Introduction to Nuclear Physics
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S.PÉRU
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
The nucleus a complex system
?
• What
is the heaviest nucleus ?
• How many nuclei do exist ?
• What about the shapes of the nuclei ?
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
The nucleus : a complex system
I) Some features about the nucleus
discovery
radius, 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
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
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.
screen
Target
Au
source
 particles
The unexpected results demonstrated the existence of the atomic nuclei.
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
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
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
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 ?
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
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 ?
At the distance « a0 » from the center of the nucleus, when the  particle go back :
Coulomb repulsion = kinetic energy of the  particle
The size of the gold nucleus is 2.8 10-14 m
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
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
proton
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
proton
neutron
?
electron
neutron
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.
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
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 :
Nuclear interaction
?
Introduction to Nuclear Physics
S. Péru
Nuclear interaction
CERN Summer student program 2011
features of the nucleus : the scale of a nucleus
A nucleus is almost 100000 times
smaller than an atom
ATOM
(10-9 m)
NUCLEUS
(10-14 m)
NUCLEON
(10-15 m)
Do all the nuclei have the same radius ?
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
R(fm)
features of the nucleus : radius
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
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
features of the nucleus : shape
Ground–state 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
Introduction to Nuclear Physics
or
S. Péru
oblate
CERN Summer student program 2011
features of the nucleus : shape, density
208Pb
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
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
Z
B(A,Z) ≈ A× 8 MeV
N
... Nucleus
nucleus : M(A,Z) ≈ A× (1000 - 8) MeV
...
A=Z+N
B(A,Z)
M(A,Z) = N Mn + Z Mp – B(A,Z)
Stable bound system for B > 0
Note :
B is the “missing mass”
Matomic(A,Z)=A (1amu) + Δm
Δm = «mass excess »
Δm= 0 for 126C
=> 1 amu = 931,500 MeV
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
Binding energy: nucleon-nucleon potential
VNN
1 GeV
r
1
pp
s
p
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
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
Binding energy: nuclear interaction
Nuclear interaction is repulsive for small distances and attractive for large ones,
it’s a binding interaction.
Coulomb interaction is repulsive for protons.
Z
coulomb repulsion
N=Z Symmetry
N
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
features of the nucleus : binding energy
Binding energy per nucleon:
B(A,Z)/A ≈ 8 MeV
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
features of the nucleus: stability
ITER project
The most
stable nuclei
Nuclear power plant
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
features of the nucleus: stability
....free... ... nucleons...
Mass (MeV)
...
B(D)+B(T)
10.71
D
≈1800
226
4He
88Ra
A
Q=4.871
222
Introduction to Nuclear Physics
≈2 × 1000
B(Rn)+B(4He)
1736.492
B(4He)+n
28.30
fusion
... ... ...
...
B(Ra)
1731.626
T
Q=17.60
...
86Rn
Α radioactivity
S. Péru
QF≈200
4He
A/2
A/2
fission
CERN Summer student program 2011
features of the nucleus: separation energy
Separation energies
Mass (MeV)
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)
B(A-1,Z,N-1)+ mn
For one proton
A-1
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)
B(A,N,Z)
n
S(n)
A=Z+N
α particle
S(n) = separation energy of one
neutron in the A nucleus
S(α) = B(A,N,Z)-[B(A-4,N-2,Z-2)+B(α)]
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
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.
J=0
J=+1/2J=1
neutron
proton
neutron
proton
J=-1/2
Introduction to Nuclear Physics
neutron
neutron
proton
J=0
S. Péru
CERN Summer student program 2011
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
dN
 N (t )
dt
Half –life T defined as the time for which the number of remaining nuclei
is half of its the initial value.
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
Different types of radioactivity
A
Z 1
A 1
Z
X N1
XN1

A 4
Z2
bn X
p
A
Z
A 1
N
XN
Z 1
b+,e
A
Z 1
XN1
XN2
Neutrons
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
Total versus partial life times
226
89Ac
(29 h)
e (170 h)

b (35 h)
 (55 y)
226 Ra
88
226 Th
90
1
1
1
1



29 h 35 h 170 h 55 y
222
Introduction to Nuclear Physics
87Fr
S. Péru
CERN Summer student program 2011
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
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
How do we study a nucleus ?
Nuclear reactions
a
A
B
A+a
b
b+B
A(a,b)B
Photonuclear reaction A(γ,b)B
Radiative capture A(a,γ)B
Elastic scattering A(a,a)A
Inelastic scattering A(a,a’)A*
A*=excited state
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
How do we study a nucleus ?
The reaction energy: Q value
A(b,d)C
b
C
A
B(b)+B(A)
d
B(C)+B(d)
Q = B(C) +B(d) - (B(A) + B(b))
Q is a constant, a feature of each reaction.
Q>0 exoergic
Q=0 cold (elastic scattering)
Q<0 endoergic: the minimum energy of the incident particle needed is the
threshold energy
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
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) …
…
Introduction to Nuclear Physics
R(fm)
S. Péru
CERN Summer student program 2011
How do we experimentally study a nucleus ?
III) Gamma spectroscopy
1) To excite the nucleus
2) To observe its decay
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
Number of detected photons
Energy in MeV
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
The barcode of a nucleus
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
148Sm
Introduction to Nuclear Physics
160Gd
S. Péru
CERN Summer student program 2011
Odd nuclei
61Ni
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
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 …)
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
Some applications of Nuclear Science (2)
 Art and archaeology
* datation
* identification of constituent materials
(ex : AGLAE Accélérateur Grand Louvre pour l’Analyse 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
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011
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
Introduction to Nuclear Physics
S. Péru
CERN Summer student program 2011