1. NUCLEAR PHYSICS

2. Composition of Matter
All of matter is composed of at least three
All of matter is composed of at least three
fundamental particles (approximations):
fundamental particles (approximations):
Electron e- 9.11 x 10-31 kg -1.6 x 10-19 C
Proton p 1.673 x 10-27 kg +1.6 x 10-19 C 3 fm
Neutron n 1.675 x 10-31 kg 0 3fm

3. Definitions
A nucleon is a general term to denote a nuclear particle -
that is, either a proton or a neutron.
The atomic number Z of an element is equal to the number
of protons in the nucleus of that element.
The mass number A of an element is equal to the total
number of nucleons (protons + neutrons).

4. Nuclear Size
The shape of the nucleus is taken spherical, because for
a given volume this shape possesses the least surface
area.
The nuclear density remains approximately constant
over most of the nuclear volume. This means that the
nuclear volume is proportional to the number of nucleons
i.e. mass number A.
Rα A3
1
Hence radius of nucleus
R = Ro A 3
1
where Ro is a constant having value 1.48 x 10 -15 m

5. Atomic Mass Unit, u
One atomic mass unit (1 u) is equal to one-
twelfth of the mass of the most abundant form
of the carbon atom--carbon-12.
Atomic mass unit: 1 u = 1.6606 x 10-27 kg
Common atomic masses:
Proton: 1.007276 u Neutron: 1.008665 u
Electron: 0.00055 u Hydrogen: 1.007825 u

6. Mass and Energy
Einstein’s equivalency formula for m and E:
E = mc ; c = 3 x 10 m/s
2 8
The energy of a mass of 1 u can be found:
E = (1 u)c2 = (1.66 x 10-27 kg)(3 x 108 m/s)2
E = 1.49 x 10-10 J Or E = 931.5 MeV

7. The Mass Defect
The mass defect is the difference between the rest mass
of a nucleus and the sum of the rest masses of its
constituent nucleons, A.
Binding Energy
The binding energy of a nucleus is the energy required to
separate a nucleus into its constituent parts.
EB = mDc2 where mD is the mass defect

8. Binding Energy Vs. Mass Number
Curve shows that EB
Binding Energy per nucleon
8
increases with A and
peaks at A = 60. 6
Heavier nuclei are
less stable. 4
Green region is for 2
most stable atoms.
50 100 150 200 250
Mass number A
For heavier nuclei, energy is released when they break up
(fission). For lighter nuclei, energy is released when they
fuse together (fusion).

9. Radioactivity
• The phenomenon of spontaneous emission
of radiations (α,β and γ radiations) from a
substance (generally elements having their
atomic number higher than 82 in the periodic
table).
• Discovered by Henry Bacquerel in 1896.
• Properties of α,β and γ radiations-
Composition, Ionization Power,
Penetration power, Effect on photographic
plate

10. Laws of Radioactive
disintegrations-
1- The Radioactive disintegrations happens due to the
emission of α, β and γ radiations.
2- The natural disintegration is totally statistical, i.e.
which atom will disintegrate first is only a matter of
chance.
3- The number of atoms which disintegrate per second is
proportional to the number remaining atoms present at
any instant, i.e.-
-dN/dt α N
or -dN/dt = λN
(where λ is a constant of proportionality and is known
as the decay constant)
or N = N0e-λt

11. Half Life Period (T)-
• The time in which half of the radioactive
substance gets disintegrates is known as
half life of that material.
T = 0.693/λ

12. General Properties of Nucleus—
1- Nuclear mass= Mass of all Neutrons + Mass of all protons
mp= 1.67261 x 10-27 Kg = 1.007277 a.m.u.,
mn= 1.67492 x 10-27 Kg = 1.008666 a. m. u.
2- Nuclear Charge- Total charge due to the protons
3- Nuclear radius- Nuclear radius is measured by the measurement of
the directions of scattered protons/ neutrons / electrons.
R = R0A1/3
Where R0 is a constant with value = 1.4 x 10-15 Meter
A = Mass Number of the element
4- Nuclear density= Nuclear Mass/ [4/3( π R3)]

13. The Mass Difference and Nuclear
Binding Energy-
• The mass of the nucleus is always less than
the sum of masses of its constituents.
• The difference in measured mass (M in a. m.
u.) and mass number (A) is called mass
defect (∆M).
• The Binding energy of the nucleus (E) = ∆M
(in a.m.u.) x (931 MeV)

14. Nuclear Forces
• A nucleus contains positively charged
protons and uncharged neutrons.
• A repulsive force works between protons
inside the nucleus.
• Nuclear forces overcome with these
repulsive forces to give a stable nucleus.
• Neutrons and protons can be converted
in to each other by the exchange of a new
particle meson.

15. Meson theory of Nuclear Forces by
Yukawa (1935)
• A meson may be π+, π- or π0.
A neutron, by accepting a π+ meson
converted in to a proton.
A proton, by ejecting a π+ meson converted in
to a neutron.
• A neutron, by ejecting a π- meson converted
in to a proton.
• A proton, by accepting a π- meson converted
in to a neutron.

16. • Two neutron can exchange π0 mesons,
which result in the exchange forces
between them.
• This exchange of meson is responsible for
the generation of exchange forces which
is responsible for the stability of nucleus.

17. Nuclear Fission
• The phenomenon of breaking of heavy
nuclie in to two or more light nuclei of
almost same masses is known as the
nuclear fission.
• Discovered by Otto Hahn and Strassman
(Germans) in 1939.
• In nuclear fission large amount of energy
is liberated

18. • Theory of Nuclear Fission- Liquid Drop Model-
• By Bohr and Wheeler
• The nucleus is assumed to be similar to a drop of the liquid.
• Nucleus remains in balance due to the exchangeforces and the
repulsive forces between its constituents.
• Due to this balance nucleus remains in spherical size.
• When this balance is disturbed by the incident neutrons, the
spherical shape is distorted.
• The surface tension force tend to recover the spherical size, so drop
attains a dumb-bell shape.
• Due to disbalance in the exchange and coulombic forces, the dumb-
bell breaks in two spherical parts (i.e. two separate nuclie).

20. • Nuclear fusion is the formation of a heavier
nucleus by fusing of two light nuclei.
• In this process mass of the resulting nucleus
is less than the masses of constituent ,
therefore according to Einstein’s mass
energy equivalence, enormous amount of
energy is released.
• Fusion reactions take place at very high
temperature.

21. Spontaneous Fission
Some radioisotopes contain nuclei which are highly
unstable and decay spontaneously by splitting into 2
smaller nuclei.
Th234
90
Gamma ray
U238
92
He4
2
Energy is being released as a result of the fission reaction.

22. Induced Fission
Nuclear fission can be induced by bombarding atoms with
neutrons resulting in the splitting of nuclei into two smaller
nuclei.
Induced fission decays are also accompanied by the
release of neutrons.
235
92 U + n→ Ba + Kr +3 n
1
0
141
56
92
36
1
0
Energy is being released as a result of the fission reaction.

23. Nuclear Fusion
In nuclear fusion, two nuclei with low mass numbers
combine to produce a single nucleus with a higher mass
number.
2
1 H + H → He+ n + Energy
3
1
4
2
1
0

24. Hydrogen (proton) fusion
Like electrical charges repel. So, protons in a gas avoid
`collisions’
p+
p+

25. Hydrogen (proton) fusion
However, as a gas temperature goes up, the average speed
of the particles goes up and the protons get closer before
repelling one another. If the proton get very close, the short-
range nuclear force fuses them together.
p+
p+

26. Antimatter
When two protons fuse, almost immediately one turns
into a neutron by emitting a positively charged electron
(known as a positron). The e+ is antimatter. When it
comes into contact with its matter partner (e-) it
annihilates entirely into energy.
Neutrino
This is a chargeless, perhaps massless particle which has a
tiny crossection for interaction with other types of matter.
The mean free path in lead is five light years.
Neutrinos were first postulated in 1932 to account for
missing angular momentum and energy in beta-decay
reactions (when a proton becomes a neutron and emits a
positron).

27. Nuclear Force
The nuclear force is the force between two or more nucleons.
It is responsible for binding of protons and neutrons into
atomic nuclei.
The force is powerfully attractive between nucleons at distances
of about 1 femtometer (fm) between their centers, but rapidly
decreases to insignificance at distances beyond about 2.5 fm.
At very short distances less than 0.7 fm, it becomes repulsive,
and is responsible for the physical size of nuclei, since the
nucleons can come no closer than the force allows.
At short distances (less than 1.7 fm or so), the nuclear force is
stronger than the Coulomb force between protons; it thus
overcomes the repulsion of protons inside the nucleus.

28. Proton-Proton Cycle
ν neutron
ν neutrino
β + β positron
+
H 1
H1
He3
H1 109years
1 sec
He4
H1
106year
H1
H1
H1 Gamma ray
H β +
1
ν

29. Proton-Proton Cycle
• The net result is
4H1 --> He4 + energy + 2 neutrinos
where the released energy is in the form of
gamma rays.
Each cycle releases ~25 MeV
For the proton-proton cycle the gas temperature
needs to be >107K

30. CNO cycle
Energy released ~26.72 MeV per cycle

31. Source of Energy of Stars
• The source of energy of stars is Fusion reaction.
• Our sun shares the “Proton-Proton Fusion Cycle”
with the smallest known stars.
• Larger stars known to “burn” with different cycles,
such as the “carbon cycle”

32. Nuclear Radiation Measurements
All the methods for detection of radioactivity are based on
interactions of the charged particles because interaction results in
the production of ions and release of energy.
Detectors are used to detect and record the number of particles
emitted in various experiments involved in the study of nuclear
radiation, disintegration and transmutation.
Detectors
Based on Ion Based on Light
collection method emission method
Example: Proportional Example: Scintillation
Counter, G.M. Counter Counter

33. Types of detectors
– Gas-filled detectors consist of a volume of gas
between two electrodes
– In scintillation detectors, the interaction of ionizing
radiation produces UV and/or visible light
– Semiconductor detectors are especially pure
crystals of silicon, germanium, or other materials to
which small amounts of I mpurity atoms have
been added so that they act as diodes

34. Types of detectors (cont.)
• Detectors may also be classified by the type of
information produced:
– Counters indicate the number of interactions
occurring in the detector.
– Spectrometers yield information about the energy
distribution of the incident radiation.
– Dosimeters indicate the net amount of energy
deposited in the detector by multiple interactions.

35. Modes of operation
• In pulse mode, the signal from each
interaction is processed individually
• In current mode, the electrical signals from
individual interactions are averaged
together, forming a net current signal

36. Dead time
• The minimum time taken by a radiation detector
in between two successive detections.
• GM counters have dead times ranging from tens
to hundreds of microseconds, most other
systems have dead times of less than a few
microseconds.

37. Detection efficiency
• The efficiency (sensitivity) of a detector is
a measure of its ability to detect radiation
• Efficiency of a detection system is defined
as the probability that a particle or
photon emitted by a source will be
detected.

38. Number detected
Efficiency =
Number emitted
Number reaching detector
Efficiency = ×
Number emitted
Number detected
Number reaching detector
Efficiency = Geometric efficiency × Intrinsic efficiency

39. Gas-filled detectors
• A gas-filled detector consists of a volume of gas
between two electrodes, with an electrical
potential difference (voltage) applied between
the electrodes
• Ionizing radiation produces ion pairs in the gas
• Positive ions (cations) attracted to negative
electrode (cathode); electrons or anions
attracted to positive electrode (anode)
• In most detectors, cathode is the wall of the
container that holds the gas and anode is a wire
inside the container

40. Schematic diagram of a Gas Filled Detector

41. Types of gas-filled detectors
• Three types of gas-filled detectors in common
use:
– Ionization chambers
– Proportional counters
– Geiger-Mueller (GM) counters
• Type determined primarily by the voltage applied
between the two electrodes
• Ionization chambers have wider range of
physical shape (parallel plates, concentric
cylinders, etc.)
• Proportional counters and GM counters must
have thin wire anode

42. GM counters: Main Features
• GM counters used for the detection of α,β,γ
rays, protons etc.
• Gas amplification produces billions of ion pairs
after an interaction.
• The only difference with a Proportional
Counter is of operating voltage.
• Operating voltage is 800-2000 Volts
• Works on pulse mode.

43. Gas Multiplication
–+
↓
–+–+–+
↓
–+–+–+–+–+–+–+–+–+
↓
–+–+–+–+–+–+–+–+–+–+–+–+–+–
+–+–+–+–+–+–+–+–+–+–+–+–+–
+–+–+–+–+–+–+–+–+–+

44. CONSTRUCTION-A Metallic tube with thin wire (anode) in center,
wall of the tube works as cathode.
Tube is usually filled with noble gas (e.g. argon) at low pressure, with
some additives as quenchers e.g. carbon dioxide, methane,
isobutane)
-Charged particle in gas ⇒ ionization ⇒ electrons liberated;
-Electrons accelerated in electric field ⇒ liberate other electrons by
ionization which in turn are accelerated and ionize ⇒ “avalanche of
electrons”;
-Quenching is the process of terminating the discharge after each
detection.
- The time taken for this is known as dead time of the counter

45. Mixture of Argon and ethyl alcohol
ANODE
PULSE
Cathode
Pulse Counter

46. Geiger-Muller Counter
α - particle Vacuum
tube
amplifier

47. Geiger-Muller Counter
The efficiency of the counter is defined as the ratio of the
observed counts/sec to the number of ionizing particles
entering the counter per second.
Counting efficiency is its ability of counting, if at least one
ion-pair is produced in it.
∈= 1 − e slp
Where, s = specific ionization at one atmosphere
p = pressure in atmosphere
l = path length of the ionization particle in the
counter

48. Proportional Counter

49. Proportional Counters:
􀂄 similar in construction to Geiger-Müller counter,
but works in different HV regime . (200- 800 Volts)
􀂄 metallic tube with thin wire in center, filled with
gas, HV between wall (-, “cathode”) and central wire
(+,”anode”); ⇒ strong electric field near wire;
􀂄 gas is usually noble gas (e.g. argon), with some
additives e.g. carbon dioxide, methane,
isobutane,..) as “quenchers”;
􀂄Radiation detected - α,β,γ rays

50. Scintillation Counter
Incident Light
Radiation Pulse Photomultiplier
Phosphor
tube
Electric
Pulse
Amplifier
scaler and
register

51. Scintillation detectors
• Scintillators are used in conventional film-screen
radiography, many digital radiographic
receptors, fluoroscopy, scintillation cameras,
most CT scanners, and PET scanners
• Scintillation detectors consist of a scintillator and
a device, such as a PMT, that converts the light
into an electrical signal

52. Scintillators
• Desirable properties:
– High conversion efficiency
– Decay times of excited states should be short
– Material transparent to its own emissions
– Color of emitted light should match spectral sensitivity
of the light receptor
– For x-ray and gamma-ray detectors, µ should be large
– high detection efficiencies
– Rugged, unaffected by moisture, and inexpensive to
manufacture

53. Scintillators (cont.)
• Amount of light emitted after an interaction
increases with energy deposited by the
interaction
• May be operated in pulse mode as
spectrometers
• High conversion efficiency produces
superior energy resolution

54. Materials
• Sodium iodide activated with thallium
[NaI(Tl)], coupled to PMTs and operated in
pulse mode, is used for most nuclear
medicine applications
– Fragile and hygroscopic
• Bismuth germanate (BGO) is coupled to
PMTs and used in pulse mode as
detectors in most PET scanners

55. Photomultiplier tubes
• PMTs perform two functions:
– Conversion of ultraviolet and visible light
photons into an electrical signal
– Signal amplification, on the order of millions to
billions
• Consists of an evacuated glass tube
containing a photocathode, typically 10
to 12 electrodes called dynodes, and an
anode

57. Dynodes
• Electrons emitted by the photocathode are
attracted to the first dynode and are accelerated
to kinetic energies equal to the potential
difference between the photocathode and the
first dynode
• When these electrons strike the first dynode,
about 5 electrons are ejected from the dynode
for each electron hitting it
• These electrons are attracted to the second
dynode, and so on, finally reaching the anode

58. Βeta minus (β -) decay
example: 6C14 7N14 + -1β 0 + 0υ 0
A neutron turned into a proton by emitting an
electron; however, one particle [the neutron]
turned into two [the proton and the electron].
Charge and mass numbers are conserved,
but since all three (neutron, proton, and
electron) are fermions [spin 1/2 particles],
angular momentum, particle number, and
energy are not! Need the anti-neutrino [0 υ 0]
to balance everything!

59. Positron (β ) decay +
example: 6C11 5B11 + +1β 0 + 0υ 0
A proton turns into a neutron by emitting a
positron; however, one particle [the proton]
turned into two [the neutron and the positron].
Charge and mass numbers are conserved,
but since all three are fermions [spin 1/2
particles], angular momentum, particle
number, and energy are not! Need the
neutrino [0 υ 0] to balance everything!