Key Definitions Flashcards
What is the liquid drop model?
The liquid drop model is described by the semi empirical mass equation. Where nuclei with even number of protons and neutrons are the most strongly bound and magic numbers correspond to shell closures in the nuclear shell model.
How is the binding between protons and neutrons mediated?
mediated by the exchange of pions.
What is Isospin?
Isospin describes the similarity between protons and neutrons, including their independence of the strong interaction on the electric charge of a particle.
What is the phenomenon known as confinement?
The strong interaction allows mediating gluons to interact with each other
Where is alpha decay most commonly found?
In heavy nuclei
Where is beta minus decay more commonly found?
In nuclides with excess neutrons
What does the fermi function depend on?
The fermi function depends on atomic number of the daughter nucleus, and the kinetic energy of the emitted charged particle.
What is the decay rate of beta decay given by?
The interaction strength, the matrix element Mfi and a momentum dependent integral over the Fermi function.
What is an Isobar?
Nuclei with the same A.
What is an Isotone?
Nuclei with the same N but different Z.
What is an Isomer?
Metastable excited state
What is an Isotope?
Nuclei with the same Z different N.
What is the force between a nucleon and how is it mediated?
Strong force by exchange of gluons.
What is the force between two nucleons and how is it mediated?
Nuclear force by exchange of virtual meson.
Describe Electron scattering
Electrons are not subject to strong interaction. They are pointlike particles that can exploit polarisation.
What reveals the size and form factor of nuclei?
Elastic electron scattering
How is the size of a nucleus estimated and what are the challenges involved?
Rutherford’s experiments with alpha-decay showed the size of the nucleus. With challenges due to the modification scattering probability due to a tiny, dense nucleus.
How is the mass of a nucleus determined?
From the molar mass of a substance
What are the Q value conditions?
When Q > 0 it is exothermic and for Q < 0 it is endothermic.
How do we determine the mass of isobars?
From a second-order polynomial obtained from the semi-empirical mass equation and A.
What are the conditions of the pairing term?
For δ = 0 we have odd-A and a single parabola. For even A we have two parabolas separated by 2δ/sqrt(A).
Describe electromagnetic interaction probes.
Using electromagnetic interaction probes probe the charge distribution of the nucleus.
What does Fermi’s golden rule link?
Quantum theory to experimental observation (cross section)
How can the density of a nuclei be described?
Nuclei have near constant density and a diffuse rim.
What does the Segre chart show?
A region of stability for roughly N = Z in low masses
How can features in the Segre chart be explained?
The semi empirical mass equation explains several gross features.
What are shell effects?
Smooth variation of properties within shell
What are magic numbers?
Sudden changes in properties
2, 8, 20, 50, 82, 126 - shell like phenomena.
Describe closed shell atoms.
They have small radii and larger ionisation energies
Describe the neutron neutron interaction.
The main strength of the interaction is an attractive central potential. It is strongly spin dependent and repulsive at short range. The interaction is charge symmetric and almost charge independent. It is invariant with respect to parity and time reversal.
Describe the Fermi Gas Model.
Nucleons can move freely in spherical cavity and exist in energy levels up to the Fermi energy. Where there can be two nucleons per energy level and there are separate potential for neutrons and protons. The energy distribution is well modelled by the Fermi gas model.
Describe the nuclear shell model.
Magic numbers and excitation spectrum are given in the nuclear shell model. Alongside single particle/hole states.
How are nuclear energy levels predicted in the shell model?
They are predicted by considering the coupling of angular momentum and spin of nucleons.
What is the Nilsson model?
The Nilsson model is a modification of the shell model that accounts for the ellipsoidal shape of the nuclear mean field potential.
Why do we need spin orbit coupling?
We cannot reproduce all magic numbers and energy levels from gamma spectroscopy.
What does the quadrupole momentum measure?
Measures deviation from spherical symmetry
How do we modify the Woods-Saxon potential?
We modify it through strong spin orbit coupling
Why is alpha decay possible?
It is possible through pre-formed alpha particles tunnelling through the potential barrier
Describe beta decay modes.
Beta decay conserves Baryon and lepton number and is mediated by the weak interactions. Fermi showed that for short range it allows a point like treatment.
Describe branching ratios.
Competing decays can contribute to total lifetime. The details depend on nuclear matrix elements. The branching ratio is given by the sum of the partial decay.
What does the Fermi-Kurie plot account for?
The Fermi-Kurie plot takes Coulomb into account
Describe the Wu experiment.
Also known as the 60Co experiment showed beta emission is preferentially in the direction opposite the nuclear spin, in violation of conservation of parity.
What do transition rates in beta decay depend on?
Nuclear structure and nuclear matrix elements.
What is violated in beta decay?
Parity
Describe gamma radiation.
Nuclei have the same A, Z and N while the nuclear state changes.
Describe spontaneous fission.
Spontaneous fission produces neutron rich nuclei due to the mass ratio of the parent nucleus being largely conserved in the two fragments.
What is the binding energy of an alpha particle?
The binding energy of an alpha particle is very high compared with most nuclei hence it is more favourable to heavy nuclei.
Which term does the Fermi Gas Model justify?
The inclusion of the volume term.
Describe alpha decay.
Alpha decay represents transitions between states of definite energies. Alpha decays are two body reactions and are emitted mono energetic and have a vertical line spectrum.
Describe beta decay
Beta decay represents transition between two states of definite energy. A beta transition is a three body decay and it has a continuous spectrum from zero to a definite energy point. The measurement of the beta spectrum indicates the emission of a third particle. Conservation of energy demands it be light and conservation of charge demands it be neutral.
How can we determine the mass of a neutrino?
From measurements of a beta decay spectrum.
What does the B(Z,N) represent.
The binding energy for a nucleus of given number of protons and of neutrons.
What does a measurement of the Q value determine?
An identification of the parent isotopes
What are the two selection rules in beta decay?
Fermi and Gamov-Teller selection rules.
Describe neutrinoless double beta decay.
If observed would imply that neutrinos are their own anti-particle.
What is the Coulomb barrier?
The Coloumb barrier represents the energy barrier that must be overcome for fission to occur.
What are mirror nuclei?
The number of protons in one nuclide is equal to the number of neutrons in the mirror nuclide : Z1 = N2 and N1 = Z2
What is the reaction probability given by?
The reaction probability is given by the differential cross section.
what is a barn?
1b = 10^-28m
What is the form factor?
The fourier transform of the charge density normalised by the total charge.
What is the mean field potential?
A potential generated and experienced by the surrounding nucleons. The woods-saxon potential is a mean field potential for nucleons.
What are degenerate states?
Combinations of states that give the same energy.
Describe heavy nuclei.
For heavier nuclei the density is described by the fermi-distribution, which is described by the woods-saxon potential.
Describe the Hund rules.
Nucleons in partially filled shells have a choice of different orbital, spatial and spin-states. The Hund rules takes this into account.
What is an allowed beta decay according to Fermi’s theorem?
A decay is allowed if the first term of the matrix element is finite.
What is a first forbidden beta decay according to Fermi?
If the first term of the matrix element is zero.
What are fermi-transitions?
when the spin of electron and neutrino is 0.
What are Gamov-Teller transitions?
when the spin of electron and neutrino is 1.
What are allowed Gamov-Teller transitions?
transitions with L = 0 are allowed.
What are forbidden Gamov-Teller transitions?
transitions with L > 0 are forbidden.
Describe log10ft values?
They quantify the number of allowed and forbidden transitions according to the selection rules of beta decay.
What is a super-allowed transition?
Where the log10ft value for the 0+ -> 0+ transition is ~ 3.5.
Describe single beta-decays.
Nuclides that cannot decay further despite the existence of an isobar with a lower mass due to the fact that the intermediate nuclide would have a higher mass.
Describe double beta-decays.
Two beta decays occuring simultaneously. This is a very rare processes.
Describe the short comings of the Fermi Gas model.
The fermi gas model assumes a potential that does not depend on the neutron excess. The Pauli principle weakens the interaction between like particles forbidding some two particles while, the interaction between neutron and proton is allowed in all states.
Separation energy of a neutron
Sn = B(Z,N) - B(Z, N-1)
Separation energy of a proton.
Sp = B(Z,N) - B(Z-1,N)
Describe the volume term.
The volume term proportional to the number of nucleons inside the nucleus, stemming from the nearest neighbour interaction of the effective strong force.
Describe the surface term.
The surface term is proportional to the surface energy of the nucleus, which gives a negative contribution.
Describe the Coulomb term.
The Coulomb term is proportional to the total charge of the nucleus.
Describe the symmetry and pairing term.
The symmetry and pairing term ensures nuclei with even numbers of protons and neutrons are the most strongly bound.
What is the result of the Hund rules?
Prolate or oblate deformation
Describe light nuclei.
Light nuclei can be approximated by a harmonic oscillator.
