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Nuclear Relativity > Week 2 > Flashcards

Week 2 Flashcards

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1
Q

What is the liquid drop model?

A

Semi-classical model
-described by semi empirical mass formula
- predicts nuclei mass

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2
Q

What is the shell model?

A

A quantum approximation which explains why some elements are very stable and predicts spin and parity

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3
Q

What is nuclear binding energy?

A

The energy required to break a nucleus into neutrons and protons

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4
Q

How much of the total mass energy is nuclear binding energy?

A

Only a fraction, but still very important

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5
Q

What is the atomic mass of an atom?

A

The sum of the masses of the constituent particles, less the nuclear binding energy

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6
Q

Why do we use mass of a hydrogen atoms for binding energy?

A

This avoids the necessity of adding electron masses

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7
Q

What is ignored in binding energy calculations?

A
  1. Mass of electron by using hydrogen masses
  2. Electron binding energy
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8
Q

What is u?

A

The atomic mass unit (AMU) 1/12 the mass of neutral 12C6 carbon atom

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9
Q

What is mass defect?

A

The difference between the rest masss and the sum of the rest masses of its constituent nucleons

(Nabla = m ((azX) - Au) x c^2

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10
Q

What is mass deficit?

A

the negative of the binding energy

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11
Q

What is binding energy proportional to?

A

A -> why written as B/A

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12
Q

What are the key features of a binding energy graph?

A
  • Virtually constant except for a few light nuclei (approx 8.8MeV)
  • High gradient for light nuclei
  • Curve peaks near A = 60
  • Very gradual decay for A>100
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13
Q

Why does curve of B/A increase for light nuclei?

A

Adding nucleons strongly attracts nearby nucleons, making the whole nucleus more tightly bound

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14
Q

Why does the curve of B/A peak near A = 60?

A

Nuclear is larger than the extent of the nuclear force, so force saturates.

Implies adding more nucleons does not increase binding energy per nucleon.

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15
Q

Why is there a gradual decay in B/A when A>100

A

Nuclei are so large the Coulomb forces across the nucleus are stronger than the attractive nuclear forces, decreasing strength of binding.

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16
Q

What happens on B/A curve as A=120?

A

B/A decreases - implies spitting a nucleus can release energy (fission)

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17
Q

What is the binding energy per nucleon related to?

A

The separation energy (required to remove a proton or a neutron).

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18
Q

What is nuclear force?

A

The residual part of the strong force

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19
Q

What does strong force do?

A

Holds quarks together to form protons and neutrons

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20
Q

How does nuclear force work?

A

Thought to be through transitory interactions between neutral molecules but no complete theory

  • thought to be mediated through meson exchange on n-body problem
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21
Q

What are the key features of nuclear force?

A
  • Short range (few fm)
  • Nearly spherical ( model with central potential)
  • Repulsive < 0.5fm
  • Charge symmetric and almost charge independent
  • Spin dependent
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22
Q

What is the Pauli Exclusion Principle?

A

2 identical fermions cannot occupy the same quantum state simultaneously

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23
Q

What is spin of fermions?

A

Half-integer

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24
Q

What is spin of bosons?

A

Integer

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25
What is spin of photons?
Integer
26
What concept is liquid drop model based on?
Nucleus shares properties with a drop of liquid - constant density - spherical - Incompressible - Adjusts shape to minimise internal energy due to surface tension
27
What does the volume term in liquid drop model account for?
Constant density by being proportional to A - nucleons interact mainly with nearest neighbours - nuclear force is short range and saturates
28
What does the surface term in liquid drop model account for?
The nucleons near the surface as they interact with fewer nucleons reducing binding energy
29
What does the Coulomb term in liquid drop model account for?
Protons with charge Ze which push each other apart, reducing overall binding energy
30
Why is Liquid Model inaccurate?
It misses out on quantum effects
31
How does the liquid drop model depict energy levels?
Continuous degree of freedom - excited vibrational modes can be of any amplitude
32
What happens when there is a differing number of neutrons to protons?
It must occupy a higher energy level due to PEP
33
What is asymmetry and what is its effect?
When there is a different number of protons to neutrons and causes lower binding energy (as higher energy levels occupied to accommodate more of 1 type of nucleons (FIgure 30, week 2)
34
What does the pairing term in liquid drop model account for?
That pp or nn bonds are stronger than np and pairs with net spin of zero (oe or eo) are tightly bound
35
How is change in energy between levels related to atomic mass?
Proportional to inverse of volume of potential well ( inverse of A)
36
How does the even/odd - ness of Z indicate that of A and N?
- If Z even - ee or oo - If Z odd - eo or oe
37
What is an important feature of the pairing term?
It oscillates depending on ee and oo
38
What shape is the SEMF?
Upside down parabola
39
Where do stable nuclei lie on a graph and why?
Below the Z=N line and are therefore neutron rich - Coloumb force becomes more important for large nuclei as nuclear force only short range
40
Value of pairing term for SEMF
- If ee aP/sqrt A - If oo, -aP/sqrt A
41
For a fixed A, which nuclei are more stable?
More neutrons (compared to one with more protons)
42
What are the striking features of a graph of binding energy vs SEMF?
- Overestimates B for light and heavy nuclei - Underestimates B for medium mass nuclei - Spikes where binding energy is really strong
43
What are nuclear magic numbers?
Spikes in SEMF corresponding to strong being in energy
44
Which medium nuclides are most stable?
If Z>20, it must have more neutrons than protons to be stable
45
When is B increased?
If Z or N is magic
46
What is N is magic?
There are more isotones
47
What if Z is magic?
There are more isotopes and have higher natural abundance
48
What if N AND Z are magic?
Nucleus very stable e.g. Helium or oxygen
49
What concept is the shell model based on?
Explanation of magic numbers using full outermost valence shells
50
What features do magic number elements have?
Higher excitation energies
51
What does spdf stand for?
Nuclear angular momentum states in shell model: - sharp, principal, diffuse, fundamental
52
What is the form of the potential such that magic numbers appear?
Large gaps between 2 energy levels and all possible spaces are filled up to that level
53
Why is the harmonic oscillator not realistic?
- Potential goes to infinity at edges making removal of an item impossible - At large distances, the potential should become positive due to coulomb repulsion but instead goes to 0 at large r
54
What is the issue with infinite square well and shell model?
Misses magic numbers
55
What is the occupancy number in infinite square well vs wood-Saxon with spin?
The number of nucleons (or electrons) which can be put in each level (Neutrons and protons counted separately) - 2 ( 2L + 1) vs j( j+1)
56
What are the eigenvalues of the potential well?
The energy levels
57
How does Wood-Saxon potential model magic numbers?
This lowers energy levels as wavefunctions spill over the edges and some energy levels split. Still misses some magic numbers
58
What does the spin-orbital potential add?
Combines angular momentum and nucleon spin in such a way that total angular momentum is conserved.
59
Where is the spin orbital potential most important?
Near the surface
60
What is spin-orbital coupling?
Spin and angular momentum couple together
61
62
Why are neutron and proton levels slightly different in WS SPC model?
Coulomb repulsion
63
Do magic numbers change?
With large A
64
How are magic numbers related to shell closure?
Their presence indicates closed shells - singly closed shell = single magic - doubly closed shell = doubly magic
65
What can be predicted with the shell model?
- Nuclear spin, J (sum over all the internal angular momenta and spins) - Parity - Some excited states
66
How to find ground state nuclear spin?
From last odd nuclei as filled levels contribute nothing to spin
67
Which nuclei have zero nuclear spin?
All with last energy shell completely filled including even-even, doubly magic
68
What is parity?
The behaviour of a quantum state under spatial reflection e.g. corkscrew or handedness and it is preserved in strong force
69
What is the angular momentum of odd-odd?
Some point in middle of both j values
70
How are excited states predicted with the shell model?
A nucleon occupies a higher level than it should, leaving a hole and energy is emitted when drops down to fill it
71
Evidence for magic numbers
- Higher binding energy - Abundance in nature - Nuclear shell model success - Higher separation energies - Gaps in excitation spectra

Nuclear Relativity (5 decks)

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