Upload
doanmien
View
225
Download
3
Embed Size (px)
Citation preview
1
Nuclear Reactions
Reactions
A + a → B + bA (a,b) BElastic scattering: 12C (p,p)12C Inelastic scattering: 12C (p,p´)12C*
Rearrangement reaction: 54Fe (32S,28Si)58NiCapture reaction: 12C (p,γ)13NOthers: 2H(n,2n)1H
2
Terminology
Channels (Entrance and Exit) p – proton d – deuteron (deuterium): 2H t – triton (tritium): 3H α – alpha (Helium-4): 4He Photodisintegration – reaction with γ in entrance
channel Capture – nucleon absorbed and γ in exit channel
Q-value in Reactions
The Q-value in reactions is the difference betweenthe mass energies of the entrance channel particlesand the exit channel particles.
The Q-value is the energy release in the reaction. For elastic collisions Q = 0 in inelastic collisions
Q < 0.
( ) ( ) 2]ExitEntrance[ cMMQ !=
3
Q-value and Kinetic energy
The Q-value can also be expressed in terms of theincoming and outgoing kinetic energies.
For fixed target experiments KA = 0. For exothermic reactions Q > 0 some of the mass
energy is converted to kinetic energy. For endothermic reactions Q < 0 some of the
incoming particle’s kinetic energy is converted tomass.
aABb KKKKQ !!+=
Threshold Kinetic Energy
In endothermic reactions the kinetic energy of theincoming particle must be sufficient to supply the neededmass and conserve momentum.
The minimum kinetic energy of the incoming particleneeded to initiate the reaction is called the thresholdenergy.
!!"
#$$%
& +'=
A
Aath
M
MMQK
4
A Typical Experiment
Incoming particle beam
Detector
Faraday Cup
Target
What do we measure?
Detector might measure the outgoingparticle’s: Type of particle Energy Momentum (direction and magnitude) Number of particles (of each type)
5
Number of particles
The number of particles detected dependson a variety of factors: Beam flux Number of “targets” – target thickness Detector placement, size and efficiency Physical properties of the reaction
Cross-section
The cross-section is related to the probability thata certain reaction will take place.
Independent of other factors such as beam flux ortarget size.
σ has units of area: barn (b) = 10-28 cm
spot) beam within nuclei target ofer area)(numbnit incident/u particles of(number
emitted particles outgoing ofnumber =!
6
Cross-section as Effective Area
One way tovisualize cross-section is to thinkof it as theeffective area ofthe target(assuming theincident particleis point-like.)
Cross-section of a Reaction
Cross-section is a measure of the reactionprobability.
R1
R2
b b R1 + R2
Collision of two classical spheres.
7
Calculating Cross-section fromExperimental Parameters Y = yield = number of reactions/unit time n = particle density
= number of target particles/unit volume t = thickness of target A = area of beam spot Φi = incident flux
= beam particles/[(unit time)(unit area)]
Experimental Cross-section
The yield is Y = ΦinAtσso the total cross-section is
nAt
Y
i!
="
8
Differential Cross-section
An actual experiment does not measure thetotal yield but the yield of particles thatscatter into the detector.
The detector is placed at a position (r,θ,φ)and has an active area facing the target.
In general the cross-section is not isotropic– it depends on (θ,φ) .
Nuclear Reactions
Mechanisms
9
Direct reactions
Reaction energy ~ 20 MeV or greaterDominated by strong interactionExamples:
Knockout Pickup Stripping
Compound Nucleus Mechanism
Low energy (< 20 MeV)A composite nucleus is formed.Time scale on order of 10-15 s.
16O
p + 15Nd + 14N
3He + 13C4He + 12C6Li + 10B
p + 15Nd + 14N
3He + 13C4He + 12C6Li + 10B
n + 15Ot + 13Nγ + 16O
10
Energy Level of CompoundNucleusResonances
2
h!"#
Fission and Fusion
11
Fission
Nucleus splits into two roughly equal sizedfission fragments ( and a few stray nucleonsin some cases.)
Moves lower on the binding energy curve.Spontaneous fission: Z2/A >48, A > 220Spontaneous fission has low rates compared
to alpha decay.
Induced fission
Neutron is absorbed producing acompound nucleus that quicklyfissions.
12
Prompt and Delayed Neutrons Neutrons released with the
fragments are called promptneutrons. These have high kineticenergies and a low cross sectionfor absorption.
The neutron-rich fission fragmentsmay also emit neutrons during thetheir beta decay back to the line ofstability. These have low kineticenergies and high absorption crosssections. Fission fragments usually
have unequal masses.
Chain Reactions
Emitted neutrons can be used to create secondaryfission reactions and so on.
13
Controlled Chain Reactions
Moderating material is used to slow fastneutrons. (water, graphite)
Control rods absorb neutrons (cadmium).
Nuclear Reactors
14
Fusion
Two light nucleicombine to form aheavier nucleus.
Fusion vs. Fission
15
Stellar Fusion
The p-p chain
Stellar Nucleosynthesis
All elements with the exception of H, He and Liwere made in stars.
Nuclear processes that provide the energy of a starmake heavier nuclei out of the H and He.
Some nuclei are made during the normal lifetimeof a star.
The nuclei above 56Fe on the binding energy curveare made only during supernovae explosions.
16
The r-process100
150
200
250
10
-310
-210
-1
10
010
1
28
30 32 34 36 38 40 42 44 46 48 50 52 54 56 58
60
62
64
66 68
70
72
74 76
78
80
82
84
86
88 90
92 94
96
98
100 102
104
106
108
110
112 114
116 118
120
122
124
126
128
130 132
134 136
138
140 142 144 146 148
150
152
154
156
158
160
162
164 166 168 170 172 174
176
178
180 182
184
186
188 190
26
28
30
32
34
36
38
40
42
44
46
48
50
52
54
56
58
60
62
64
66
68
70
72
74
76
78
80
82
84
86
88
90
92
94
96
98
100
Known massKnown half-lifer process waiting point (ETFSI-Q)
Solar
r-ab
unda
nces
Fusion Power –Magnetic confinement
http://ippex.pppl.gov/
17
Fusion Power –Magnetic Confinement
National Spherical Torus Experiment
Fusion Power –Inertial Confinement
NOVA Laser test chamber
18
Fusion Power –Inertial Confinement
National Ignition Facility