Download Nuclear Reactions Reactions

Nuclear Reactions
Reactions
A + a → B + b
 A (a,b) B
(p,p)12C
 Inelastic scattering: 12C (p,p´)12C*
 Rearrangement reaction: 54Fe (32S,28Si)58Ni
 Capture reaction: 12C (p,γ)13N
 Others: 2H(n,2n)1H
 Elastic scattering:
12C
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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 between
the mass energies of the entrance channel particles
and the exit channel particles.
Q = [ M (Entrance)! M (Exit )]c 2
 The Q-value is the energy release in the reaction.
 For elastic collisions Q = 0 in inelastic collisions
Q < 0.
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Q-value and Kinetic energy
 The Q-value can also be expressed in terms of the
incoming and outgoing kinetic energies.
Q = Kb + K B ! K A ! K a
 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 to
mass.
Threshold Kinetic Energy
 In endothermic reactions the kinetic energy of the
incoming particle must be sufficient to supply the needed
mass and conserve momentum.
 The minimum kinetic energy of the incoming particle
needed to initiate the reaction is called the threshold
energy.
& M + MA #
!!
K th = 'Q$$ a
M
%
"
A
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A Typical Experiment
Detector
Faraday Cup
Incoming
particle beam
Target
What do we measure?
 Detector might measure the outgoing
particle’s:




Type of particle
Energy
Momentum (direction and magnitude)
Number of particles (of each type)
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Number of particles
 The number of particles detected depends
on a variety of factors:




Beam flux
Number of “targets” – target thickness
Detector placement, size and efficiency
Physical properties of the reaction
Cross-section
!=
number of outgoing particles emitted
(number of particles incident/unit area)(number of target nuclei within beam spot)
 The cross-section is related to the probability that
a certain reaction will take place.
 Independent of other factors such as beam flux or
target size.
 σ has units of area: barn (b) = 10-28 cm
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Cross-section as Effective Area
 One way to
visualize crosssection is to think
of it as the
effective area of
the target
(assuming the
incident particle
is point-like.)
Cross-section of a Reaction
 Cross-section is a measure of the reaction
probability.
Collision of two classical spheres.
R2
b
R1
b
R 1 + R2
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Calculating Cross-section from
Experimental 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 = ΦinAtσ
so the total cross-section is
Y
"=
! i nAt
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Differential Cross-section
 An actual experiment does not measure the
total yield but the yield of particles that
scatter 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
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Direct reactions
 Reaction energy ~ 20 MeV or greater
 Dominated by strong interaction
 Examples:
 Knockout
 Pickup
 Stripping
Compound Nucleus Mechanism
 Low energy (< 20 MeV)
 A composite nucleus is formed.
 Time scale on order of 10-15 s.
p + 15N
d + 14N
3He
+ 13C
4He
+ 12C
6Li
+ 10B
16O
γ + 16O
t + 13N
n + 15O
p + 15N
d + 14N
3He + 13C
4He + 12C
6Li + 10B
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Energy Level of Compound
Nucleus
 Resonances
"# !
h
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Fission and Fusion
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Fission
 Nucleus splits into two roughly equal sized
fission fragments ( and a few stray nucleons
in some cases.)
 Moves lower on the binding energy curve.
 Spontaneous fission: Z2/A >48, A > 220
 Spontaneous fission has low rates compared
to alpha decay.
Induced fission
 Neutron is absorbed producing a
compound nucleus that quickly
fissions.
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Prompt and Delayed Neutrons
 Neutrons released with the
fragments are called prompt
neutrons. These have high kinetic
energies and a low cross section
for absorption.
 The neutron-rich fission fragments
may also emit neutrons during the
their beta decay back to the line of
stability. These have low kinetic
energies and high absorption cross
sections.
Fission fragments usually
have unequal masses.
Chain Reactions
 Emitted neutrons can be used to create secondary
fission reactions and so on.
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Controlled Chain Reactions
 Moderating material is used to slow fast
neutrons. (water, graphite)
 Control rods absorb neutrons (cadmium).
Nuclear Reactors
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Fusion
 Two light nuclei
combine to form a
heavier nucleus.
Fusion vs. Fission
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Stellar Fusion
 The p-p chain
Stellar Nucleosynthesis
 All elements with the exception of H, He and Li
were made in stars.
 Nuclear processes that provide the energy of a star
make heavier nuclei out of the H and He.
 Some nuclei are made during the normal lifetime
of a star.
 The nuclei above 56Fe on the binding energy curve
are made only during supernovae explosions.
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25
0
The r-process
20
0
r-a
bu
nd
an
ce
s
Known mass
Known half-life
r process waiting point (ETFSI-Q)
100
98
96
So
lar
94
92
90
88
86
84
186
188 190
82
80
15
0
78
76
164 166 168 170 172 174
74
158
68
66
64
140 142 144 146 148
62
58
128
130 132
134 136
150
152
154
156
138
46
44
116 118
10 -3
10
0
10 -1
56
54
52
10 -2
10 1
180 182
160
60
10 0
178
162
72
70
50
48
42
92 94
40
38
36
34
74 76
32
30
28
26
28
176
184
30 32 34 36 38 40 42 44 46 48 50 52 54 56 58
60
62
64
66 68
70
78
80
82
84
86
96
98
100 102
104
106
108
110
120
122
124
126
112 114
88 90
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Fusion Power –
Magnetic confinement
http://ippex.pppl.gov/
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Fusion Power –
Magnetic Confinement
National Spherical Torus Experiment
Fusion Power –
Inertial Confinement
NOVA Laser test chamber
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Fusion Power –
Inertial Confinement
National Ignition Facility
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