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Introduction to Nuclear Physics
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S.PÉRU
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The nucleus a complex system
?

• What is the heaviest nucleus ?
• How many nuclei do exist ?
• What about the shapes of the nuclei ?

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The nucleus a complex system
I) Some features about the nucleus discovery rad
ius, shape binding energy nucleon-nucleon
interaction stability and life time
nuclear reactions applications
I) Some features about the nucleus discovery rad
ius, shape binding energy nucleon-nucleon
interaction stability and life time
nuclear reactions applications
II) Modeling of the nucleus liquid drop shell
model mean field
III) Examples of recent studies
figures of merit of mean field approaches
exotic nuclei
isomers shape coexistence
IV) Toward a microscopic description of the
fission process
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The discovery of the nucleus
The structure of the atom was first probed by the
Rutherford experiment in 1909. A beam of ?
particles generated by the radioactive decay of
radium was directed onto a sheet of a very thin
gold foil.
The unexpected results demonstrated the existence
of the atomic nuclei.
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• Before this exp. people thought that ? particles
  should all be deflected by at most
• a few degrees.
• But some ? s were deflected through angles much
  larger than 90 degrees !!
• The results suggest that the greater part of the
  mass of the atom was
• concentrated into a very small region.
• Atoms are almost empty except a hard scattering
  center the atomic nuclei

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Some questions about the Rutherford experiment

• ? Why a thin target ?
• ? What about electrons ?
• ? Why in the vacuum ?
• How can we determine the size of the atomic
  nucleus
• from this experiment ?

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Some tracks about the Rutherford experiment
? Why a thin target ?
To be sure that the projectile do interact with
only one nucleus
? What about electrons ?
Electrons do not affect the trajectory of the
projectile which is much heavier
? Why in the vacuum ?
In the air, the slowing down of the beam and of
the scattered ? make the analysis more
complicated and can even stop the particles
before detection.

• How can we determine the size of the atomic
  nucleus from
• this experiment ?

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What is the nucleus of the atom ?
?
The nucleus contains A nucleons A Z
protons N neutrons Nucleons are hadron
particles (particles governed by the strong
interaction) Nucleons are baryons (made of 3
quarks) protons (uud) are positive charged
particles 2000 times heavier than electrons. Mpc2
938.272 MeV Mec2 0.511
MeV neutrons (udd) are electric neutral particles
with mass comparable to the proton one. Mnc2
939.565 MeV
electron
proton
neutron
neutron
proton
proton
Nucleons are fermions, as well as electrons.
A nucleus is characterized by its mass number A
and its atomic number Z. It is written AZX.
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?
What is the nucleus of the atom ?
The nucleus contains A nucleons A Z
protons N neutrons
The nucleus is a bound system its mass is lower
than the mass of its components. There is a
missing mass connected to the binding energy by
the famous Einstein formula
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Nuclear interaction
Nuclear interaction
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features of the nucleus the scale of a nucleus

A nucleus is almost 100000 times smaller than an
atom
ATOM
NUCLEUS
NUCLEON
(10-9 m)
(10-14 m)
(10-15 m)
Do all the nuclei have the same radius ?
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features of the nucleus radius
R(fm)
Radii are extracted from elastic scattering of ?
particles on different targets.
R 1.25 x A1/3 (fm)
1fm 10-15 m
The radius increases with A1/3 ? The volume
increases with the number of particles
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features of the nucleus shape
Groundstate nuclear deformation predicted with
the Hartree-Fock-Bogoliubov approach with the
Gogny force
www-phynu.cea.fr
Nuclei are predicted to be either
spherical prolate
or oblate
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features of the nucleus shape, density
208Pb
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features of the nucleus binding energy
A nucleus is a bound system i.e. its mass is
lower than the mass of its components. (if not
the nucleus would release its excess of energy by
spontaneously evolving to a state of lower energy
composed of free particles)
Mass Energy Instability
free nucleons A 1000 MeV B(A,Z) A 8
MeV nucleus M(A,Z) A (1000 - 8) MeV
Z
N
...
...
...
...
Nucleus
AZN
B(A,Z)
M(A,Z) N Mn Z Mp B(A,Z)
Stable bound system for B gt 0 Note B is
the missing mass Matomic(A,Z)A (1amu) ?m
?m mass excess  ?m 0 for 126C gt 1
amu 931,500 MeV
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Binding energy nucleon-nucleon potential
VNN
1 GeV
pp s
p
r
1
2
3
Distance between the nucleons (fm)
-50 MeV
hard core attractive part
The nucleon-nucleon interaction is still unknown
nowadays !!! Phenomenological parameterization of
the interaction THIS IS ONE OF THE MOST
IMPORTANT PROBLEM NOWADAYS
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Binding energy nuclear interaction

• Nuclear interaction is repulsive for small
  distances and attractive for large ones,
• its a binding interaction.
• Coulomb interaction is repulsive for protons.

NZ
Z
coulomb repulsion
Stability valley
Stability valley
NZ Symmetry
N
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features of the nucleus binding energy
fission
Binding energy per nucleon B(A,Z)/A 8 MeV
fusion
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features of the nucleus stability
The most stable nuclei
ITER project
Nuclear power plant
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features of the nucleus stability
....free... ... nucleons...
Mass (MeV)
...
...
...
...
...
...
B(D)B(T) 10.71
D
T
B(Ra) 1731.626
1800
B(4He)n 28.30
B(Rn)B(4He) 1736.492
2 1000
Q17.60
22688Ra
A
4He
Q4.871
QF200
22286Rn
A/2
A/2
4He
? radioactivity
fusion
fission
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features of the nucleus separation energy
Separation energies For one neutron S(n)
M(A-1,N-1,Z)mn M(A,N,Z) S(n)B(A,N,Z)-B(A-1,N-1
,Z) For one proton S(p) B(A,N,Z)-B(A-1,N,Z-1)
Two-neutron separation energy S(2n)B(A,N,Z)-B(A
-2,N-2,Z) a particle S(a) B(A,N,Z)-B(A-4,N-2,
Z-2)B(a)
Mass (MeV)
B(A-1,Z,N-1) mn
B(A,N,Z)
A-1
n
S(n)
AZN
S(n) separation energy of one neutron in the A
nucleus
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features of the nucleus spin

• The nucleus contains A nucleons A Z protons
  N neutrons
• Nucleons are spin one-half particles, they are
  fermions.
• Even-even or odd-odd nuclei are whole spin
  systems.
• Even-odd and odd-even nuclei are half-whole spin
  systems.

J0
J1/2
J1
neutron
neutron
J-1/2
J0
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features of the nucleus nuclear life times
A few nuclei are stable their lifetimes are
infinite (comparable to the lifetime of the
proton 1033 years.) The others are unstable
they transform into more stable nuclei
Exponential decay
Half life T defined as the time for which the
number of remaining nuclei is half of its the
initial value.
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Different types of radioactivity
Protons
b-
n
b,e
p
a
Neutrons
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(No Transcript)
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Total versus partial life times
(29 h)
22689Ac
e (170 h)
b- (35 h)
a (55 y)
22690Th
22688Ra
22287Fr
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Examples half lives
Life times span many orders of
magnitude Nitrogen 16 T1/2 7.13
s Oxygen 15 2.037 mn Radium 224
3.62 d Carbon 14 5730
y Molybdenum 100 1019 y Tellurium
124 2.2 1028 y
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Nuclear reactions
How do we study a nucleus ?
A
B
b
a
A a
bB
A(a,b)B
Photonuclear reaction A(?,b)B Radiative
capture A(a,?)B Elastic scattering
A(a,a)A Inelastic scattering A(a,a)A
Aexcited state
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The reaction energy Q value
How do we study a nucleus ?
A(b,d)C
C
A
d
b
B(b)B(A)
B(C)B(d)
Q B(C) B(d) - (B(A) B(b))
Q is a constant, a feature of each reaction. Qgt0?
exoergic Q0? cold (elastic scattering) Qlt0?
endoergic the minimum energy of the incident
particle needed is the threshold energy
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How do we experimentally study a nucleus ?
I ) Elastic and inelastic scattering
Excitation energy (MeV)
e- ,e p n Heavy ions ........
Momentum transferred
II ) Transfer ex (p,n), (d,p)
R(fm)
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How do we experimentally study a nucleus ?
III) Gamma spectroscopy
1) To excite the nucleus
2) To observe its decay
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Number of detected photons
Energy in
MeV
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Example of a level scheme
The barcode of a nucleus
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148Sm
160Gd
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Odd nuclei
61Ni
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Some applications of Nuclear Science
Nuclear physics makes indeed many essential
contributions to
? Energy production Electricity generation
fission research on new generations of
power plants, new fuel cycles reduction by
transmutation of the long term impact of
the nuclear wastes produced (ADS or GEN IV
reactors) fusion for the far future (ITER
project)
? Medicine diagnostic detection of the
decay of radioactive isotopes SPECT
Single Photon Emission Computer Tomography
PET Positron Emission Tomography IRM Imaging
by Magnetic Resonance therapy (proton-,
hadron-therapy )
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Some applications of Nuclear Science (2)
? Art and archaeology datation
identification of constituent materials
(ex AGLAE Accélérateur Grand Louvre pour
lAnalyse Elémentaire)
? Environmental studies ex observation of
modification of ocean circulation
patterns (measurement of 129I /127I in seawater
as a function of depth and distance to the
coast)
?
From NuPECC long Range Plan 2004
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Some features of the nuclei Summary

• The existence of the atomic nuclei the
  Rutherford experiment in 1909
• The nucleon-nucleon interaction is not precisely
  known.
• Many nuclei are predicted but not observed up to
  now
• Most of them are neutron rich, and are supposed
  to have played a role
• during the nucleosynthesis.
• Nuclei are characterized by their level scheme
  their barcode.
• Many applications of the nuclear physics