Nuclear Physics I (PHY 551)
Text books:
S. Wong “Introductory Nuclear Physics”
Povh, Rith, Scholz, Zetsche, “Particles and Nuclei”
Supplementary tex: C. Bertulani, “Nuclear Physics in a Nutshell”
Course Time and Place: Monday,Wednesday 11-12:23pm (P123)
Course URL: http://skipper.physics.sunysb.edu/~joanna/Lectures/PHY551/
Office hours: (proposed time) Wednesday 2-3pm (C109)
Contact: E-mail: Joanna.Kiryluk (at) stonybrook.edu
Attention!
April 27, 29 – no classes. Need to find alternative time.
Proposed times: Fridays (March 6, 27)
1
Nuclear Physics I (PHY 551)
Homework: every 2 weeks, 2 weeks to turn it in.
No credit for late homework. Students are encouraged to work together, but
write up should be their own (copies will be disqualified). Any (serious!)
excuses (medical or otherwise) are to be documented and discussed with the
instructor in a timely manner.
Exams: There will be two midterm exams and a final exam (final exam
covers the whole course material). Midterm exams will be given during the
regular lecture hour.
Grading: Your final course grade will be determined by weighting the various
portions of the course as follows:
40% midterm (20% each), 20% homework, 40% final
2
PHY551 Questionnaire
Your name: …………………………..
1.
Please identify your level (G0, G1, etc)
2.
Have you taken or are you taking a course on
Modern Physics
b.  Quantum Mechanics
c.  Quantum Field Theory
d.  Elementary Particle Physics
e.  Other?
a.
3.
Are you part of a research group? If so, which one (experiment/field)?
4.
Have you taken any course on nuclear physics before?
Is so, when and at what level?
5.
Why are you taking this course?
Nuclear Physics
The aim of Nuclear Physics is to understand:
•  The force between the nucleons
•  The structure of nuclei
•  How nuclei interact with each other and
other subatomic particles
4
Nuclear Physics I (PHY 551)
Joanna Kiryluk
Spring Semester Lectures 2014/2015
Department of Physics and Astronomy, Stony Brook University
Lecture 1:
1. Introduction
§  Brief History of Nuclear Physics
§  General Properties of the Nuclei
2. Nucleon Structure
§  Parity, Isospin, Charge Conjugation
§  Quark Parton Model
§  Elementary Particles, Fundamental Interactions and
the Standard Model
Homework 1:
Wang, Chapter 1, problems 1,2,3,4
5. For:

Ψ ( r ) = Ψ ( r, θ , ϕ ) = Rnl ( r ) Yl m (θ , ϕ )
prove:


PΨ ( r ) = nΨ ( r ),
n = (−1)
l
Deadline: 02/18/2015 11am.
1. Introduction
§  Brief History of Nuclear Physics
§  General Properties of the Nuclei
Nuclear Physics – History (1)
§  1896: Henri Becquerel – discovery of
radioactivity
Photographic plates blackened when
placed near certain minerals (uranium
salts). Radioactivity could not be explained
by e-m (or gravity), and was one of the
unsolved problems.
§  1898: Maria and Pierre Curie –
discovery of Polonium and Radium
(much more radioactive than uranium)
Becquerel and the Curies shared the Nobel Prize
in Physics in 1903.
Later, Marie Curie isolates metallic radium and receives
the Nobel Price in Chemistry in 1911.
8
Nuclear Physics – History (2)
Ernest Rutherford – “the father of nuclear physics”
§  1899: Rutherford shows 2 types of radiation exits and calls
them named α and β.
§  1900: Villard gives evidence for a 3rd type of radiation
coming from radium and calls it γ
§  1902: Curies show that β radiation is electrons
§  1904: Rutherford shows α particles are helium
Ernest Rutherford was awarded the Nobel Prize in Chemistry in 1908
"for his investigations into the disintegration of the elements, and the
chemistry of radioactive substances".
“I have dealt with many different transformations with various periods of time, but the
quickest that I have met was my own transformation in one moment from a physicist to
a chemist.” E. Rutherford (Nobel banquet 1908).
9
Nuclear Physics – History (3)
Ernest Rutherford – “the father of nuclear physics”
§  1911: Rutherford proposed the existence of
a massive nucleus as a small central part of
an atom
J.J. Thompson’s
Plum Pudding Model (1904)
Rutherford’s
Planetary Model (1911)
10
Nuclear Physics – History (4)
§  Rutherford designed an experiment to use α particles as atomic bullets
(then new technology).
§  The “gold-foil experiment” was performed in 1909 by Hans Geiger and
Ernest Marsden (under Rutherford’s direction)
Radium
11
“Progress almost always depends on
experimental results, without which the smartest
individual will not get anywhere.
On the other hand, to devise useful experiments
an experimental physicist needs some
understanding of the existing theory.
It is the combination of experiment and theory
that has let to today’s understanding of Nature.”
- Martinus Veltman
12
Nuclear Physics – History (5)
§  1925: Uhlenbeck and Goudsmit proposed that each electron rotates with
angular momentum  2 (~10-34 Js) and carries µ B = e 2 m
http://www.lorentz.leidenuniv.nl/history/spin/goudsmit.html
G.E.Uhlenbeck
€
H.Kramers
Paul Ehrenfest (1925):
“This is a good idea.
Your idea may be wrong,
but since both of you are
so young and without any
reputation, you would
not loose anything making
a stupid mistake.”
S.A.Goudsmit
…. spin (internal angular momentum)
as a fundamental property of particles
(and purely quantum mechanical phenomenon)
S=1/2
13
Spin: The golden years "
Reminder: In classical mechanics
the magnetic moment due to the
orbital momentum of a point charge:

e 
µ class = −
L
2m
W. Pauli"
N. Bohr"
spinning top"
§  The magnetic moment

of a particle is related to its angular momentum L

e 
µ = −g
L
2m

L -  spin, orbital or total angular
momentum
gS = ge = −ge
µ B = e 2 m
g=2
for Dirac particles"
(QED)"
€
Modern experiments: “g-2” experiment14
(BNL/Fermilab) to search for physics beyond
Standard Model
Spin: The golden years "
§  1922 - measured the magnetic moment of the electron (Stern-Gerlach)
§ Any given particle has a specific amount of spin
§ Spin in quantized
S=1/2 (electron spin)
§  Total angular momentum
S=
1"1 %
3

$ +1'  =
2#2 &
2
§  z-component of the total angular momentum
€
1
Sz = ± 
2
€
The experiment showed clearly that spatial quantization existed, a phenomenon
.
that could be accommodated only within a quantum mechanical theory
15
Spin: The golden years "
§  1933 - measured the magnetic moment of the proton (Stern et. al.)

e 
µ p = −5.8
Sp
2m
Proton is not point-­‐like. It has a sub-­‐structure. !
?
Stern received the Nobel Prize in Physics in 1943.
16
Nuclear Physics – History (5)
§  1932: Nobel Prize in Physics for James
Chadwick for a discovery of the neutron
Nucleus = protons + neutrons
(short range nuclear force)
17
Nuclear Physics – History (5)
Chadwick’s discovery made it possible to create elements heavier than Uranium in the lab.
Later, Enrico Fermi discovered nuclear reactions (slow neutrons) which led to a
revolutionary discovery of nuclear fission (Otto Hanh and Fritz Strassmann).
Chadwick's discovery was crucial for the fission of uranium 235. Unlike α particles, neutrons
do not need to overcome Coulomb barrier and thus can penetrate and split the nuclei of the
heaviest elements. The release of neutrons sustains the fission reaction.
These discoveries led to a development of nuclear weapons and nuclear power.
neutron
Uranium-235 has the distinction of being the only
naturally occurring fissile isotope.
neutrons
Uranium-238 cannot fission with low energy neutrons
(stable nuclear shell structure)
18
Nuclear Physics – History (6)
§  1935: Hideki Yukawa proposed
the force between nucleons
arises from meson exchange.
Awarded the Nobel Prize in Physics in 1947 "for his
prediction of the existence of mesons on the basis of
theoretical work on nuclear forces”.
The meson-exchange concept (where hadrons
are treated as elementary particles) continues to
represent the best working model for a
quantitative NN potential.
19
Nuclear Physics – History (7)
§  1914: J. Chadwick shows spectrum of β radiation is
continuous, contrary to the fundamental principle of energy
conservation
§  1930: W. Pauli proposed a neutrino to explain
the continuous spectrum of β decay.
“I have done a terrible thing, I have postulated a
particle that cannot be detected.” W. Pauli
Wolfgang Pauli was awarded the Nobel Prize in Physics in 1945 "for the discovery
of the Exclusion Principle, also called the Pauli Principle”.
20
Nuclear Physics – History (8)
§  1933: E. Fermi used the neutrino to explain
neutron β decay (model of weak interactions)
Enrico Fermi was aworded the Nobel Prize in Physics in 1938 "for his demonstrations
of the existence of new radioactive elements produced by neutron irradiation, and for
his related discovery of nuclear reactions brought about by slow neutrons".
21
Nuclear Physics – History (9)
§  1956: F. Reines and C. Cowan
detection of a neutrino via
inverse beta decay reaction
ν e + p → n + e+
From then on Reines dedicated his career to the study of the neutrino’s properties
and interactions, including the discovery of neutrinos emitted from SN1987A by the
Irvine-Michigan-Brookhaven Collaboration. This discovery helped to inaugurate the
field of neutrino astronomy.
F. Reines was awarded the Nobel Prize in Physics in 1995 for his co-detection
of the neutrino with Clyde Cowan in the neutrino experiment”
22
Neutrino Detection
ν e + p → n + e+
Cadium – a strong neutron absorber
23
Parity
Parity - a symmetry property of physical quantities or
processes under spatial inversion
Mirror symmetry
Under parity:


r → −r
( x, y, z) → (−x, −y, −z)
(r, θ, ϕ )€→ (r, π − θ, ϕ + π )
This is equivalent to:
reflection (x-y)
and then
rotation around z
24
Parity
Parity - a symmetry property of physical quantities or
processes under spatial inversion
Mirror symmetry
Under parity:


r → −r
( x, y, z) → (−x, −y, −z)
(r, θ, ϕ )€→ (r, π − θ, ϕ + π )
This is equivalent to:
reflection (x-y)
and then
rotation around z
25
Nuclear Physics – History (10)
§  1957: Lee and Yang – proposed the concept
of parity violation in weak interactions
(Nobel Prize in Physics)
Implications: if parity is not conserved in weak interactions, it means that
the Universe sometimes distinguishes between left and right"
§  1958: C.S. Wu experimentally confirmed parity
violation in weak interactions (β decay of polarized
cobalt-60 nuclei)
26
Nuclear Physics – History (11)
§  1958: C.S. Wu experimentally confirmed
parity violation in weak interactions
"
C.S. Wu at al studied β decay of polarized cobalt-60 nuclei:
Observed electrons emitted preferentially in direction opposite to to applied field:
If parity were conserved, expect equal rate of electrons in directions along
and opposite to the nuclear spin.
27
The periodic Table of Elements
Atomic number = number of protons in the nucleus
Isotops = atoms of the same element (Z) but with
different numbers of neutrons. Isotops have very similar
element’s chemical properties.
Nuclides = atoms with a specific number of protons and
neutrons in the nucleus (nuclear properties)
28
Table of nuclides
Isotopes for elements Z=0-14
Half-live
Gd=Gadolinium
All elements have some isotopes that are radioactive
(naturally or artificially produced)
29
Different types of decay of a radionuclide
radionuclide = atom with an unstable nucleus (occur naturally or can be artificially produced)
+ neutrino
−
n → p + e +νe
(table of nuclides)
30
Table of nuclides
§  Isotopes: Z=const
§  Isobars: A=Z+N=const
§  Isotones: N=const
Choices for representation of data
§  Stability (half-live based)
Coulomb force increases ~ Z2
Nuclear force increases with A
Z
N
Magic number is a number of nucleons (either p or n) such that are arranged
into complete shells within the atomic nucleus.
Choices for representation of data
§  Decay modes
The Valley of Stability
New nuclear machines such as the Rare Isotope Accelerator (RIA) at
Facility for Rare Isotope Beams (FRIB) at Michigan State University
will open up studies of nuclear phenomena using beams of short-lived
isotopes, which form the high "walls" of the valley.
Nuclei - Terminology
A
Z
X
X – element
A – number of nucleons ( mass number)
Z - proton number
(atomic number)
N – neutron number, N=A-Z
36
Nuclear Radius and Nuclear Density
§  Nuclear radius
R = r0 A1 3 where r0 ~ 1.2 fm "#1 fm = 10 −15 m$%
Volume ~ A
§  Nuclear density
nucleons
17 kg
ρ0 ~ [ 0.16 ± 0.02 ]
= 3×10
3
fm
m3
1
ρ (r ) = ρ0
"r − c%
1+ exp $
# z '&
z - measures the “diffuseness” of the nuclear surface (z ~ 0.5fm)
c – distance from the center where density drops to a half value
37
Nuclear shapes
§  spherical for stable nuclei
§  deformations for 150 < A < 190
(competition between Coulomb and nuclear forces)
ΔR
δ=
R
r2
r1
ΔR = 0 for a sphere
δ < 0.1 typically
δ ~ 0.6 fusion of 2 nuclei
38
(large deformations)
Nuclear Binding Energy ΕΒ(A,Z)
- binding energy of nucleons into a nuclide (only ground state!)
EB (A, Z) = ZM H + ( A − Z ) M n − M ( A, Z )
M H = M p + M e (−13.6eV )
Mp – proton mass = 938.272 MeV
Mn – neutron mass = 939.566 MeV
Me – electron mass = 0. 511 MeV
[c=1]
Nucleon mass ~ 2000 electron mass
39
Energy Units
1 keV = 10 3 eV
6
0.13 keV
Ionization energy
of the hydrogen atom
2
1 MeV = 10 eV
0.511 MeV/c
1 GeV = 10 9 eV
0.938 GeV/c 2
200 GeV = 2 × 1011 eV
200 GeV
1 TeV = 1012 eV
7 TeV
Electron mass
Proton mass
Center of mass energy
(Au+Au per nucleon)
at RHIC
Center of mass energy
at LHC (2010)
1 PeV = 1015 eV
18
1 EeV = 10 eV €
1 ZeV = 10 21 eV
Cosmic rays
highest energies
40
Binding energy increases with nucleon number:
Average Nuclear Binding Energy per Nucleon
rising Coulomb repulsion
For A<20 (4He, 8Be, 12C, 16O i.e. 4n nuclei) sharp rise comes from
increasing number of nucleon pairs
41
Scattering Cross Section
Experiment: “beam” of particles hitting “target”
What’s the probability for a projectile scattering
off a target?
n – number of nuclei per unit volume
Target dimensions: thickness
area
Cross section:
Cross section units:
T
A = L1× L2
T
σ = πd2
d =r+R
1 barn = 10-28m2
Area of nuclei and particles nT Aσ
Probability of a single particle colliding:
p=
=
= nσ T
(“scattering probability”)
Target area
A
43
Exercise: What’s the probability that N particles penetrate to depth x, where dN
Differential Scattering Cross Section
p = nσ T
dσ
p(θ , ϕ ) =
nT
dΩ
4π
2π
dσ
σ=∫
dΩ = ∫
0 dΩ
0
44
π
∫
0
dσ
sin θ dθ dϕ
dΩ
Results of a collision:
a+b→ a+b
a + b → c + d +....
elastic scattering
inelastic scattering
(new particles produced in the final state)
Each reaction takes place with a different probability
Total cross section:
σ = σ el + ∑σ i
i
44
Cross section in proton-proton collisions
45
Elementary
Particle Physics
Applications
§
§
Nuclear Reactors
Nuclear medicine:
diagnostic, terapeutic
§
§
Radioactive dating
Smoke Detectors …
Nuclear Physics
Astrophysics
Nuclear Chemistry
The aim of Nuclear Physics is to
understand:
•  The force between the nucleons
•  The structure of nuclei
•  How nuclei interact with each other and
other subatomic particles
2. Nucleon Structure
§  Parity, Isospin, Charge Conjugation
§  Quark Parton Model
§  Elementary Particles, Fundamental Interactions and
the Standard Model
Classical (Reminder)
Parity
Parity - a symmetry property of physical quantities or
processes under spatial inversion


Under parity: r → − r
( x, y, z) → (−x, −y, −z)
(r, θ, ϕ€) → (r, π − θ, ϕ + π )
This is equivalent to:
reflection (x-y)
and then
rotation around z
Does orbital momentum change under parity
transformation?
49
Parity
Parity - a symmetry property of physical quantities or
processes under spatial inversion
§  The parity operator
Pˆ corresponds to a discrete transformation x → −x
§  Under the parity transformations (also called parity inversion):
Vectors:
(change sign)
€
€
Scalars:
(unchanged)
| |
| |
| |
| |
  
L=r×p
Orbital angular momentum  
µ∝L
(unchanged)
€
€
50
Parity

Let the quantum state of a particle be described by the wavefunction Ψ ( r )
The parity operator acting on a wavefunction is defined:


PΨ ( r ) = Ψ (−r )



P 2 Ψ ( r ) = PΨ (−r ) = Ψ ( r )
P2 = I (parity operator is unitary)
If the interaction Hamiltonian (H) conserves parity then the commutator
[H,P]=0 (which means that simultaneous eigenstates of H and P exist)



PΨ ( r ) = Ψ (−r ) = nΨ ( r )
and:




2
2
P
Ψ
r
=
PPΨ
r
=
nPΨ
r
=
n
Ψ
r
The quantum number
( ) n (eigenvalue
( ) of P)( is) called (the) intrinsic parity of a particle.


Ψ ( r ) = n 2 Ψ ( r ) ⇒ n = ±1
51
Algebra (example)
Which vector is an eigenvector of a matrix:
a) V1 =!
b) V2 =!
52
Parity

Let the quantum state of a particle be described by the wavefunction Ψ ( r )
The parity operator acting on a wavefunction is defined:


PΨ ( r ) = Ψ (−r )



P 2 Ψ ( r ) = PΨ (−r ) = Ψ ( r )
P2 = I (parity operator is unitary)
If the interaction Hamiltonian (H) conserves parity then [H,P]=0
(which means that simultaneous eigenstates of H and P exist)



PΨ ( r ) = Ψ (−r ) = nΨ ( r )




2
2
P
Ψ
r
=
PPΨ
r
=
nPΨ
r
=
n
Ψ
r
The quantum number
( ) n (eigenvalue
( ) of P)( is) called (the) intrinsic parity of a particle.
  2 

Ψ
r
=
n
Ψ
r
⇒
n
=
±1
PΨ
r
=
Ψ
−
r
=
nΨ
r
( () ) (( ))
( )
What is n=?




P 2 Ψ ( r ) = PPΨ ( r ) = nPΨ ( r ) = n 2 Ψ ( r )


Ψ ( r ) = n 2 Ψ ( r ) ⇒ n = ±1
and:
53
Parity

Let the quantum state of a particle be described by the wavefunction Ψ ( r )
The parity operator acting on a wavefunction is defined:


PΨ ( r ) = Ψ (−r )



P 2 Ψ ( r ) = PΨ (−r ) = Ψ ( r )
P2 = I (parity operator is unitary)
If the interaction Hamiltonian (H) conserves parity then [H,P]=0
(which means that simultaneous eigenstates of H and P exist)



PΨ ( r ) = Ψ (−r ) = nΨ ( r )




2
2
P
Ψ
r
=
PPΨ
r
=
nPΨ
r
=
n
Ψ
r
The quantum number
( ) n (eigenvalue
( ) of P)( is) called (the) intrinsic parity of a particle.


Ψ ( r ) = n 2 Ψ ( r ) ⇒ n = ±1


If n= +1 the particle has even parity.
Ψ (−r ) = +Ψ ( r )


If n= -1 the particle has odd parity.
Ψ (−r ) = −Ψ ( r )
and:
54
Parity
For a wavefunction which contains spherical harmonics: 
Ψ ( r ) = Ψ ( r, θ , ϕ ) = Rnl ( r ) Yl m (θ , ϕ )
Reminder (Modern Physics/undergrad QM)
Time Independent Schroedinger equation in 3-dim;
Central Forces:V=V(r)


2 2 
−
∇ ψ ( r ) +V ( r ) ψ ( r ) = Eψ ( r )
2m

ψ (r ) = R(r)Θ(θ )Φ(φ )
,1 ∂ & 2 ∂ )
1
∂ &
∂ )
1
∂2 /
R(r)Θ(θ )Φ(φ ) +
++ 2
( sin θ + + 2 2
. 2 (r
21
∂θ * r sin θ ∂φ 0
- r ∂r ' ∂r * r sin θ ∂θ '
+
2m ,
E −V ( r )/0 R(r)Θ(θ )Φ(φ ) = 0
2 
56
Reminder (Modern Physics/undergrad QM)
The Hydrogen-like atom constitutes the central force problem

ψ (r ) = Rnl (r)Yl ml (θ , φ )
Electron is in a state described by three
quantum numbers n, l and ml
3
l
! 2Z $ ( n − l −1)! − arn ! 2Zr $

ψ (r ) = #
e 0 #
&
&
3
" a0 n % 2n ()( n + l )!*+
" a0 n %
o
2
a0 =
= 0.529 A
me ke 2
ke 2 " Z 2 %
En = −
$ 2'
2a0 # n &
Associated Laguerre
polynomials
Bohr radius
n = 1, 2, 3,....
n
( 2l+1 ! 2Zr $* m
, Ln−l−1 #
&-Yl l (θ , φ )
" a0 n %+
)
Ground state:
ke 2 2
E1 = −
Z = − (13.6eV ) Z 2
2a0
principal quantum number
l = 0,1, 2,..., ( n −1) orbital quantum number
−l ≤ ml ≤ l
magnetic quantum number
For hydrogen-like atoms the quantum numbers n, l(l+1) and ml
are associated with the sharp observables E, L2 and Lz
Reminder (Modern Physics/undergrad QM)
Wave function:

ψ nlml (r ) = Rnl (r)Yl ml (θ , φ )
Electron is in a state described by three quantum numbers n, l and ml
Parity
For a wavefunction which contains spherical harmonics: 
Ψ ( r ) = Ψ ( r, θ , ϕ ) = Rnl ( r ) Yl m (θ , ϕ )
the eigenvalues of the parity operator are:


l
PΨ ( r ) = PΨ ( r, θ , ϕ ) = Rnl ( r ) Yl m (π − θ , ϕ + π ) = (−1) Rnl ( r ) Yl m (θ , ϕ ) = nΨ ( r )
Homework1
The parity of the single particle would then be:
i.e. determined by the orbital momentum.
n = (−1)
l
In addition to the parity associated with the spacial wave function, the
intrinsic wave function of a particle can have a definite parity, related to the
internal structure of the particle.
Parity is a multiplicative quantum number:
If the particle has positive intrinsic parity, the total parity =
If the particle has negative intrinsic parity, the total parity =
l
(−1)
l+1
(−1)
59
See you on Monday 02/09 !
Questions, comments:
e-mail: Joanna.Kiryluk (at) stonybrook.edu
Or
C109 (Physics Building)
60