applications of nuclear physics
DESCRIPTION
Applications of Nuclear Physics. Fusion How the sun works Fusion reactor Radioactive dating C dating Rb/Sr age of the Earth. 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 - PowerPoint PPT PresentationTRANSCRIPT
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
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
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~)(~
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
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
Tony Weidberg Nuclear Physics Lectures 6
Example C
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
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~
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
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
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
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.
Tony Weidberg Nuclear Physics Lectures 13
Jet
Tony Weidberg Nuclear Physics Lectures 14
Tony Weidberg Nuclear Physics Lectures 15
Magnetic Confinement Fusion
• JET passed break-even (ie achieved Lawson criteria).
Tony Weidberg Nuclear Physics Lectures 16
Inertial Confinement Fusion
Very Big Laser
Mirrors
D-T Pellet
Tony Weidberg Nuclear Physics Lectures 17
Inertial Confinement Fusion
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.
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?
Tony Weidberg Nuclear Physics Lectures 20
Carbon Dating Calibration
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
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
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
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
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 )
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
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
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
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
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
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
Tony Weidberg Nuclear Physics Lectures 32
Breit-Wigner Cross Section
4/)EE(k 2201
fi2
n + 16O 17O
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
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
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
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
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
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.