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Principi fisici dell’energia nucleare
F.V. Frazzoli
Giornata di studioEnergia nucleare - Nuove prospettive ed opportunità
Terni 7Marzo 2008
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• energy - electron-volt1 electron-volt = kinetic energy of an electron when
moving through potential difference of 1 Volt;• 1 eV = 1.6 × 10-19 Joules• 1 kW•hr = 3.6 × 106 Joules = 2.25 × 1025 eV• 1 MeV = 106 eV
• mass - eV/c2
• 1 eV/c2 = 1.78 × 10-36 kg• electron mass = 0.511 MeV/c2
• proton mass = 938 MeV/c2
• neutron mass = 939.6 MeV/c2
• amu = (mass of 121266CC atom)/12
• amu = 1.66 x 10-27kg • amu = 931.494 MeV/c2
About Units
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• Proton – Charge = 1 elementary charge e = 1.602 x 10-19 C– Mass = 1.673 x 10-27 kg = 938.27 MeV/c2 =1.007825 u
= 1836 me– spin ½, magnetic moment 2.79 eħ/2mp
• Neutron– Charge = 0– Mass = 1.675 x 10-27 kg = 939.6 MeV/c2 = 1.008665 u =
1839 me– spin ½, magnetic moment -1.9 eħ/2mn
Properties of Nucleons
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Symbolism
XAZ
• X: Chemical symbol of the element• Z : Atomic number = number of protons in nucleus• A: Mass Number = Z+N
• N: Number of neutrons in nucleusExample:
» Mass number is 27» Atomic number is 13» Contains 13 protons» Contains 14 (27 – 13) neutrons
Al2713
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n-p and p-p interactions
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Beta- DecayAZ A(Z+1) + e- + an anti-neutrino
• A neutron has converted into a proton, electron and an anti-neutrino.
Beta+ DecayAZ A(Z-1) + e+ + a neutrino
• A proton has converted into a neutron, positron and a neutrino.
Electron CaptureAZ + e- A(Z-1) + a neutrino
• A proton and an electron have converted into a neutron and a neutrino.
~9944
9943 ν++→ −eRbTc
ν++→ +eCN 126
127
ν+→+ − CeN 126
127
Radioactivity
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• Alpha DecayAZ A-4(Z-2) + 4He
• Number of protons is conserved.• Number of neutrons is conserved.
• Gamma EmissionAZ* AZ + γ
• An excited nucleus loses energy by emitting a photon.
HePbPo 42
20682
21084 +→
)140(9943
*9943 keVTcTc γ+→
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• Activity A: number of decays per unit time
• decay constant λ: probability of decay per unit time
• Rate of decay ∝ number N of nuclei
• Solution of diff. equation (N0 = nb. of nuclei at t=0)
• Mean life τ = 1/ λ
Law of radioactive decay.
dtdNA =
.NdtdN λ−=
.)( 0teNtN λ−=
λτ
λ
λ
1
0
0 ===
∫
∫
∫∫
∞−
∞−
dte
dtet
dN
dNt
t
t
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• The decay curve follows the equation– N = No e- λt
• The half-life is also a useful parameter– The half-life is defined as the
time it takes for half of any given number of radioactive nuclei to decay
Decay Curveλλ
0.6932ln21 ==T
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Radioactive Decay Paths
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• It has a single bound state with a binding energy of 2.22463 ± 0.00004 MeV, which is measured with
- the formation reactions
- or inverse reaction
γ dn p +→+
n p d +→+γ
Properties of the Deuterium
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ΔE = Nuclear binding energy = ∆mc2
1 proton 1.00728 u1 neutron 1.00866 u mass of deuterium:2.01355 u
________mass of parts: 2.01594 u missing mass 0.00239 u
The photon released in forming deuterium has anenergy of 2.225 MeV, equivalent to the 0.00239 u
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PH320 APPLIED NUCLEAR PHYSICS PH320 APPLIED NUCLEAR PHYSICS –– PartPart 1 1 –– INTERACTIONS INTERACTIONS 17
~0.025eV THERMAL ~1eV EPITHERMAL ~1keV SLOW 100 keV – 100 MeV FAST >100 MeV HIGH ENERGY
They are calledthermal because they
are in thermalequilibrium with their
surroundings
Neutrons are classified in vague groups depending on their kinetic energy
1 keV 10 keV 100 keV 1 MeV 10 MeV
Fission
NuclearReactions
Radiative Capture
Elastic Scatter
Inelastic Scatter
Neutron energies
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σ: Microscopic Cross Section
• Units: cm2
• Describes the theoretical “size” that an atom presents, like a target, to be hit by an approaching neutron
• Frequently reported in “barns”• 1 barn = 10-24 cm2
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H1 σ (n,el)σ (n,γ)
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Reaction Rate (R)
• Basic Equation:
R=NΦσ
interactions/cm3•s
atoms/cm3
neutrons/cm2•s
cm2
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( ) neutronsYXUnU ++→→+*236
9223592
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σ (n,f)fissile isotopesU233, U235, Pu239
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σ (n,f)fertile isotopesTh232, U238
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Prompt Fission Neutron Energy Spectrumfor Thermal Fission of Uranium-235
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Delayed neutron emission
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σ (n,f) U235, σ (n,γ) U235
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ν: number of neutrons per fissionη: number of neutrons in fission per neutron absorbed
3.042.582.51
Fast (>0.5 MeV)
2.932.492.42
Thermal (0.025eV)
ν
239Pu
233U
235U
Isotope(100%)
2.902.152.402.292.352.07
Fast (>0.5 MeV)
Thermal (0.025eV)
η
fa
f
σσ
αα
νσσ
νη γ=+
=×= ,1
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• Thermal fission U235 • LWR reactor (PWR)
JMeVQ
bbf
af
11102.3200:07.2:42.2:
%5.17:,681:,584:
−=
=
ην
σσ
ασσ γ
yearperrefuelling
tonUGWdupburnfuelwatercoolant
tonfueltotalCdInAGorCBrodcontrol
UUOfueldiametermlengthmcore
MWpowerelectricalefficiency
MWpowerthermal
e
th
31:
/33::
115::
)%3.3(:)(4.3),(2.4:
1300:%34:
3800:
4
2352
−
−−
⇒≈
⇒≈
dUKgdfissions
/7.4/10
235
25
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Properties of some important moderators
0.00450.0010.66σa (barns)
4.710.643.8σs (barns)
1153620no. of collision tothermalize
fissionneutrons
GraphiteHeavywaterD2O
WaterH2O
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Kinetic Energy of Fission Products 167 MeV Energy of Fission Neutrons 5 “Instantaneous Gamma-rays Energy 5 “Capture Gamma-rays Energy 10 “Beta Particles From Fission Products 7 “Gamma-rays from Fission Products 6 “
_________200 MeV
Recoverable Energy from Fission
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Neutron cycle in reactor
Follow the fate of a neutron from one generation to the nextwith conditional probabilities of various loss mechanisms.
Fissionneutron
Leak out of system
Absorbed in system
Absorbed in fuel
Radiativecapture
Fission
Absorbed innon-fuel
ν new fission neutrons
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Neutron Economy Equation
LCRRdtdn −−×+−×= )1( αν
neutrons/fission
fission rate
capture-to-fission ratio
fertile conversion rate
neutron loss rate
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σ (n,f)U235, U238
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σ (n,γ)U235, U238
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Conversion or Breeding
238 23992 92U Un γ+ → +
23993 Np β ν−+ +
23.5min
23994 Pu β ν−+ +
2.35 d
24110 yr
Fertile:
Fissile:
232 23390 90Th Thn γ+ → +
23391Pa β ν−+ +
22.3min
23392 U β ν−+ +
27.0 d
159200 yr
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average number of neutrons/absorption for breeding
21
1)(
)(>
+×=×=
αν
σσνηabsorption
fission
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Characteristics of spent fuel
• Highly radioactive– Emits very strong radiation – needs shielding– Emits heat – needs cooling– Contains many different nuclides – with very
different half life (seconds to millions of years)
• Contains valuable material (U, Pu)
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Composition of a PWR assembly
Fresh Fuel
Spent Fuel
Uranium (4% 235U) : 500 kg
Uranium (0,9% 235U) : 475 kg Pu : 5kg FP : 20 kgrecyclables
480 Kg U238+20 Kg U235
470.7 Kg U238+4.3 Kg U235
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1E+00
1E+01
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
1E+08
1E+09
10 100 1 000 10 000 100 000 1 000 000
Time (years)
Pote
ntia
l rad
ioto
xici
ty*
(Sv/
thm
) Classic glass (MA + FP)
Spent fuel without reprocessing(Pu + MA + FP)
Light glass (FP)
Initial Uranium in mined ore
* as if incorporated, per tonnes of heavy metal
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Partitioning & Transmutation• P&T is a potential HLW
management strategy toprocess the waste bypartitioning specific hazardouselements or nuclides and thentransmuting them into lesshazardous forms
• P&T aims to reduce the radiotoxicity of disposed wasteor reduce the duration forwhich the waste represents a threat to the environment
Transmutation technologies under investigation:
• neutron flux in a fast reactor• neutron flux in a thermal reactor• fast sub-critical reactor coupled
to a particle accelerator
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Np237 burning with fast and thermal neutron fluxes
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