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What have we learned last time?What have we learned last time?
• Q value
• Binding energy
• Semiempirical binding energy formula
• Stability
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Nuclear ReactionsNuclear Reactions
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Scattering ReactionsScattering Reactions
• Elastic scattering
A(a,a)A
• Inelastic scattering
A(a,a’)A*
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Other reactionsOther reactions
FedCo
FeHedCo
NindCo
CopdCo
NidCo
CoddCo
CoddCo
5726
5927
5826
32
5927
6028
5927
6027
5927
6128
5927
5927
5927
5927
5927
),(
),(
),(
),(
),(
*'),(
),(
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Energetics of nuclear reactionsEnergetics of nuclear reactions
• Energy, mass number, momentum conservation
• Q-value : positive exoergic; negative endoergic
• Example of endoergic14N + 4He 1H + 17O + Q
Q = -1.19 MeV
Is it enough to start the reaction?
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Momentum correctionMomentum correction
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Coulomb barrier correctionCoulomb barrier correction
14N + 4He 1H + 17O + Q
yx
yx
yx
yx
RR
ZZ
RR
eZZV
44.12
MeV6.3)14()4(4.1
7244.144.13/13/1
yx
yx
RR
ZZV
Threshold energy in SL: 3.6 MeV [(4+14)/14] = 4.6 MeV
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Cross sectionCross section
• Symbol σ
• Geometrical cross section
σ = π (Rtarget)2
10-24 cm2
Barn, 1 b = 10-24 cm2 = 100 fm2
1 mb = 10-27 cm2
1 μm = 10-30 cm2
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Measurements of cross Measurements of cross sectionssections
• Thin targets
• Thick targets
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Compound Nucleus ReactionsCompound Nucleus Reactions
yrast line – lowest energy for a given angular momentum
3-4 MeV/A
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Discovery of FissionDiscovery of Fission
• 1938
• average number of 2.4 neutrons.
• statistical phenomenon, Gaussian distribution, independent of
the fissioning nucleus.
QnKrBaUUn 38936
14456
*23692
23592
10
Otto Hahn and Lise Meitner, 1913, at the KWI for Chemistry in Berlin
1944 Nobel Prize in Chemistry for Otto Hahn "for his discovery of the fission of heavy atomic nuclei”
Until 1938 all scientists believed that the elements with Z > 92 (transuranium elements) arise when uranium atoms are bombarded with neutrons.
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Radioactive Decay ProcessesRadioactive Decay Processes
Pr141331414141min1814125141
9310931093min793693 6
dhs
yhs
CeLaBaCs
NbZrYSrRb
QnRbCsUUn 29337
14155
*23692
23592
10
These radioactive products are the waste products of nuclear reactors.
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The fragments in the vicinity of A = 95 and A = 140 share 92 protons.Prompt neutrons are emitted in 10-16 s.Delayed neutrons intensity 1 in 100 fissions or 0.02 neutrons per fission(from neutron emission). Delayed neutrons are essential for controlling the reactors.
Mass Distribution of FissionMass Distribution of Fission
95 140
symmetric
Source: University of Waterloo
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Neutron Cross Sections for Neutron Cross Sections for fission of U and Pufission of U and Pu
1 b = 10-28 m2; 1 MeV = 1.6 x 10-13 J
1/v -dependence
Source: World Nuclear Association
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Binding energy per nucleonBinding energy per nucleon
http://hyperphysics.phy-astr.gsu.edu/
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Q-valueQ-valueEnergy released in a nuclear reaction (> 0 if energy is released, < 0 if energy is used)
Example: The sun is powered by the fusion of hydrogen into helium:
4p 4He + 2 e+ + 2e
Mass difference dMreleased as energydE = dM x c2
mmmmcQ eHenucpnuc 224/ 42
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Fusion ReactionFusion Reaction
QnHeHH
QnHeHH
QHepH
432
322
32
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How Do We Produce Exotic Nuclei?How Do We Produce Exotic Nuclei?
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5858Zn and the Zn and the rprp-process-process
Astrophysicsrp-process:• hot and explosive hydrogen burning environments (X-ray burst) • stops at 56Ni?• beyond 56Ni: 56Ni(p,γ)57Cu(p,γ)58Zn• rates 56Ni(p,γ)57Cu; spectroscopy of 57Cu• rates 56Ni(d,p); spectroscopy of 57Cu• 57Cu(p,γ)58Zn – no information• calculations based on 58Ni-58Zn mirror symmetry
Spectroscopic Information58Zn (Z=30, N=28)• no excited states, spin and parity• predicted from 58Ni
29
30
5958
60
60
5856 57
61
59
Cu
Ni
Zn
28
59
30
58
57
29 3128
N=Z
?
• no excited states in Z > N
• mirror symmetry
– 59Zn-59Cu
– 58Zn-58Cu
• rp-process
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5858ZnZn2828
36Ar + 24Mg → 60Zn*→ 58Zn + 2nnμb (20 x 10-34 m2)
Spokespersons: C. Andreoiu and P.E. Garrett, University of Guelph @ Argonne National Laboratory, Chicago, 2006
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Gammasphere + Ancillary DetectorsGammasphere + Ancillary Detectors
• Gammasphere (100 Ge detectors)• MICROBALL (95 CsI) • 20 neutron detectors
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Particle Detectors - MICROBALLParticle Detectors - MICROBALL
• 95 CsI detectors• average efficiency
80% alphas70% protons
D.G. Sarantites et al. Nucl. Instrum. Meth. A 400, 87 (1997)