Flashcards in Nuclear Physics Deck (62):

1

## What is the nuclear scale and the proton charge radius?

###
~ 10^-15 m = fm

Proton charge radius = 0.877 fm

2

## Define an atomic mass unit, amu

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

3

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

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

4

## What does A equal?

### A = Atomic mass = Z+N

5

## 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.

6

## 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.

7

## 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.

8

## 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).

9

## 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.

10

## 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.

11

## 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.

12

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

###
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

13

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

###
l = 0 : s

l = 1 : p

l = 2 : d

l = 3 : f

14

## 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)

15

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

### Find spin and parity of unpaired nucleons.

16

## How do you find the degeneracy of an orbital?

### 2j + 1

17

## 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.

18

## What is the mean field?

### A potential corresponding to the average interaction encountered by nucleons.

19

## How do you find the parity of a nuclear state?

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

20

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

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

21

## What is the mass and lifetime of a neutron?

###
939.6 MeV

881.5 seconds

22

## How are atomic mass and BE related?

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

23

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

### Those with higher binding energy and lower mass.

24

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

### Some processes involve electron participation.

25

## How do you calculate the mass excess of an atom?

### Δm(Z,N) = m(Z,N) - A*u

26

## What is the relationship between mass excess and stability?

### Lower (more negative) mass excess = more stable

27

## What is the atomic energy scale?

### eV

28

## What is the nuclear decay energy scale?

### keV

29

## What is the nuclear mass energy scale?

### MeV

30

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

###
Strong : 1

EM : 0.01

Weak : 10^-10

31

## What is the range of the strong force?

### ~ 2 fm

32

## What is meant by the 'Coulomb' force?

### EM

33

## 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.

34

## 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).

35

## 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

36

## Which mesons are exchanged in the strong force?

###
- π mesons for long range attraction

- ρ & ω mesons for short range repulsion

37

## 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.

38

## 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 (-)

39

## 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

40

## 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.

41

## 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.

42

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

###
R = 1.4A^(1/3)

R= 1.3A^(1/3)

43

## 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.

44

## What are the 4 main groups of decay?

###
- Fission

- α-decay

- β-decay and eco torn capture

- Internal decay: electron conversion, γ-ray emission, pair production

45

## 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

46

## What is the branching ratio?

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

47

## What is the decay equation?

### dN/dt = -λN

48

## What does half-life equal in terms of λ?

### T(1/2) = ln(2)/λ

49

## What is the decay constant, λ?

### Probability per unit time that a nucleus will decay.

50

## What is the mean lifetime of a decaying nucleus?

### τ = 1/λ

51

## 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.

52

## Define fissile.

###
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

## Define activation energy.

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

54

## Define fertile.

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

55

## State evidence for pairing.

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

56

## 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)

57

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

### Ratio of atomic numbers

58

## State beta minus decay equation and beta plus decay equation.

###
n -> p + e(-) + neutrino

p -> n + e(+) +antineutrino

59

## What is electron capture? State the equation.

###
Inner shell electron is captured by nucleus.

p + e(+) -> n + antineutrino

60

## 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.

61

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

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

62