupy.
• studying phase space helps physicists understand the probabilities of different particle interactions or decay processes occurring
Ex: collision between particles, the phase space represents all the potential positions and momenta of the particles before and after the collisions.
Consider the distribution plots of momentum and kinetic energy for beta plus and beta minus decay. Why are both plots for beta plus decay shifted towards the right?
Must factor in Coulomb repulsion. The daughter nuclei and beta plus particle both have positive charge, hence will have a strong repulsive force.
Coulomb potential proportional to Z
What is the Fermi-Kurie plot and why isn’t it always a straight line?
Used in beta decay to analyse the shape of beta spectra. It displays the square root of the number of beta particles emitted per unit energy, divided by the Fermi function (accounting for Coulomb field experienced by the emitted particle) versus the beta particle energy.
- Phase space factor - accounts for for available energy states for the decay products and affects the shape of the plot
- Spectral shape - angular momentum coupling
- Final state interactions - interactions of emitted particle with surrounding matter or other particles
** it is far more likely that the particles will not carry any orbital angular momentum***
What is fermi decay? What plays a crucial role?
Explains beta decay
Fermi decay (transition) the spins of the two emitted particles are anti parallel (electron and neutrino) for a combined spin, S = 0.
•spin vectors are anti-parallel
Total angular momentum of the nucleus is unchanged by the transition.
What is Gamow-Teller transition? What is the significant rule?
Discussing transition of beta decay
The spins of the two emitted particles are parallel, with a total spin S = 1, leading to a change in angular momentum between the initial and final states of the nucleus.
• the spin of the parent nucleus can either remain unchanged or change by +-1.
Define the energy-momentum relation (equation) and explain its parts
E^2 = p^2c^2 + (mc^2)^2
Particles with zero mass (photons) have total energy, E = pc
The rest mass of a particle (mc^2) is invariant in all inertial frames
Lorentz Invariant = these are quantities which are the same regardless of which reference frame you are in. The above equation is one such invariant.
If v approaches c (relativistic limit) then E ~ pc
If v/c «_space;1 (classical limit) then E ~ mc^2
