Upload
others
View
5
Download
0
Embed Size (px)
Citation preview
1
Nuclear and Particle PhysicsNuclear and Particle Physics
3 lectures:Nuclear Physics
Particle Physics 1Particle Physics 2
2
Nuclear Physics TopicsNuclear Physics Topics
Composition of Nucleusfeatures of nucleiNuclear Modelsnuclear energy
FissionFusion
Summary
3
About UnitsAbout UnitsEnergy - electron-volt
1 electron-volt = kinetic energy of an electron when moving through potential difference of 1 Volt;
o 1 eV = 1.6 × 10-19 Jouleso 1 kW•hr = 3.6 × 106 Joules = 2.25 × 1025 eVo 1 MeV = 106 eV, 1 GeV = 109 eV, 1 TeV = 1012 eV
mass - eV/c2
o 1 eV/c2 = 1.78 × 10-36 kgo electron mass = 0.511 MeV/c2
o proton mass = 938 MeV/c2 = 0.938 GeV/ c2
o neutron mass = 939.6 MeV/c2
momentum - eV/c: o 1 eV/c = 5.3 × 10-28 kg m/so momentum of baseball at 80 mi/hr ≈ 5.29 kgm/s ≈ 9.9 × 1027
eV/cDistance
o 1 femtometer (“Fermi”) = 10-15 m
4
RadioactivityRadioactivityDiscovery of Radioactivity
Antoine Becquerel (1896): serendipitous discovery of radioactivity: penetrating radiation emitted by substances containing uraniumA. Becquerel, Maria Curie, Pierre Curie(1896 – 1898):
o also other heavy elements (thorium, radium) show radioactivityo three kinds of radiation, with different penetrating power
(i.e. amount of material necessary to attenuate beam): “Alpha (α) rays” (least penetrating – stopped by paper)“Beta (β) rays” (need 2mm lead to absorb) “Gamma (γ) rays” (need several cm of lead to attenuated)
o three kinds of rays have different electrical charge: α: +, β: −, γ: 0
Identification of radiation:Ernest Rutherford (1899)
o Beta (β) rays have same q/m ratio as electrons o Alpha (α) rays have same q/m ratio as Heo Alpha (α) rays captured in container show He-like emission spectrum
5
Geiger, Geiger, MarsdenMarsden, Rutherford , Rutherford exptexpt..(Geiger, Marsden, 1906 - 1911) (interpreted by Rutherford, 1911)get α particles from radioactive source make “beam” of particles using “collimators”
(lead plates with holes in them, holes aligned in straight line)bombard foils of gold, silver, copper with beam measure scattering angles of particles with scintillating screen (ZnS)
7
Geiger Geiger MarsdenMarsden experiment: resultexperiment: result
most particles only slightly deflected (i.e. by small angles), but some by large angles - even backward measured angular distribution of scattered particles did not agree with expectations from Thomson model (only small angles expected), but did agree with that expected from scattering on small, dense positively charged nucleus with diameter < 10-14 m, surrounded by electrons at ≈10-10 m
Ernest Rutherford1871-1937
8
ProtonProton“Canal rays”
1898: Wilhelm Wien: opposite of “cathode rays”
Positive charge in nucleus (1900 – 1920)
Atoms are neutralo positive charge needed to cancel electron’s negative chargeo Rutherford atom: positive charge in nucleus
periodic table ⇒ realized that the positive charge of any nucleus could be accounted for by an integer number of hydrogen nuclei -- protons
9
NeutronNeutronWalther Bothe 1930:
bombard light elements (e.g. 49Be) with alpha particles ⇒neutral radiation emitted
Irène and Frederic Joliot-Curie (1931)pass radiation released from Be target through paraffin wax ⇒
protons with energies up to 5.7 MeV released if neutral radiation = photons, their energy would have to be 50
MeV -- puzzlepuzzle solved by James Chadwick (1932):
“assume that radiation is not quantum radiation, but a neutral particle with mass approximately equal to that of the proton”identified with the “neutron” suggested by Rutherford in 1920observed reaction was: α (24He++) + 49Be → 6
13C*6
13C* → 612C + n
10
Beta decay Beta decay ---- neutrinoneutrino
Beta decay puzzle : o decay changes a neutron into a proton o apparent “non-conservation” of energyo apparent non-conservation of angular momentum
Wolfgang Pauli predicted a light, neutral, feebly interacting particle (called it neutron, later called neutrino by Fermi)
Although accepted since it “fit” so well, not actually observed initiating interactions until 1956-1958 (Cowan and Reines)
11
Puzzle with Beta SpectrumPuzzle with Beta Spectrum
Three-types of radioactivity: α, β, γBoth α, γ discrete spectrum because
Eα, γ = Ei – EfBut β spectrum continuous
Energy conservation violated??Bohr:: “At the present stage
of atomic theory, however, we may say that we have no argument, either empirical or theoretical, for upholding the energy principle in the case of β-ray disintegrations”
F. A. Scott, Phys. Rev. 48, 391 (1935)
13
PositronPositronPositron (anti-electron)
Predicted by Dirac (1928) -- needed for relativistic quantum mechanics existence of antiparticles doubled the number of known particles!!!
Positron track going upward through leadplate
P.A.M. DiracNobel Prize (1933)member of FSU faculty (1972-1984)one of the greatest physicists of the 20th century
14
Structure of nucleusStructure of nucleussize (Rutherford 1910, Hofstadter 1950s):
R = r0 A1/3, r0 = 1.2 x 10-15 m = 1.2 fm; i.e. ≈ 0.15 nucleons / fm3
generally spherical shape, almost uniform density;made up of protons and neutrons
protons and neutron -- “nucleons”; are fermions (spin ½), have magnetic moment
nucleons confined to small region (“potential well”) ⇒ occupy discrete energy levelstwo distinct (but similar) sets of energy levels, one for protons, one for neutronsproton energy levels slightly higher than those of
neutrons (electrostatic repulsion)spin ½ ⇒ Pauli principle ⇒ only two identical nucleons per eng. level
15
Nuclear Sizes Nuclear Sizes -- examplesexamples
)(Ar r 31
o= ro = 1.2 x 10-15 m
Find the ratio of the radii for the following nuclei:
1H, 12C, 56Fe, 208Pb, 238U
31
31
31
31
31
238:208:56:12:1
1 : 2.89 : 3.83 : 5.92 : 6.20
16
A, N, ZA, N, Z
for natural nuclei: Z range 1 (hydrogen) to
92 (Uranium)A range from 1 ((hydrogen)
to 238 (Uranium)N = neutron number = A-ZN – Z = “neutron excess”;
increases with Znomenclature:
ZAXN or AXN orAX or X-A
17
Atomic mass unitAtomic mass unit
“atomic number” ZNumber of protons in nucleus
Mass Number ANumber of protons and neutrons in nucleus Atomic mass unit is defined in terms of the mass of 1212
66CC, with A = 12, Z = 6: 1 amu = (mass of 1212
66CC atom)/12 1 amu = 1.66 x 10-27kg 1 amu = 931.494 MeV/c2
18
Properties of NucleonsProperties of Nucleons
Proton Charge = 1 elementary charge e = 1.602 x 10-19 CMass = 1.673 x 10-27 kg = 938.27 MeV/c2 =1.007825 u = 1836 mespin ½, magnetic moment 2.79 eħ/2mp
NeutronCharge = 0Mass = 1.675 x 10-27 kg = 939.6 MeV/c2 = 1.008665 u = 1839 mespin ½, magnetic moment -1.9 eħ/2mn
19
Nuclear masses, isotopesNuclear masses, isotopes
Nuclear masses measured, e.g. by mass spectrographymasses expressed in atomic mass units (amu),
energy units MeV/c2
all nuclei of certain element contain same number of protons, but may contain different number of neutronsexamples:
deuterium, heavy hydrogen 2D or 2H; heavy water = D2O (0.015% of natural water)
U- 235 (0.7% of natural U), U-238 (99.3% of natural U),
20
Nuclear energy levels: exampleNuclear energy levels: example
Problem: Estimate the lowest possible energy of a neutron contained in a typical nucleus of radius 1.33×10-15 m.
E = p2/2m = (cp)2/2mc2
Δx Δp = h/2π Δx Δ(cp) = hc/2π
Δ(cp) = hc/(2π Δx) = hc/(2π r)
Δ(cp) = 6.63x10-34 Js * 3x108 m/s / (2π * 1.33x10-15 m)
Δ(cp) = 2.38x10-11 J = 148.6 MeV
E = p2/2m = (cp)2/2mc2 = (148.6 MeV)2/(2*940 MeV) = 11.7 MeV
21
Nuclear Masses, binding energyNuclear Masses, binding energyMass of Nucleus < Z(mp) + N(mn)
“mass defect” Δm = difference between mass of nucleus and mass of constituentsenergy defect = binding energy EB
EB = Δm c2
binding energy = amount of energy that must be invested to break up nucleus into its constituentsbinding energy per nucleon = EB /A
22
Nuclear Binding EnergyNuclear Binding Energy
The energy (or mass) difference between the nucleus and its constituent neutrons and protons.Energy needed to break the nucleus apart.Average binding energy per nucleon = total binding energy divided by the number of nucleons (A).Example: Fe-56
1 amu = 931.5 MeVm(proton) 1.00782m(neutron) 1.00867
A = 56Z = 26N = 30
Mass (amu) 55.92066Ebinding -505.58094EB/A -9.02823
23
ProblemProblem
Compute binding energy per nucleon for 4
2He 4.00153 amu16
8O 15.991 amu56
26Fe 55.922 amu235
92U 234.995 amuIs there a trend?If there is what might be its significance?
25
Nuclear RadioactivityNuclear Radioactivity
Alpha DecayAZ A-4(Z-2) + 4Heo Number of protons is conserved.o Number of neutrons is conserved.
Gamma DecayAZ* AZ + γo An excited nucleus loses energy by emitting
a photon.
26
Beta DecayBeta Decay
Beta DecayAZ A(Z+1) + e- + an anti-neutrino
o A neutron has converted into a proton, electron and an anti-neutrino.
Positron DecayAZ A(Z-1) + e+ + a neutrino
o A proton has converted into a neutron, positron and a neutrino.
Electron Capture AZ + e- A(Z-1) + a neutrino
o A proton and an electron have converted into a neutron and a neutrino.
27
RadioactivityRadioactivity
Several decay processes:α decay:
β− decay:
β+ decay:
HePbPoge
HeYX AZ
AZ
42
20682
21084
42
42
.,. +→
+→ −−
~9944
9943
~
1
.,. ν
ν
++→
++→
−
−+
eRbTcge
eYX AZ
AZ
ν
ν
++→
++→
+
+−
eCNge
eYX AZ
AZ
126
127
1
.,.
Electron capture:
γ decay:ν
ν
+→+
+→+
−
−−
CeNge
YeX AZ
AZ
126
127
1
.,.
)140(.,. 9943
*9943
*
keVTcTcge
XX AZ
AZ
γ
γ
+→
+→
28
Law of radioactive decayLaw of radioactive decay
Activity A = number of decays per unit timedecay constant λ =
probability of decay per unit timeRate of decay ∝ number N of nuclei Solution of diff. equation (N0 = nb. of nuclei at t=0)Mean life τ = 1/ λ
.dtdNA =
.NdtdN λ−=
λτ
λ
λ
1
0
0 ===
∫
∫
∫∫
∞−
∞−
dte
dtet
dN
dNt
t
t
.)( 0teNtN λ−=
29
Nuclear decay ratesNuclear decay rates
Nuclear Decay
0.0
200.0
400.0
600.0
800.0
1000.0
0.0 1.0 2.0 3.0 4.0 5.0
Time(s)
Nuc
lei R
emai
ning
At t = 1/λ,N is 1/e (0.368) of the original amount
.)( 0teNtN λ−=
30
Nuclear (Nuclear (““strongstrong””) force) force
atomic nuclei small -- about 1 to 8fmat small distance, electrostatic repulsive forces are of macroscopic size (10 – 100 N)there must be short-range attractive force between nucleons -- the “strong force”strong force essentially charge-independent
“mirror nuclei” have almost identical binding energiesmirror nuclei = nuclei for which n → p or p → n (e.g. 3He and 3H, 7Be and 7Li, 35Cl and 35Ar); slight differences due to electrostatic repulsion
strong force must have very short range – << atomic size otherwise isotopes would not have same chemical properties
31
Strong force Strong force ---- 22
range: fades away at distance ≈ 3fmforce between 2 nucleons at 2fm distance ≈
2000Nnucleons on one side of U nucleus hardly
affected by nucleons on other sideexperimental evidence for nuclear force from
scattering experiments; low energy p or α scattering: scattered particles
unaffected by nuclear forcehigh energy p or α scattering: particles can overcome electrostatic repulsion and can penetrate deep enough to enter range of nuclear force
32
NN--Z and binding energy Z and binding energy vsvs AAsmall nuclei (A<10):
All nucleons within range of strong force exerted by all other nucleons;add another nucleon ⇒ enhance overall cohesive force ⇒ EB rises
sharply with increase in Amedium size nuclei (10 < A < 60)
nucleons on one side at edge of nucl. force range from nucleons on other side ⇒ each add’l nucleon gives diminishing return in terms of binding energy ⇒ slow rise of EB /A
heavy nuclei (A>60)adding more nucleons does not increase overall cohesion due to
nuclear attractionRepulsive electrostatic forces (infinite range!) begin to have
stronger effect N-Z must be bigger for heavy nuclei (neutrons provide attraction
without electrostatic repulsionheaviest stable nucleus: 209Bi – all heavier nuclei unstable
(radioactive)
34
Nuclear Models Nuclear Models –– liquid drop modelliquid drop model
liquid drop model (Bohr, Bethe, Weizsäcker):nucleus = drop of incompressible nuclear fluid. fluid made of nucleons, nucleons interact
strongly (by nuclear force) with each other, just like molecules in a drop of liquid. introduced to explain binding energy and mass of
nucleipredicts generally spherical shape of nuclei
Good qualitative description of fission of large nuclei
provides good empirical description of binding energy vs A
35
BetheBethe –– WeizsWeizsääckercker formula for binding energyformula for binding energy
Bethe - Weizsäcker formula:an empirically refined form of the liquid drop model for the
binding energy of a nucleus of mass number A with Z protons and N neutrons
binding energy has five terms describing different aspects of the binding of all the nucleons:
o volume energyo surface energyo Coulomb energy (electrostatic repulsion of the protons,)o an asymmetry term (N vs Z)o an exchange (pairing) term (even-even vs odd-even vs odd-odd
number of nucleons)
( ) 3/4-P
2
Sym1/3
2
C3/2
SV A a A
NZaAZaAaAa)Z,A(B λ−
−−−−=
37
Independent Particle ModelsIndependent Particle Models
assume nucleons move inside nucleus without interacting with each otherFermi- gas model:
Protons and neutrons move freely within nuclear volume, considered a rectangular boxProtons and neutrons are distinguishable and so move in separatepotential wells
Shell Model formulated (independently) by Hans Jensen and Maria Goeppert-MayerEach nucleon (proton or neutron) moves in the average potential of
remaining nucleons, assumed to be spherically symmetric. Also takes account of the interaction between a nucleon’s spin and its angular momentum (“spin-orbit coupling”)derive “magic numbers” (of protons and/or neutrons) for which
nuclei are particularly stable: 2, 8, 20, 28, 50, 82, 126, ..
38
FermiFermi--Gas Model of NucleusGas Model of Nucleus
Ground StateIn each potential well, the lowest energy states are occupied.
Because of the Coulomb repulsion the proton well is shallower than that of the neutron.
But the nuclear energy is minimized when the maximum energy level is about the same for protons and neutrons
Therefore, as Z increases we would expect nuclei to contain progressively more neutrons than protons.
U has A = 238, Z = 92
Potential well
39
Collective modelCollective model
collective model is “eclectic”, combining aspects of other models
consider nucleus as composed of “stable core”of closed shells, plus additional nucleons outside of coreadditional nucleons move in potential well due to
interaction with the coreinteraction of external nucleons with the core ⇒
agitate core – set up rotational and vibrationalmotions in core, similar to those that occur in dropletsgives best quantitative description of nuclei
40
Nuclear energyNuclear energyvery heavy nuclei:
energy released if break up into two medium sized nuclei“fission”
light nuclei:energy released if two light nuclei combine -- “fuse” into a
heavier nucleus – “fusion”
44
SunSun’’s Power Outputs Power Output
Unit of Power1 Watt = 1 Joule/second100 Watt light bulb = 100 Joules/second
Sun’s power output3.826 x 103.826 x 102626 WattsWatts
45
The ProtonThe Proton--Proton CycleProton Cycle 1H + 1H → 2H + e+ + νe+ + e- → γγ + γγ
2H + 1H → 3He + γγ
3He + 3He → 4He + 1H + 1H
Deuterium creation 3He creation 4He creation
4H → 4He
1 pp collision in 1022 → fusion!
48
Life of a 20 Solar Mass SuperLife of a 20 Solar Mass Super--GiantGiant
Hydrogen fusion~ 10 million years
Helium fusion ~ 1 million years
Carbon fusion ~ 300 years
Oxygen fusion ~ 9 months
Silicon fusion ~ 2 days
http://cassfos02.ucsd.edu/public/tutorial/SN.html
52
SummarySummary
nuclei made of protons and neutrons, held together by short-range strong nuclear forcemodels describe most observed features, still
being tweaked and modified to incorporate newstobservationsno full-fledged theory of nucleons yetdevelopment of nuclear theory based on QCD has
begun nuclear fusion is the process of energy production
of Sun and other starswe (solar system with all that’s in it) are made of
debris from dying stars