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Nuclear & Neutrino Physics > Nuclear Physics > Flashcards

Nuclear Physics Flashcards

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1
Q

What is the nuclear scale and the proton charge radius?

A

~ 10^-15 m = fm

Proton charge radius = 0.877 fm

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2
Q

Define an atomic mass unit, amu

A

A scale on which 12 amu = mass of NEUTRAL C-12 in its ground state configuration.

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3
Q

How find the atomic mass (weight) of an element with natural isotopes?

A

Weight each isotopic mass by its natural abundance and add together.

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4
Q

What does A equal?

A

A = Atomic mass = Z+N

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5
Q

If an element has an m in the top right corner what does it mean?

A

It is a metastable isomer, i.e. a state that is not stable but has a significant lifetime.

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6
Q

Define the terms isotope, isotone and isobar and what they look like on a Segrè chart.

A
  • 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.
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7
Q

Describe the Segrè chart.

A

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.

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8
Q

What are drip-lines?

A

Where the addition of a proton/neutron produces a nuclear which decays back by proton/neutron emission (Fermi-level lies above the nuclear potential).

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9
Q

Why are some vertical and horizontal bands in the Segrè chart associated with longer lifetimes?

A

They highlight nuclei with magic numbers of neutrons or protons.

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10
Q

How can some nuclei exist beyond the drip-lines?

A

If there is a barrier (e.g. Coulomb barrier) then nucleus can have significant lifetime even if beyond drip-line.

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11
Q

What does it mean if parity of a nuclear state is positive, or negative?

A

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.

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12
Q

What notation is uses to label the spin and parity of a nuclear state?

A

J^π

  • 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
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13
Q

What are the possible values of orbital angular momentum for a nucleon?

A 
l = 0 : s
l = 1 : p
l = 2 : d
l = 3 : f
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14
Q

What is the spin-parity (J^π) of even-even nuclei, and why?

A

0^+, because all nucleons are paired (hence spins cancel and parity is positive)

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15
Q

How do you find the spin-parity of even-odd nuclei?

A

Find spin and parity of unpaired nucleons.

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16
Q

How do you find the degeneracy of an orbital?

A

2j + 1

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17
Q

What are m(l) and m(s)? How many values do they have?

A

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.

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18
Q

What is the mean field?

A

A potential corresponding to the average interaction encountered by nucleons.

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19
Q

How do you find the parity of a nuclear state?

A

(-1)^l , if multiple unpaired nucleons then product of all these.

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20
Q

How do you find the total angular momentum (J) of a nuclear state?

A

Vector sum of total angular momenta (j) of all nucleons.

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21
Q

What is the mass and lifetime of a neutron?

A
  1. 6 MeV

881. 5 seconds

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22
Q

How are atomic mass and BE related?

A

Atomic mass = (mass of protons, neutrons, electrons) - BE

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23
Q

In terms of atomic mass and binding energy, which nuclei are most stable?

A

Those with higher binding energy and lower mass.

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24
Q

Why is atomic mass (and not nuclear mass) used in BE calculations?

A

Some processes involve electron participation.

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25
Q

How do you calculate the mass excess of an atom?

A

Δm(Z,N) = m(Z,N) - A*u

26
Q

What is the relationship between mass excess and stability?

A

Lower (more negative) mass excess = more stable

27
Q

What is the atomic energy scale?

A

eV

28
Q

What is the nuclear decay energy scale?

A

keV

29
Q

What is the nuclear mass energy scale?

A

MeV

30
Q

What are the strengths of the fundamental forces relative to the strong force?

A

Strong : 1
EM : 0.01
Weak : 10^-10

31
Q

What is the range of the strong force?

A

~ 2 fm

32
Q

What is meant by the ‘Coulomb’ force?

A

EM

33
Q

Why are there no p+p or n+n bound states?

A

Anti-aligned spin states have too much energy to be bound in strong force potential, aligned states disobey Pauli exclusion principle.

34
Q

Describe the shape of the strong (nuclear) force potential.

A

0 for separations above 2fm, then curves down to a minimum at ~ 1fm and shoots up to infinity at ~0.5fm (called repulsive core).

35
Q

Summarise the main features of the strong (nuclear) force.

A
  • 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
36
Q

Which mesons are exchanged in the strong force?

A
  • π mesons for long range attraction

- ρ & ω mesons for short range repulsion

37
Q

What are the terms of the Liquid drop model?

A
  • 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.
38
Q

Describe the pairing term in the liquid drop model.

A
  • δ = -12/A^(1/2)

0 if A is odd; - if N and Z are even (+); + if N and Z are odd (-)

39
Q

What is the valley of stability?

A

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

40
Q

Describe the graph that Rutherford created for a constant scattering angle.

A

Cross-section (probability) vs α-particle energy.

Curve downwards due to Coulomb force, then straight line down due to diffuseness of nucleus.

41
Q

How can we find the charge density of a nucleus? Describe a typical graph.

A

Use electron scattering.
Graph of ρ vs radius gives constant charge density throughout nucleus then exponential decay at surface which is independent of mass.

42
Q

What values for nuclear radius were found from α-particle scattering and electron scattering?

A 
R = 1.4A^(1/3)
R= 1.3A^(1/3)
43
Q

What is a Q value? What does its sign tell you?

A

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.

44
Q

What are the 4 main groups of decay?

A
  • Fission
  • α-decay
  • β-decay and eco torn capture
  • Internal decay: electron conversion, γ-ray emission, pair production
45
Q

What are the factors influencing decay rate?

A
  • Q value, greater the Q value the higher the decay probability
  • Barrier height
  • Angular momentum of initial and final states
46
Q

What is the branching ratio?

A

The fraction of the time that a nucleus will decay via a certain mode rather than another.

47
Q

What is the decay equation?

A

dN/dt = -λN

48
Q

What does half-life equal in terms of λ?

A

T(1/2) = ln(2)/λ

49
Q

What is the decay constant, λ?

A

Probability per unit time that a nucleus will decay.

50
Q

What is the mean lifetime of a decaying nucleus?

A

τ = 1/λ

51
Q

What are magic number nuclei?

A

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.

52
Q

Define fissile.

A

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.

53
Q

Define activation energy.

A

The minimum energy required for a nucleus to fission, associated with the increased potential energy of the nucleus as it deforms.

54
Q

Define fertile.

A

A material not itself fissionable by thermal neutrons but can be converted into fissile material by neutron absorption.

55
Q

State evidence for pairing.

A

Valley of stability is smooth for odd A but staggered for even A

56
Q

How do you derive the series decay equation? A -> B -> C

A

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)

57
Q

How do you calculate a ratio of masses without the actual masses?

A

Ratio of atomic numbers

58
Q

State beta minus decay equation and beta plus decay equation.

A

n -> p + e(-) + neutrino

p -> n + e(+) +antineutrino

59
Q

What is electron capture? State the equation.

A

Inner shell electron is captured by nucleus.

p + e(+) -> n + antineutrino

60
Q

Do beta plus and EC compete? Which has the greater Q value?

A

Yes, they compete.

EC has a Q value 1.022MeV greater than beta plus, so is preferred.

61
Q

Which decay methods usually leave the nucleus in an excited state?

A

Beta plus and EC, nucleus then de-excites though internal decay.

62
Q

What are the 3 internal decay methods? Which is best for low energy (keV) and high Z nuclei?

A

Internal electron conversion: low energy, high Z, gives large angular momentum change

Gamma ray emission: Medium energy (up to MeV), gives small angular momentum change

Pair production: High energy (»2m(e))

Nuclear & Neutrino Physics (2 decks)

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