Upload
elfrieda-benson
View
299
Download
5
Tags:
Embed Size (px)
Citation preview
1
Nuclear and Particle Physics 3 lectures:
Nuclear Physics Particle Physics 1 Particle Physics 2
2
Nuclear Physics Topics
Composition of Nucleus features of nuclei Nuclear Models nuclear energy
Fission Fusion
Summary
3
About Units Energy - 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/c
Distanceo 1 femtometer (“Fermi”) = 10-15 m
4
Radioactivity Discovery of Radioactivity
Antoine Becquerel (1896): serendipitous discovery of radioactivity: penetrating radiation emitted by substances containing uranium
Antoine Becquerel, Marie Curie, Pierre Curie (1896 – 1898):
o also other heavy elements (thorium, radium) show radioactivity
o three kinds of radiation, with different penetrating power (i.e. amount of material necessary to attenuate beam):
“Alpha (a) rays” (least penetrating – stopped by paper) “Beta (b) rays” (need 2mm lead to absorb) “Gamma (g) rays” (need several cm of lead to be attenuated)
o three kinds of rays have different electrical charge: : +, : -, : 0a b g
Identification of radiation: Ernest Rutherford (1899)
o Beta (b) rays have same q/m ratio as electrons o Alpha (a) rays have same q/m ratio as He nucleuso Alpha (a) rays captured in container show He-like emission
spectrum
5
Geiger, Marsden, Rutherford expt. (Geiger, Marsden, 1906 - 1911) (interpreted by Rutherford,
1911) get 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)
6
7
Geiger Marsden experiment: 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 fromscattering on small, dense positively charged nucleus with diameter < 10-14 m, surrounded by electrons at 10-10 m
Ernest Rutherford1871-1937
8
Proton “Canal rays”
1898: Wilhelm Wien: opposite of “cathode rays”
Positive charge in nucleus (1900 – 1920)Atoms are neutral
o positive charge needed to cancel electron’s negative charge
o Rutherford atom: positive charge in nucleusperiodic table realized that the positive charge of
any nucleus could be accounted for by an integer number of hydrogen nuclei -- protons
9
Neutron Walther Bothe 1930:
bombard light elements (e.g. 49Be) with alpha particles
neutral radiation emitted Irène and Frédéric 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 -- puzzle
puzzle 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 1920
observed reaction was: (2
4He++) + 49Be 6
13C*
613C* 6
12C + n
10
Beta decay -- neutrino 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 Spectrum
Three-types of radioactivity: a, b, g
Both a, g discrete spectrum because
Ea, g = Ei – Ef
But b 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)
12
Desperate Idea of Pauli
13
Pauli’s neutrino letter Dear Radioactive Ladies and
Gentlemen! I have hit upon a desperate remedy to
save…the law of conservation of energy.
…there could exist electrically neutral particles, which I will call neutrons, in the nuclei…
The continuous beta spectrum would then make sense with the assumption that in beta decay, in addition to the electron, a neutron is emitted such that the sum of the energies of neutron and electron is constant.
But so far I do not dare to publish anything about this idea, and trustfully turn first to you, dear radioactive ones, with the question of how likely it is to find experimental evidence for such a neutron…
I admit that my remedy may seem almost improbable because one probably would have seen those neutrons, if they exist, for a long time. But nothing ventured, nothing gained…
Thus, dear radioactive ones, scrutinize and judge. http://www.symmetrymagazine.org/cms/?pid=1000450
14
Positron Positron (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
15
Structure of nucleus size (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 levels two distinct (but similar) sets of energy levels,
one for protons, one for neutrons proton energy levels slightly higher than those of
neutrons (electrostatic repulsion) spin ½ Pauli principle
only two identical nucleons per energy level
16
Nuclear Sizes - examples
)(Ar r 3
1
o ro = 1.2 x 10-15 m
Find the ratio of the radii for the following nuclei:
1H, 12C, 56Fe, 208Pb, 238U
3
1
3
1
3
1
3
1
3
1
238:208:56:12:1
1 : 2.89 : 3.83 : 5.92 : 6.20
17
A, N, Z for natural nuclei:
Z range 1 (hydrogen) to 92 (Uranium)
A range from 1 ((hydrogen) to 238 (Uranium)
N = neutron number = A-Z N – Z = “neutron excess”;
increases with Z nomenclature:
ZAXN or AXN or
AX or X-A
18
Atomic 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 126C, with A = 12, Z = 6:
1 amu = (mass of 126C atom)/12
1 amu = 1.66 x 10-27kg 1 amu = 931.494 MeV/c2
19
Properties 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 me
spin ½, magnetic moment 2.79 eħ/2mp
NeutronCharge = 0Mass = 1.675 x 10-27 kg = 939.57 MeV/c2
= 1.008665 u = 1839 me
spin ½, magnetic moment -1.9 eħ/2mn
20
Nuclear masses, isotopes
Nuclear masses measured, e.g. by mass spectrography
masses 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 neutrons
examples: 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),
21
Nuclear 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
x p = h/2 x (cp) = hc/2
(cp) = hc/(2 x) = hc/(2 r)
(cp) = 6.63x10-34 Js * 3x108 m/s / (2 * 1.33x10-15 m)
(cp) = 2.38x10-11 J = 148.6 MeV
E = p2/2m = (cp)2/2mc2 = (148.6 MeV)2/(2*940 MeV) = 11.7 MeV
22
Nuclear Masses, binding energy Mass of Nucleus Z(mp) + N(mn) “mass defect” m = difference
between mass of nucleus and mass of constituents
energy defect = binding energy EB EB = mc2
binding energy = amount of energy that must be invested to break up nucleus into its constituents
binding energy per nucleon = EB /A
23
Nuclear Binding Energy
Nuclear binding energy = difference between the energy (or mass) of the nucleus and the energy (or mass) of its constituent neutrons and protons.
= (-) the 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 = 931.49 MeVm(proton) 1.00782m(neutron) 1.00867
A = 56Z = 26N = 30
Mass (amu) 55.92066Ebinding (MeV) -505.58094EB/A(MeV) -9.02823
24
Problem – set 4
Compute binding energy per nucleon for 4
2He 4.00153 amu
168O 15.991 amu
5626Fe 55.922 amu
23592U 234.995 amu
Is there a trend? If there is, what might be its significance? note:
1 amu = 931.5 MeV/c2
m(proton) = 1.00782 amum(neutron)= 1.00867 amu
25
Binding energy per nucleon
26
Nuclear Radioactivity
Alpha DecayAZ A-4(Z-2) + 4He
oNumber of protons is conserved.oNumber of neutrons is conserved.
Gamma DecayAZ* AZ +
oAn excited nucleus loses energy by emitting a photon.
27
Beta Decay
Beta Decay AZ A(Z+1) + e- + an anti-neutrino
o A neutron has converted into a proton, electron and an anti-neutrino.
Positron Decay AZ 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.
28
Radioactivity
Several decay processes:
a decay:
b- decay:
b+ decay:
HePbPoge
HeYX AZ
AZ
42
20682
21084
42
42
.,.
~9944
9943
~
1
.,.
eRbTcge
eYX AZ
AZ
eCNge
eYX AZ
AZ
126
127
1
.,.
Electron capture:
g decay:
CeNge
YeX AZ
AZ
126
127
1
.,.
)140(.,. 9943
*9943
*
keVTcTcge
XX AZ
AZ
29
Law of radioactive decay
Activity A = number of decays per unit time
decay constant = 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 = 1/
dNA
dt
dNN
dt
1
0
0
dte
dtet
dN
dNt
t
t
0( ) tN t N e
30
Nuclear 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)
Nu
cle
i R
em
ain
ing
At t = 1/, N is 1/e (0.368) of the original amount
0( ) tN t N e
31
Nuclear (“strong”) force
atomic nuclei small -- about 1 to 8fm at 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 energies mirror 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
32
Strong force -- 2
range: fades away at distance ≈ 3fm force between 2 nucleons at 2fm distance
≈ 2000N nucleons on one side of U nucleus hardly
affected by nucleons on other side experimental evidence for nuclear force from
scattering experiments; low energy p or scattering: scattered
particles unaffected by nuclear force high energy p or scattering:
particles can overcome electrostatic repulsion and can penetrate deep enough to enter range of nuclear force
33
N-Z and binding energy vs A small nuclei (A<10):
All nucleons are within range of strong force exerted by all other nucleons;
add another nucleon enhance overall cohesive force EB rises sharply with increase in A
medium size nuclei (10 < A < 60) nucleons on one side are 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 attraction Repulsive electrostatic forces (infinite range!) begin to
have stronger effect N-Z must be bigger for heavy nuclei (neutrons provide
attraction without electrostatic repulsion heaviest stable nucleus: 209Bi
– all nuclei heavier than 209Bi are unstable (radioactive)
34
EB/A vs A
35
Nuclear Models – liquid 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 nuclei predicts generally spherical shape of nuclei good qualitative description of fission
of large nuclei provides good empirical description
of binding energy vs A
36
Bethe – Weizsäcker formula 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
NZa
A
ZaAaAa)Z,A(B λ
37
“liquid drop” terms in B-W formula
38
Independent Particle Models assume nucleons move inside nucleus
without interacting with each other Fermi- gas model:
Protons and neutrons move freely within nuclear volume, considered a rectangular box
Protons and neutrons are distinguishable and so move in separate potential wells
Shell Model formulated (independently)
by Hans Jensen and Maria Goeppert-Mayer each 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”)
derives “magic numbers” (of protons and/or neutrons) for which nuclei are particularly stable: 2, 8, 20, 28, 50, 82, 126, ..
39
Fermi-Gas Model of Nucleus
Ground State In 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
40
Collective 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 core
additional nucleons move in potential well due to interaction with the core
interaction of external nucleons with the core agitate core – set up rotational and vibrational motions in core, similar to those that occur in droplets
gives best quantitative description of nuclei
41
Nuclear energy very 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”
42
A, N, Z for natural nuclei:
Z range 1 (hydrogen) to 92 (Uranium)
A range from 1 ((hydrogen) to 238 (Uranium)
N = neutron number = A-Z N – Z = “neutron excess”;
increases with Z nomenclature:
ZAXN or AXN or
AX or X-A
43
Nuclear Energy - Fission
+ about 200 MeV energy
44
Fission
45
Nuclear Fusion
46
Sun’s Power Output
Unit of Power 1 Watt = 1 Joule/second 100 Watt light bulb = 100
Joules/second
Sun’s power output 3.826 x 1026 Watts exercise: calculate sun’s power output
using Stefan-Boltzmann law (assume sun is a black body)
47
The Proton-Proton Cycle1H + 1H → 2H + e+ + n
e+ + e- → g + g2H + 1H → 3He + g
3He + 3He → 4He + 1H + 1H
Deuterium creation 3He creation 4He creation
4H → 4He
1 pp collision in 1022 → fusion!
48
Super Kamiokande: Solar Neutrinos
Solar neutrino
Electron
49
A Nearby Super-Giant
50
Life of a 20 Solar Mass Super-Giant
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
51
Carbon fusion
7.65 MeV above 12C ground state
52
Oxygen fusion
7.12 MeV7.19 MeV
53
Supernova 1987A Before
After
54
Summary
nuclei made of protons and neutrons, held together by short-range strong nuclear force
models describe most observed features, still being tweaked and
modified to incorporate newest observations
no full-fledged theory of nuclei yet development of nuclear theory based on
QCD has begun nuclear fusion is the process of energy
production of Sun and other stars we (solar system with all that’s in it)
are made of debris from dying stars