Lesson 12 - Oregon State Universityoregonstate.edu/instruct/ch374/ch418518/Lesson12-rev.pdf ·...
Transcript of Lesson 12 - Oregon State Universityoregonstate.edu/instruct/ch374/ch418518/Lesson12-rev.pdf ·...
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Lesson 12
Nuclear Reactions --Part 2
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Compound Nuclear Reactions
• The compound nucleus is a long-lived reaction intermediate that is formed by a complex set of interactions between the projectile and the target.
• The projectile and target nuclei fuse and the energy of the projectile is shared among all the nucleons of the composite system.
• The lifetime of the CN is ~ 10-18-10-16 s. This lifetime is directly measurable by crystal-blocking techniques.
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Independence Hypothesis or “Amnesia Assumption”
• The mode of decay of the CN is independent of its mode of formation.
• Caveat: Conservation laws apply. • Experimental evidence: the Ghoshal expt. • Angular distributions symmetric about 90°
in CN frame.
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62Cu>63Zn>62Ni
ang. mom effects
The Ghoshal Experiment
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€
σ = πD 2 2l +1( )l=0
∞
∑ Tl
Cross Sections--General
€
probability =Tlβ Eβ( )Tlγ Eγ( )
l γ ,Eγ
∑
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
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Cross Sections--Energy Dependence
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Γ/D << 1
For reaction a + A →C→b + B
€
σ = πD 2 2JC +1( )2JA +1( ) 2Ja +1( )
ΓaAΓbB
ε −ε0( )2 +Γ
2⎛
⎝ ⎜
⎞
⎠ ⎟ 2
Applying this to (n,γ) reactions
€
σn,γ = πD 2 2JC +1( )2JA +1( ) 2( )
ΓnΓγ
ε −ε0( )2 +Γ
2⎛
⎝ ⎜
⎞
⎠ ⎟ 2
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Γ/D >>1
For reaction a + A →C→b + B
σab = σC PC(b)
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Γ/D >>1 • Assumption is that of statistical equilibrium • For reaction a + A →C→b + B
σab = σC PC(b) • So the problem is to calculate the probability that
C will decay to B + b.
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Level densities
€
ρ(E*) = Cexp[2(aE*)1/ 2]
a =A12
to A8
E* = aT 2 −T
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If emitted particles are neutrons
€
N(ε )dε =εT 2 exp −ε /T( )dε
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If emitted particles are charged particles
€
N(ε )dε =ε −εsT 2 exp −(ε −εs )/T( )dε
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Excitation functions
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Photonuclear Reactions
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Photonuclear Reactions
• GDR-- a giant oscillation of the nuclear protons vs the nuclear neutrons
• dipole sum rule
€
σabs Eγ( )dEγ ∝NZA
≈ 0.058 NZAMeV − barns
0
∞
∫
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Heavy Ion Reactions
• Classical motion • Dominated by high angular momentum • Aproj > 4
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Mechanisms
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Mechanisms
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Elastic scattering
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Fusion
€
σR = πRint2 1−
V Rint( )Ecm
⎡
⎣ ⎢
⎤
⎦ ⎥
Rint = R1 + R2 + 3.2 fm
RI = 1.12 Ai1/3 - 0.94 AI
-1/3 fm
€
V Rint( ) = 1.44 Z1Z2Rint
− b R1R2R1+ R2
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Deep Inelastic Scattering
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High Energy Reactions
• Low energy (< 10 MeV/A) • Intermediate Energy ( 20-250 MeV/
A) • High Energy (>250 MeV/A)
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Spallation
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New high energy mechanisms
• Spallation • IMF formation • Cascade processes • Participant-Spectator Picture
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Cascades nucleon-nucleon collisions
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Participant-Spectator Physics
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Multifragmentation • “Multifragmentation” refers to central collisions
where several IMFs are emitted. • Caloric curve