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Structure of atomic nucleus
2006/07
Structure of atomic nucleus
(Bohr-Sommerfeld model, 1915)
The created models are based on the recent knowledge of
the science.
Atom models according to Democritos, Dalton, Thomson,
Rutherford, Bohr
Frank-Hertz experiment, photoelectric effect, Compton
scattering, Zeeman-effect, Stern-Gerlach experiment,
Pauli, de Broglie, Einstein, Schrödinger, Wiegner, Teller,
Szilárd, Yukawa, Sommerfeld ...
Elements of the atom:
Electron cloud (electrons, e-) and nucleus (nucleons: protons
+ neutrons, p+, n0)
Categorisation of atoms
Content
(number of protons: Z, number of neutrons: N, num. of nucleons: N+Z=A)
isotope: same Z, different N ( 11H és 21H)
nuclid: same content (N, Z equals in each: one type of isotop)
isoton: same N, different Z ( 21H, 32He )
isobar: same A, different N (86C, 85B )
isomer: same content, different energystates
Stability
stable nuclei
Radioactivity not occurs. Approx. 264 nuclei, 12C, 14N, 16O
natural radionuclids
Natural radionuclids can be found in the Universe from the time of BigBang. These have long half-life time. 26 nuclei.
238U ( T = 4,47·109 year), 40K ( T = 1,28·109 year), 87Rb ( T = 48·109
year)
artificial radionuclids
Made by people (scientist). Approx. 2000, 60Co, 137Cs, 24Na
Categorisation of particles,
classification
fermions: ½ spin particles –
Fermi-Dirac statistic
bosons: integer spin number –
Bose-Einstein statistic
An electron can be classified as: fermion, lepton
A proton (neutron): fermion, baryon
Interactions
Current
Theory
Mediator
Rel.
strength
range
(m)
Strong
Quantum
chromodynamics
(QCD)
gluons
1038
10-15
Electromagnetic
Quantum
electrodynamics
(QED)
photons
1036
∞
Weak
Quantum
flavourdynamics
(GWS
theory)
W and Z
bosons
1025
10-18
gravitons
1
∞
Interaction
Gravity
General
Relativity
Long-Distance
Behavior
Discovery of the neutron
Rutherford’s nucleus alteration experiment (1917)
Irradiated nitrogen gas with α-particles:
14
7
N  24He 178O 11H
Internuclear reactions took place, therefore it is not
compulsory that the alteration of elements is allways
connected to radioactive decomposition.
Ernest Rutherford
1871-1937
Experiment of Bothe and Becker (1930)
They bombed Berilium with α-particles, and detected a
ray with great penetration ability, which did not diverge
in magnetic nor in electric field. Neutral.
Walther Bothe
1891-1957
(Nobel-prize in
physics,1954)
Chadwick’s interpretation (1932)
During the collision of Be and α-particle an unknown
particle radiation was found, which had the same mass
as a proton but had not any electric charge.
He named this new particule as neutron.
9
4
Be  He  C  n
4
2
12
6
1
0
James Chadwick
1891-1974
(Nobel-prize in
physics 1935)
Heisenberg and Tamm (1932)
They developed a new nucleus model including neutrons, too.
New signification is brought to atomic number!
Neutron (quarkstructure)
1932, James Chadwick
High energy a-particles can cause in certain ”light chemical
elements” (Be, B, Li), that a special radiation with high penetration
ability leaves the irradiated matter. It was thought to be X-ray.
He assumed that a neutral particle with approximately same mass as
proton is emitted.
Properties
The free neutron is not stable, its mean half-life time is 885 s= 18,6
min.
Its decomposition is caused by the weak interaction.
A lot of nuclei can absorb neutron radiation → absorption →
generally radioactive isotopes appear!
n 0  p   e  
Atom energy!
Discovery of the positron
positively charged electron (antiparticle)
Iréne Curie and Fréderic Joliot-Curie
Aluminium foil irradiated by α-particles:
27
13
Al  He  P  n
4
2
30
15
1
0
The arisen phosphor isotope does not occurs in the nature,
immediately transforms to stable silicium.
30
15
P Si
30
14
How did one positive charge disappear?
During the process one proton transformed to neutron!
b+ radiation:

p  n  e 

0

The proton (quarkstructure)
1918, Ernest Rutherford
Scattering of a-particles on nuclei.
Composed of two u and one d quark, the proton is a baryon
(its spin is ½ → fermion).
The main properties of the proton are determined by those
three (two type) quarks.
The quarks are bound together by the strong interaction.
The proton’s mass is much larger then the total mass of the
included quarks. Maybe it contains more particles?
The values of spin-quantumnumber and magnetic moment is
exactly the sum of the appropriate values (respectively) of
the quarks.
http://en.wikipedia.org/wiki/
Properties of the proton
Charge:
q = +1,6⋅10-19 C
Resting mass:
1,67⋅10-27 kg =
1836,15 × me
Magnetic
momentum
Spin
quarkstructure
1,41⋅10-26 J T-1
1/2
uud
→ fermion
→ baryon (neutrally coloured)
Deficit of mass – binding energy
• The mass of composite nuclei is always less than the total
mass of its components (protons and neutrons).
• The virtually missing mass value is proportional to the binding
energy.
• Energy is disengaged (released), while a nucleus is
constructed from free nucleons.
m  Zm pr  Nmn  mnuc
E  m  c
2
mass-energy equivalency of Einstein
(Specific) binding energy ~ A!  each nucleon
(independently of already involved ones) is bound with
approx. 7-8 MeV to the nucleus.
Quarks
name
sign
mass
2
m0 (GeV/c )
electr. charge
(*e)
Up
u
0,0015-0,005
2/3
Down
d
0,017-0,025
-1/3
Charm
c
1,1-1,4
2/3
Strange
s
0,06-0,17
-1/3
Top / True
t
165-180
2/3
Bottom / Beauty
b
4,1-4,4
-1/3
Colours of quarks
This colour is not a real colour (not connected with eye perception!) but the
properties are based on the analogy of the real colours.
Quarks does not exist separately (free). All of the quarks can have all of the three
colours. red, green and blue (r, g, and b).
Quarks generally occur in neutral-colour combinations.
The strong interaction affects every colour-charged particles: for example the
baryons.
Quarks participate in all four interactions!
Nuclear force – strong interaction
Protons push aside one another because of the Coulombforce of identical charges, however the nucleus is stable.
There must be a short-distanced but strong interaction to
compensate the repulsion of electric charges.
▪ high intensity (strong)
▪ short distance (10-15m)
▪ electric charge independent
▪ attracting effect
▪ p-p, p-n, n-n interactions have the same magnitude
The strong interaction appears amongst nucleons (neutrons too!).
In quantum-theory the strong interaction is explained by the quantumchromodynamics (QCD) theory. The mediators of the interaction are the
gluon particles, and affects the colour-charged particles: quarks, gluons
and other more complex particles composed of the previously mentionned
ones: baryons and mesons, (nucleons are also baryons.)
The weak interaction
Radioactive b-decomposition (decay of proton and neutron).
History
Pauli supposed that meanwhile of b-decomposition one
neutral particle of approximately zero mass (called
neutrino) carries a part of the energy away, and it is
indetectable. In 1934, Enrico Fermi generated his theory
which affirmed this presumption (four-fermion interaction).
Affects all of the leptons and quarks. The neutrino (and
antineutrino) participates only in this type of interaction.
Mediators are W- és Z-bosons. W+, W- are electrically
charged, Z0 is neutral boson.
Neutron decomposition can be interpreted as the following:
first, neutron emits one W-boson and that inmediately
decompose to electron and antineutrino. Meanwhile the
neutron transforms to proton. (d → u transformation)
Model’s of the nucleus
Atomic shell model
(sphere symmetric)
The atomic shell model is based on the microscopic
properties (energy levels) of the atom.
Quantummechanics can interpret the behavior of the
electrons in the electronshell.
Certain properties of the nucleus show periodic
behavior. Is it capable to describe the behavior of the
neutron too?
Nucleus with magic numbers:
We can get a stabil nucleus if either of the number of
the nucleon (N, Z) assumes the value of 2, 8, 20, 50, 82,
126.
Atomic shell model
(sphere symmetric)
Bartlet, Elsasser, 1934: „independent particule model”
Jensen and Göppert-Mayer, 1949: atomic shell model
All of the nucleon create a collective potentialfield, wherein
nucleons can move independently from each other.
The nucleons Schrödinger equation’s with quantified
parameters ( energy, angular momentum, magnetic
momentum, spin) characterize the atomic shells.
(spin can only have the value of ½, Pauli-principle is valid)
Atoms with enclosed atomic shells are more stable!
Analogy with electron shells!
Several experimental results are
not confirmed with this model!
Liquid drop model
Bohr showed it first that some properties of atoms (nucleus)
resembles to a liquid drop’s properties (especially in the case
of heavy atoms)
Observations:
1. Each of the nucleons is bound with (almost) the same
energy.
2. This concludes that the total binding energy of the nucleus
is proportional to the number of nucleons (A).
3. The volume of the nucleus is proportional to the number of
nucleons (A). Hofstaedter
4. This concludes that the density of nucleus is the same in
the case of every atom.
Liquid drop model
Carl von Weizsäcker( macroscopic properties)
Explains a lot of phenomena (binding energy, mass, stability
of nuclei).
Based on the property-similarity of atoms and liquid drops:
spherical form, size-independency of density, the
components interact only with their proximate neighbours.
r  r0 A
3
r: radius of nucleus (constant, independ. of atom type)
A: atomic number
r0  2  10 15 m
2
A

Z



2
2
2
Z
2
   A 3
 k  a  A  b  A 3   1   
A
3
A
According to the liquid drop model the binding energy is
formed from different energies.
Terms explained by classical physics:
Nucleons move (exist) in the potencial field of the
neighbouring nucleons:
a  A
volume energy
The nucleons on the surface (outer side) have less
2
b  A3
„neighbours”
surface energy
Electrostatic energy is also present because of charged
protons
Coulomb-energy
Z2
 1
A3
2
A

Z



2
2
2
Z
2
   A 3
 k  a  A  b  A 3   1   
A
3
A
Other terms explained by quantum theory:
Pauli (asymmetry) energy (fermions, Pauli-law)
anti-Hund (pairing) energy
A

Z  
2
 
A
A

2
2
3
||
, if the number of protons and neutrons
both are even (2H,6Li,10B,14N)
 = 0 , if the one of the numbers of protons and
neutrons is even, the other odd (2H,6Li,10B,14N)
-|| , if the number of protons and neutrons
both are odd, frequent in nature
Parameters a, b, , ,  are experimentally determined – semiempiric formule!
One nucleons’ binding energy as the function of atomic number
The ratio of surface and volume energies change!
(r2/r3 = 1/r)
Effect of Coulomb force increases!
Maximum: between 55-60!
The fit is good, except for the light atoms and the atoms
connected to the magic numbers.
Reason: These atoms contain closed atomic shells and that
phenomena is not taken into account in the liquid drop model!
Unified model
Some of the experiments showed that the shape of atoms
can deviate from a spherical symmetry (becomes elliptical).
According to L.J. Rainwater (1950) a nucleon(group) out of
the last closed shell can „polarise” and distort the nucleus,
causing some deformation.
The deformed nucleus can undergo some collective motion:
rotation, vibration (that motion can appear in the sphere form
too).
S.G. Nilsson, Aage Bohr, B.R. Mottelson improved the shell
model (1955-1968).
According to the unified model the total momentum of the
nucleus can not be calculated normal way (j=l+s), rather
taking into account the new momentum (R) originating from
the rotation of the distorted nucleus. Therefore: J=j+R.
Atomic reactions of elements:
b-decomposition, fusion, fission
135
56
Ba
Atomic number less than 56:
b+:
n  p  e 
0


and
fusion
Atomic number bigger than 56:
b -:

p  n  e 

0

and fission
Enrico Fermi
1901-1954
Nobel-price
in1938