PHYS 3446 – Lecture #5
Monday, Sept. 18, 2006
Dr. Jae Yu
1. Nuclear Phenomenology
2. Properties of Nuclei
•
•
•
•
•
Labeling
Masses
Sizes
Nuclear Spin and Dipole Moment
Stability and Instability of Nuclei
3. Nature of the Nuclear Force
Monday, Sept. 18, 2006
PHYS 3446, Fall 2006
Jae Yu
1
Announcements
• We will have a private lecture from Dr. H. Weerts this
Wednesday
– Current director of HEP division of Argonne National Accelerator
Laboratory
– Current member of HEPAP-P5 advisory panel
– Former spokesperson of the DØ experiment
– Expert in strong interactions
• Sorry, I still don’t have e-mail from three of you
– Please come by my office after the class to add you on the list
• Workshop on Sept. 30
– 10am – 5pm, CPB303 and HEP experimental areas
– Food and refreshments
• Quiz in the class next Monday
• First term exam on Wednesday, Oct. 4.
Monday, Sept. 18, 2006
PHYS 3446, Fall 2006
Jae Yu
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Nuclear Phenomenology
• What did Rutherford scattering experiment do?
– Demonstrated the existence of a positively charged central core in
an atom
– The formula did not quite work for high energy a particles
(E>25MeV), especially for low Z target nuclei.
• In 1920’s, James Chadwick found
– Serious discrepancies between Coulomb scattering expectation and
the elastic scattering of a particle on He.
– None of the known effects, including quantum effect, described the
discrepancy.
• Clear indication of something more than Coulomb force
involved in the interactions
• Chadwick’s discovery neutron in 1932  Nuclei consist of
Monday, Sept. 18, 2006
PHYS 3446, Fall 2006
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Jae Yu
nucleons, protons and neutrons
Nucleus Labeling
• What are good quantities to label nuclei of an atom X?
– Electrical Charge or atomic number Z (number of protons)
• Most chemical properties depends on charge
– Total number of nucleons A (=Np+Nn)
A
X
N p  Nn

A
Z
X
or
A
X
– Examples
Hydrogen
1
1
H
7
Nitrogen 14
N
Monday, Sept. 18, 2006
Helium
4
2
He
8
Oxygen 16
O
PHYS 3446, Fall 2006
Jae Yu
Carbon
12
6
C
9
Fluoride 19
F
4
Types of Nuclei
• Isotopes: Nuclei with the same Z but different A
– Same number of protons but different number of
12 6 13 6
neutrons
C C
238 92
– Have similar chemical properties
U
235
U
• Isobars: Nuclei with same A but different Z
– Same number of nucleons but different number of
protons
6 13 7 13 238 92
C
N
U
– Different Chemical properties
238
92
Pu
• Isomers or resonances of the ground state: Excited
nucleus to a higher energy level
• Mirror nuclei: Nuclei with the same A but with
switched Np and Nn 6C13 7 N 13 25 Mn51 26 Fe51
Monday, Sept. 18, 2006
PHYS 3446, Fall 2006
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Jae Yu
Ref: http://www.fas.org/nuke/intro/nuke/plutonium.htm
94
Nuclear Properties: Masses of Nuclei
• How many protons and neutrons does nucleus A X Z have?
– Np=Z and Nn=A-Z
• So what should the mass of A X Z look like?
M

Z
X
A

M  A, Z   Zm p   A  Z  mn
– Where mp=938.27MeV/c2 and mn=939.56MeV/c2
• However measured mass turns out to be
M  A, Z   Zm p   A  Z  mn
– The energy difference is used as binding energy, keeping the
nucleus together
– One of reasons why nuclei are not falling apart
Monday, Sept. 18, 2006
PHYS 3446, Fall 2006
Jae Yu
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Nuclear Properties: Binding Energy
• The mass deficit
M  A, Z   M  A, Z   Zm p   A  Z  mn
• Is always negative and is proportional to the nuclear
binding energy
• How are the BE and mass deficit related?
B.E  M  A, Z  c
2
• What is the physical meaning of BE?
– A minimum energy required to release all nucleons from a
nucleus
Monday, Sept. 18, 2006
PHYS 3446, Fall 2006
Jae Yu
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Nuclear Properties: Binding Energy
• BE per nucleon is
B  BE

A
A



M  A, Z  c
2
A

Zm p   A  Z  mn  M  A, Z  c
Monday, Sept. 18, 2006
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•
•
A
PHYS 3446, Fall 2006
Jae Yu
Rapidly increase with A till
A~60 at which point BE~9MeV.
A>60, the B.E gradually
decrease  For most the
large A nucleus, BE~8MeV.
8
Nuclear Properties: Binding Energy
• de Broglie’s wavelength:
– Where is the Planck’s constant
– And is the reduced wavelength

p
• Assuming 8MeV was given to a nucleon
(mn~940MeV), its wavelength is

p

197 Mev  fm


 1.6 fm
2
2  940  8
2mT
2mc T
c
• Makes sense for nucleons to be inside a nucleus since
the size is smaller than the nucleus.
• Could they be electrons with 8MeV?
– The wavelength is ~10fm, a whole lot larger than a nucleus.
Monday, Sept. 18, 2006
PHYS 3446, Fall 2006
Jae Yu
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Nuclear Properties: Sizes
• Sizes of subatomic particles are not as clearly
defined as normal matter
– Must be treated quantum mechanically via
• probability distributions or expectation values
• Atomic size is the average coordinate of the outermost electron
and calculable via QM using Coulomb potential
• Not calculable for nucleus since the potential is not known
– Must rely on experimental measurements
• For Rutherford scattering of low E projectile
r0min
ZZ ' e 2

E
– DCA provides an upper bound on the size of a nucleus
– These result in RAu<3.2x10-12cm or RAg<2x10-12cm
Monday, Sept. 18, 2006
PHYS 3446, Fall 2006
Jae Yu
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Nuclear Properties: Sizes
• Scatter very high E projectiles for head-on collisions
2
– As E increases DCA becomes 0.
– High E particles can probe deeper into nucleus
r0min
ZZ ' e

E
• Use electrons to probe the charge distribution (form
factor) in a nucleus
– What are the advantages of using electrons?
• Electrons are fundamental particles  No structure of their own
• Electrons primarily interact through electromagnetic force
• Electrons do not get affected by the nuclear force
– The radius of charge distribution can be regarded as an
effective size of the nucleus
Monday, Sept. 18, 2006
PHYS 3446, Fall 2006
Jae Yu
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