Week 1 Flashcards
1
Q
What holds nucleus together
A
Strong nuclear force
2
Q
Isotopes
A
Same protons / Z
- moves horizontally
3
Q
Isotones
A
Same neutrons
- moves vertically
4
Q
Isobars
A
Same A
- moves at 135 degrees
5
Q
Direction of beta decay
A
Along isobars
6
Q
Direction of alpha decay
A
Along N=Z
7
Q
Scales of length
A
Femometers or Fermi
8
Q
Area
A
Barn
- 100 fm squared
- U-238 cross section
9
Q
Nuclear potential at large distances
A
Positive due to Coulomb repulsion between proton and nucleus
10
Q
2 things when interpreting potential diagrams
A
- For fixed energy, KE = total - PE I.e. potential curve upside down
- Force = -ve derivative of potential
11
Q
Why use electrons for scattering?
A
Do not feel nuclear force but scattered by proton Coulomb force
12
Q
What energy levels needed to probe nucleus?
A
~1GeV
13
Q
Rutherford scattering
A
- alpha particles
- contradicted Thomson Plum Pudding
- elastic coloumb scattering, non relativistic
14
Q
Dominant non relativistic force
A
Coulomb
15
Q
Features of coulomb scattering
A
- small alpha to large nucleus
- minimal recoil of target
- minimal gain in kinetic energy
- therefore elastic scattering
16
Q
Differential cross section
A
Number of particles scattered into direction (theta, phi) per unit time and solid angle
- Related to reaction rate or reaction probability
17
Q
Scattered particle path
A
Hyperbolic as force is 1/r squared
18
Q
Impact parameter
A
A straight line that would pass a distance b from the nucleus in the absence of a repulsive force
19
Q
Particle energy at point of impact
A
Kinetic energy exchanged for Coulomb potential energy
20
Q
Particle energy at point of impact
A
Kinetic energy exchanged for Coulomb potential energy
21
Q
Scattering symmetry
A
Cylindrical about beam axis, because Coulomb force is symmetrical
- independent of azimuthal
22
Q
How many times incident particle scattered?
A
Assume once
23
Q
Rutherford cross section dependence
A
- dependence on sin to the -4 (theta/2), Z^2 and Ta^-2 (total energy)
- Sin dependence is characteristic
24
Q
Low vs high energy particles
A
- low alpha sees target nucleus as point source
- high energy, Coloumb repulsion can be overcome and alpha may be absorbed
25
Rutherford formula fails
- as does not account for projectile and target experiencing each others nuclear forces
- at internuclear separation which is then a measure of nuclear radius
26
Effect of adding form factor
electron scattering off an extended source is equal to scattering off a point source modulated by the form factor.
27
Rutherford vs Mott
- Rutherford: alpha particles, purely electrostatic forces (Coulomb)
- Mott: electrons, involves quantum mechanics, spin and relativistic
28
What do form factors do?
Take into account the fact that nuclei are not points and model spatial extent and charge distribution
29
Cross section can be divided into 2 factors if target has a finite spatial extent
- the Rutherford cross section
- form factor squared
30
Property of the spatial extent sampled in Colombia scattering
Charge distribution
31
What does form factor contain?
Nuclear charge distribution
32
How is form factor determined?
Measuring scattering through the differential cross section
33
What do spikes in the log scaling of models of density and form factor suggest?
Nuclei have blurred edges
34
Wood Saxon model
- describes nuclear potential
- smooth, finite distribution of charge and mass instead of point like
- smooth fall of at edges instead of hard sphere
- more accurate scattering cross section with nuclear transparency (some pass through)
35
Form factor for point like charge distribution
Constant
36
Form factor for exponential
Dipole E.g, proton
37
Form factor for Gaussian
Gaussian
38
Form factor for homogenous sphere
Oscillating
39
Form factor for sphere with diffuse surface
Oscillating
40
When wood Saxon is scaled to include all nuclei
Different nuclei show nearly the same constant nucleon densities up to the edge regions with roughly the same width, implies nuclear force is short range acting on neighbouring nucleons
41
Relation between scattering angle and impact parameter,b
Tan (θ/2) = D/ (2b)
D = distance of closest approach
42
Mirror nuclei
Have equal A (mass number) but exchanged a proton for a neutron
43
Energy for reaction in mirror nuclei
Column energy due to change be difference
44
How to calculate distance of closest approach?
- Find coloumb energy
- make equal to KE and solve for r
45
Assumptions when using Rutherford Scattering?
- Spherical symmetry
- No nuclear force
46
How to find number of particles scattered
Greg Marsden alpha- particle scattering angle distribution integral
47
How to verify scattering equations experimentally?
- Find dependent variables
- Vary 1 keeping rest fixed
48
How does scattering formula change in ultra-relativistic limit?
Beta tends to 1
49
Symbol for differential cross-section
50
Formula for differential cross section as a function of the differential cross section for Rutherford scattering
- dσ/dΩ = (dσ/dΩ)Rutherford) [ 1 - β^2sin(θ/2)^2] [F(q^2)]^2
51
What does the differential cross section for Rutherford scattering need to take into account?
- Relativistic effects due to high energy electron
- fact electron can probe the nuclei revealing a blob, not point-like
52
What is the scattering angle at distance of closest approach?
π or 180degrees
53
When do you consider fast or slow neutrons
Absorption of them to make isotope fissile
54
When are slow neutrons required
When excitation energy exceeds activation energy
55
When are fast neutrons required
When activation energy exceeds excitation energy
56
Calculate excitation energy
M (A-1,X) + Mn = M (A, X)
57
What is equipartition theorem
Degrees of freedom x 1/2KbT is kinetic energy
58
Features of double humped potential
- Caused by quantum shell structure
- potential increases due to nucleus stretched and potential energy decreases
- Metastable second minimum due to shell effects
- potential increases again and splits
- fission isomer with very long half life
- 2 energy barriers
59
Multiplication factor
K = number if generation/number in preceding generation
60
Total energy of fission
= 1.1 x prompt energy
61
What are delayed neutrons
Neutrons released after initial fission reaction (further down chain)
62
Relevance of impact parameter
- Starting distance of incoming particle’s path from centre of nucleus and predicts interaction
- If small impact parameter - particle comes very close to nucleus with large deflection
- If large, may just pass by with small deflection
63
Which type of fission has a longer lifetime?
Spontaneous > isomer
64
Change in momentum in Rutherford
- Pinitial along x; Pfinal θ above x, ΔP in between the 2
Sine rule:
- ΔP = sin θ
- Pi = sin (1/2( π- θ))
- ΔP/Pi = 2 sin (θ/2)
65
Equation for angular momentum
R x Mv
(MVob at large distances)
66
Upper estimate of nuclear radius
Where Rutherford formula fails
67
How are Mott and Rutherford scattering formulas related?
D cross section/d closed angle Mott = (1 - B^2 Sin^2 (theta/2)) x D cross section/d closed angle Rutherford
68
Differential cross section with form factor
D cross section/d closed angle = D cross section/d closed angle Mott ( F (theta) ) ^2
69
How is form factor related to density?
Higher density means more concentrated density distribution at center.
70
Formula for mass distribution of the nucleus
Nucleon density = Proton density x ( 1 + N/Z)
Rho (r) Rho sub p (r)
71
Formula relating nuclear mass to radius
R = Ro A ^ (1/3)
Where Ro is a constant (5/3)^ 1/2 Rrms = 1.2 fm
- Rrms = radius determined through scattering experiments
72
How are isotones and isotopes different?
P - Same element, different Z
Isotones - different elements
73
Describe the scattering involved in Rutherford scattering
- Charged nuclei beam off a stationary target
74
What shape would you expect for graph of number of scattered particles for Rutherford
Curve that depends on theta
75
In coulomb scattering,, how does the form factor take into account the spatial extent of the scatterer?
By modelling the charge density of the nucleus
76
How to calculate particles scattered within set angle
Use Greg-marsden α-particle scattering angle distribution integral
N = ∫1/ (sin(θ/2) ^4
Angles are limits
77
Why does the occupancy number of each energy level change when we had the spin orbit term to the woods Saxon potential?
The potential couples to the spin of the nucleon relative to the Angular momentum of the state. Each spin state has its own energy level.
78
How many separate levels compared to the woods, Saxon potential alone?
Doubles due to spin
79
Which level is split when adding spin orbit term
All, where L does not equal zero
80
Why can you not make firm J predictions for odd, odd nuclei
There are on paired nucleons and need to take into account NP interaction
