Applications of Nuclear Physics
description
Transcript of Applications of Nuclear Physics
![Page 1: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/1.jpg)
Tony Weidberg Nuclear Physics Lectures 1
Applications of Nuclear Physics
• Fusion– How the sun works– Fusion reactor
• Radioactive dating– C dating– Rb/Sr age of the Earth
![Page 2: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/2.jpg)
Tony Weidberg Nuclear Physics Lectures 2
Fusion in the Sun
• Where nuclear physics meets astrophysics and has a big surprise for particle physics.
• Neutrinos• Heavier Elements
– Up to Fe– Beyond Fe
• Sun by Numbers:L=3.86 1026 WM=1.99 1030 kgR=6.96 108 m
![Page 3: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/3.jpg)
Tony Weidberg Nuclear Physics Lectures 3
How to power the sun• Try gravity
• Too short!• By elimination must be nuclear fusion.• Energy per particle (nuclei/electron)
• Gives plasma, ionised H and He.
MYrLUt
JR
GMU
3~/
108.3 412
keVM
MUE
S
P 1~)(~
![Page 4: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/4.jpg)
Tony Weidberg Nuclear Physics Lectures 4
PP Chain
• Very long range weather forecast very cold• But only ~ 10% H atoms converted to He
MeV49.5HeHp)2( 32
21
MeV42.0eHpp)1( e21
MeV86.12ppHeHeHe)3( 42
32
32
MeV02.12ee)4(
MeV55.6)H(E
MeV26.0E
![Page 5: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/5.jpg)
Tony Weidberg Nuclear Physics Lectures 5
Physics of Nuclear Fusion• All reactions at low energy are suppressed by
Coulomb barrier (cf decay). • Reaction rate: convolution of MB distribution
and barrier penetration (EG= Gamow Energy)
• Problem:) too small to measure! Extrapolated from higher energy or from n scattering.
2
0
2212
42
)exp()0(~)(
c
eZZmcE
E
EE
G
G
![Page 6: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/6.jpg)
Tony Weidberg Nuclear Physics Lectures 6
Example C
![Page 7: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/7.jpg)
Tony Weidberg Nuclear Physics Lectures 7
Reaction Rates & Coulomb Barrier• From definition of
• Main contribution around min
)v(vNNR ba
2/3B
1/3G03/2
1/2G
BT)(kEE0
2E
E
Tk
1
dE
dφ
)Tk2
mvexp()
Tk
m()
2()v(P
B
22/3
B
2/1
mvdvdEmv2
1E;dv)v(P)v(v)v(v 2
0
E/ETk/E)E(;dE)]E(exp[)E()v(v GB0
![Page 8: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/8.jpg)
Tony Weidberg Nuclear Physics Lectures 8
Cross Sections and W.I.• Consider first reaction pp chain
• Cross section small even above Coulomb barrier because this is a weak interaction
• Order of magnitude estimate
• At 1 MeV s=36b; tnuclear~10-23s; tdecay~900s
~10-25b• This reaction is the bottleneck explains long time
scales for nuclear fusion to consume all the H in the core of the sun.
MeV42.0eHpp e21
decay
nuclearS t
t~
![Page 9: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/9.jpg)
Tony Weidberg Nuclear Physics Lectures 9
Heavier Elements• He to Si:
• 8Be unstable! Resonance in C12 enhances rate.• Heavier elements up to Fe
– Photo-disintegration n,p and . These can be absorbed by other nuclei to build up heavier nuclei up to Fe.
• Fe most stable nucleus, how do we make heavier nuclei?
HeSiOO
OCHe
CBeHe
BeHeHe
4281616
16124
1284
844
![Page 10: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/10.jpg)
Tony Weidberg Nuclear Physics Lectures 10
Fusion Reactors
• Use deuterium + tritium:
– Large energy release– Large cross-section at low energy– Deuterium abundant (0.015% of H).– Breed Tritium in Lithium blanket– .
MeV62.17nHeHH 42
31
21
MeV8.4HeHLin
nHeHMeV46.2Lin42
31
63
42
31
73
![Page 11: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/11.jpg)
Tony Weidberg Nuclear Physics Lectures 11
Fusion Reactors
• Energy out > Energy in
• Lawson criteria (assume kBT=20 keV).– number density D ions : – Cross-section: – Confinement time for plasma: tc
– Energy released per fusion: Efusion
cfusion2
out tEvE
TkE Bin c1319
inout t)sm10(~E/E
![Page 12: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/12.jpg)
Tony Weidberg Nuclear Physics Lectures 12
Magnetic Confinement
• Confine plasma with magnetic fields.– Toroidal field: ions spiral around field
lines.– Poloidal fields: focus ions away from
walls.
• Heating:– RF power accelerates electrons– Current pulse causes further heating.
![Page 13: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/13.jpg)
Tony Weidberg Nuclear Physics Lectures 13
Jet
![Page 14: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/14.jpg)
Tony Weidberg Nuclear Physics Lectures 14
![Page 15: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/15.jpg)
Tony Weidberg Nuclear Physics Lectures 15
Magnetic Confinement Fusion
• JET passed break-even (ie achieved Lawson criteria).
![Page 16: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/16.jpg)
Tony Weidberg Nuclear Physics Lectures 16
Inertial Confinement Fusion
Very Big Laser
Mirrors
D-T Pellet
![Page 17: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/17.jpg)
Tony Weidberg Nuclear Physics Lectures 17
Inertial Confinement Fusion
![Page 18: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/18.jpg)
Tony Weidberg Nuclear Physics Lectures 18
Radioactive Dating
• C14/C12 for organic matter age of dead trees etc.
• Rb/Sr in rocks age of earth.
![Page 19: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/19.jpg)
Tony Weidberg Nuclear Physics Lectures 19
Carbon Dating
• C14 produced by Cosmic rays (mainly neutrons) at the top of the atmosphere.
• C14 mixes in atmosphere and absorbed by plants/trees constant ratio C14 / C12 . Ratio decreases when plant dies. t1/2=5700 years.
• Either– Rate of C14 radioactive decays– Count C14 atoms in sample by Accelerator Mass
Spectrometer.
• Which is better?• Why won’t this work in the future?
![Page 20: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/20.jpg)
Tony Weidberg Nuclear Physics Lectures 20
Carbon Dating Calibration
![Page 21: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/21.jpg)
Tony Weidberg Nuclear Physics Lectures 21
How Old Is The Earth?
• Rb87 Sr87: decay t1/2=4.8 1010 yr
• Assume no initial daughter nuclei get age from ratio of daughter/parent now.
)t(N)t(N)t(N 0p1P1D
)tt(exp()t(N)t(N 010p1P
)t(N
)t(Nln
1t
1p
0p
)t(N
)t(N1ln
1t
1p
1D
![Page 22: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/22.jpg)
Tony Weidberg Nuclear Physics Lectures 22
Improved Calculation• Allow for initial daughters to be present.• Need another isotope of the daughter D’ which is stable
and not a product of a radioactive decay chain. • Plot vs straight line fit age and initial ratio.
)t(N)t(N)t(N)t(N 0p0D1P1D
)t(N
)t(N
1D
1D
)t(N
)t(N
1D
1P
)t(N
)t(N)t(N
)t(N
)t(N)t(N
0D
0p0D
1D
1P1D
)t(N
)t(N]1)t[exp(
)t(N
)t(N
)t(N
)t(N
0D
0D
1D
1P
1D
1D
![Page 23: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/23.jpg)
Tony Weidberg Nuclear Physics Lectures 23
Age of Earth
• Rb/Sr method• Stable isotope of
daughter is Sr86
• Fit gives age of earth=4.53 109 years. S
r87/
Sr8
6
Rb87/Sr86
1.0 4.0
![Page 24: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/24.jpg)
Tony Weidberg Nuclear Physics Lectures 24
Cross-Sections
• Why concept is important– Learn about dynamics of interaction and/or
constituents (cf Feynman’s watches).– Needed for practical calculations.
• Experimental Definition• How to calculate
– Fermi Golden Rule– Breit-Wigner Resonances– QM calculation of Rutherford Scattering
![Page 25: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/25.jpg)
Tony Weidberg Nuclear Physics Lectures 25
Definition of • a+bx
• Effective area or reaction to occur is
Beam a
dx
Na
Na(0) particles type a/unit time hit target b
Nb atoms b/unit volume
Number /unit area= Nb dx
Probability interaction = Nbdx
dNa=-Na Nb dx
Na(x)=Na(0) exp(-x/) ; =1/(Nb )
![Page 26: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/26.jpg)
Tony Weidberg Nuclear Physics Lectures 26
Reaction Rates• Na beam particles/unit volume, speed v
• Flux F= Na v
• Rate/target b atom R=F• Thin target x<<: R=(Na
T) F Total
• This is total cross section. Can also define differential cross sections, as a function of reaction product, energy, transverse momentum, angle etc.
• dR(a+bc+d)/dE=(NaT) F d(a+bc+d) /dE
![Page 27: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/27.jpg)
Tony Weidberg Nuclear Physics Lectures 27
Cross Section Calculations
• Use NRQM to calculate cross sections:
• Calculation (blackboard) gives Breit-Wigner resonance for decay of excited state
nn0nn )/tiEexp()t(a)t(;H
dti
)EE(PH2
)t(a
4/)EE(
H)t(a
nm2
mn2
n
22nm
2mn2
n
4)EE(
1
2)EE(P
22nm
nm
![Page 28: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/28.jpg)
Tony Weidberg Nuclear Physics Lectures 28
Breit-Wigner Resonance
• Important in atomic, nuclear and particle physics.
• Uncertainty relationship
• Determine lifetimes of states from width.
• t=1/=FWHM;
~tE
![Page 29: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/29.jpg)
Tony Weidberg Nuclear Physics Lectures 29
Fermi Golden Rule• Decays to a channel i (range of states n).
Density of states ni(E). Assume narrow resonance
dE)EE(P)E(nH2
P 0i2
0ii
)E(nH2
P 0i2
0ii
TotaliiTotali
i RPR;R;P
)E(nH2
R 0i2
0ii
i
![Page 30: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/30.jpg)
Tony Weidberg Nuclear Physics Lectures 30
Cross Section
• Breit Wigner cross section.
• Definition of and flux F:
v
k4
)2(
V)E(n;v
dk
dE;
m2
)k(E
k4)2(
V)k(n
vVF
)r.kiexp(V
FR
2
3
2
23
1
2/1
![Page 31: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/31.jpg)
Tony Weidberg Nuclear Physics Lectures 31
Breit-Wigner Cross Section
• Combine rate, flux & density states
4/)EE(
E
)E(n
1
2
1R
)E(nH2)E(
4/)EE(
H)t(aR
2201
f1i
210i
f22
01
201f2
o
4/)EE(
E
2
1
k4V
v)2(
v
V22
01
f1i2
3
![Page 32: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/32.jpg)
Tony Weidberg Nuclear Physics Lectures 32
Breit-Wigner Cross Section
4/)EE(k 2201
fi2
n + 16O 17O
![Page 33: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/33.jpg)
Tony Weidberg Nuclear Physics Lectures 33
Low Energy Resonances
• n + Cd total cross section.
• Cross section scales ~ 1/E1/2 at low E.
• B-W: 1/k2 and ~n(E)~k
![Page 34: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/34.jpg)
Tony Weidberg Nuclear Physics Lectures 34
Rutherford Scattering 1
cosddrrr
)cosiqrexp(2ZZVH
rdr
)r.qiexp(ZZVH
kkq
rd)r.kiexp(r
ZZ)r.kiexp(VH
)r.kiexp(V;)r.kiexp(V
1c;c4
e;
r
ZZ)r(V
221
1fi
321
1fi
fi
3f
21i
1fi
f2/1
fi2/1
i
0
221
![Page 35: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/35.jpg)
Tony Weidberg Nuclear Physics Lectures 35
Rutherford Scattering 2
2211
fi
22211
fi
211fi
211fi
2221
1fi
q
4ZZVH
q)a/1(
iq2
iq
2ZZVH
iqa/1
1
iqa/1
1
iq
2ZZVH
dr)iqa/1exp(r)iqa/1exp(iq
2ZZVH
a)a/rexp();r(xV
drriqr
)iqrexp()iqrexp(2ZZVH
![Page 36: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/36.jpg)
Tony Weidberg Nuclear Physics Lectures 36
Rutherford Scattering 3• Use Fermi Golden Rule:
f
2fi dE
dnH
2R
)2/(sinp4)cos1(p2)pp(q
qv)4(
)ZZ(p4
d
d
v
V
)2(v
Vp
Vq
4ZZ2
d
d
vVF;F/R
d)2(v
Vp)E(n
v/1dE
dp;
dE
dp
dp
dn
dE
dn;
4
d
h
Vp4
dp
dn
2222fi
2
422
221
2
3
22
221
1
3
2
32
![Page 37: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/37.jpg)
Tony Weidberg Nuclear Physics Lectures 37
Low Energy Experiment• Scattering of on Au & Ag agree with calculation
assuming point nucleus
Sin4(/2)
dN
/dco
s
![Page 38: Applications of Nuclear Physics](https://reader035.fdocuments.in/reader035/viewer/2022062221/568148a4550346895db5b890/html5/thumbnails/38.jpg)
Tony Weidberg Nuclear Physics Lectures 38
Higher Energy
• Deviation from Rutherford scattering at higher energy determine charge distribution in the nucleus.
• Form factors is F.T. of charge distribution.