Flashcards in Nuclear Physics Deck (62):
What is the nuclear scale and the proton charge radius?
~ 10^-15 m = fm
Proton charge radius = 0.877 fm
Define an atomic mass unit, amu
A scale on which 12 amu = mass of NEUTRAL C-12 in its ground state configuration.
How find the atomic mass (weight) of an element with natural isotopes?
Weight each isotopic mass by its natural abundance and add together.
What does A equal?
A = Atomic mass = Z+N
If an element has an m in the top right corner what does it mean?
It is a metastable isomer, i.e. a state that is not stable but has a significant lifetime.
Define the terms isotope, isotone and isobar and what they look like on a Segrè chart.
- Isotope: same protons (Z), different neutrons (N). Horizontal line in Segrè chart.
- Isotone: same neutrons (N), different protons (Z). Vertical line in Segrè chart.
- Isobar: same atomic mass (A). Diagonal line line in Segrè chart.
Describe the Segrè chart.
A plot of proton number (Z) vs neutron number (N), roughly straight line for medium N, then tilts to right for large N (more neutrons than protons). Top line is proton drip line, bottom is neutron drip line.
Nuclei above central line undergo β(+) decay and below central line β(-) decay, heavy nuclei undergo α-decay.
What are drip-lines?
Where the addition of a proton/neutron produces a nuclear which decays back by proton/neutron emission (Fermi-level lies above the nuclear potential).
Why are some vertical and horizontal bands in the Segrè chart associated with longer lifetimes?
They highlight nuclei with magic numbers of neutrons or protons.
How can some nuclei exist beyond the drip-lines?
If there is a barrier (e.g. Coulomb barrier) then nucleus can have significant lifetime even if beyond drip-line.
What does it mean if parity of a nuclear state is positive, or negative?
If parity is positive the spatial part of the nuclear wave-function is even.
If parity is negative the spatial part of the nuclear wave-function is odd.
What notation is uses to label the spin and parity of a nuclear state?
- J= Total angular momentum of nucleus = Vector sum of angular momenta (j) of nucleons
- π = parity = (-1)^l, where l is the orbital angular momentum of the last unpaired nucleon
What are the possible values of orbital angular momentum for a nucleon?
l = 0 : s
l = 1 : p
l = 2 : d
l = 3 : f
What is the spin-parity (J^π) of even-even nuclei, and why?
0^+, because all nucleons are paired (hence spins cancel and parity is positive)
How do you find the spin-parity of even-odd nuclei?
Find spin and parity of unpaired nucleons.
How do you find the degeneracy of an orbital?
2j + 1
What are m(l) and m(s)? How many values do they have?
The quantum numbers for orbital and intrinsic angular momentum.
• m(l) has 2l+1 values (-l, -l+1,...,l-1, l).
• m(s) is either +-1/2 for protons and neutrons.
What is the mean field?
A potential corresponding to the average interaction encountered by nucleons.
How do you find the parity of a nuclear state?
(-1)^l , if multiple unpaired nucleons then product of all these.
How do you find the total angular momentum (J) of a nuclear state?
Vector sum of total angular momenta (j) of all nucleons.
What is the mass and lifetime of a neutron?
How are atomic mass and BE related?
Atomic mass = (mass of protons, neutrons, electrons) - BE
In terms of atomic mass and binding energy, which nuclei are most stable?
Those with higher binding energy and lower mass.
Why is atomic mass (and not nuclear mass) used in BE calculations?
Some processes involve electron participation.
How do you calculate the mass excess of an atom?
Δm(Z,N) = m(Z,N) - A*u
What is the relationship between mass excess and stability?
Lower (more negative) mass excess = more stable
What is the atomic energy scale?
What is the nuclear decay energy scale?
What is the nuclear mass energy scale?
What are the strengths of the fundamental forces relative to the strong force?
Strong : 1
EM : 0.01
Weak : 10^-10
What is the range of the strong force?
~ 2 fm
What is meant by the 'Coulomb' force?
Why are there no p+p or n+n bound states?
Anti-aligned spin states have too much energy to be bound in strong force potential, aligned states disobey Pauli exclusion principle.
Describe the shape of the strong (nuclear) force potential.
0 for separations above 2fm, then curves down to a minimum at ~ 1fm and shoots up to infinity at ~0.5fm (called repulsive core).
Summarise the main features of the strong (nuclear) force.
- Spin dependant
- Repulsive core
- 3 body forces are important
- Velocity dependant (spin-orbit dependence)
- Strength is ~ same for protons and neutrons
- Linked to the exchange of mesons
Which mesons are exchanged in the strong force?
- π mesons for long range attraction
- ρ & ω mesons for short range repulsion
What are the terms of the Liquid drop model?
- Volume term: A ; due to finite range of nuclear force, nucleons only interact with nearest neighbours (saturation) and a constant energy is added per nucleon.
- Surface term: -A^(2/3) ; due to lost binging energy from nucleons at surface. Volume proportional to A.
- Coulomb term: - Z(Z-1)/A^(1/3) ; due to EM repulsion of protons. Calculate using potential energy (U) of charged sphere. U=int(Vdq). Z(Z-1) because there's no repulsion if only 1 proton.
- Symmetry term: -(N-Z)^2/A ; to maximise BE protons and neutrons should be maximally in the same orbits.
- Pairing term: δ ; due to overlap of orbits of p-p, n-n pairs.
Describe the pairing term in the liquid drop model.
- δ = -12/A^(1/2)
0 if A is odd; - if N and Z are even (+); + if N and Z are odd (-)
What is the valley of stability?
LDM is quadratic in Z for constant A -> graph of mass excess vs A is an upside-down parabola.
Smooth curve for odd A (due to pairing term), staggered curve for even A.
Beta plus decay down from right, beta minus down from left
Z on x-axis, mass excess (negative) on y-axis
Describe the graph that Rutherford created for a constant scattering angle.
Cross-section (probability) vs α-particle energy.
Curve downwards due to Coulomb force, then straight line down due to diffuseness of nucleus.
How can we find the charge density of a nucleus? Describe a typical graph.
Use electron scattering.
Graph of ρ vs radius gives constant charge density throughout nucleus then exponential decay at surface which is independent of mass.
What values for nuclear radius were found from α-particle scattering and electron scattering?
R = 1.4A^(1/3)
What is a Q value? What does its sign tell you?
The energy difference between initial and final states, calculated via mass difference (Q = initial mass - final mass), or mass excess differences.
If positive then exothermic, if negative then endothermic.
What are the 4 main groups of decay?
- β-decay and eco torn capture
- Internal decay: electron conversion, γ-ray emission, pair production
What are the factors influencing decay rate?
- Q value, greater the Q value the higher the decay probability
- Barrier height
- Angular momentum of initial and final states
What is the branching ratio?
The fraction of the time that a nucleus will decay via a certain mode rather than another.
What is the decay equation?
dN/dt = -λN
What does half-life equal in terms of λ?
T(1/2) = ln(2)/λ
What is the decay constant, λ?
Probability per unit time that a nucleus will decay.
What is the mean lifetime of a decaying nucleus?
τ = 1/λ
What are magic number nuclei?
Nuclei with full nuclear shells (s,p,d,f) for either protons or neutrons, leading to higher BE than expected by LDM.
Double-magic nuclei have both proton and neutron magic numbers.
If the Q value for neutron absorption so greater than the activation energy then the nucleus is fissile.
Fissionable by thermal neutrons and capable of sustaining a chain reaction.
Define activation energy.
The minimum energy required for a nucleus to fission, associated with the increased potential energy of the nucleus as it deforms.
A material not itself fissionable by thermal neutrons but can be converted into fissile material by neutron absorption.
State evidence for pairing.
Valley of stability is smooth for odd A but staggered for even A
How do you derive the series decay equation? A -> B -> C
B is decaying away whilst A is still decay in to B, so -dN(B)/dt = λ(b)Ν(B,0) -λ(a)N(A,0)
Solve using integrating factor e^(λ(b)t)
How do you calculate a ratio of masses without the actual masses?
Ratio of atomic numbers
State beta minus decay equation and beta plus decay equation.
n -> p + e(-) + neutrino
p -> n + e(+) +antineutrino
What is electron capture? State the equation.
Inner shell electron is captured by nucleus.
p + e(+) -> n + antineutrino
Do beta plus and EC compete? Which has the greater Q value?
Yes, they compete.
EC has a Q value 1.022MeV greater than beta plus, so is preferred.
Which decay methods usually leave the nucleus in an excited state?
Beta plus and EC, nucleus then de-excites though internal decay.