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NUCLEAR PHYSICS
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
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).
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
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
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
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
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).
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
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
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
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)]
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)
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.
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.
• 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.
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
• 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).
• 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.
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.
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.
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
Hydrogen (proton) fusion

Like electrical charges repel. So, protons in a gas avoid
`collisions’


                       p+



                        p+
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+
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).
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.
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
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
CNO cycle




Energy released ~26.72 MeV per cycle
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”
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
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
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.
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
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.
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.
Number detected
Efficiency =
             Number emitted
             Number reaching detector
Efficiency =                            ×
                 Number emitted
                     Number detected
                Number reaching detector
Efficiency = Geometric efficiency × Intrinsic efficiency
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
Schematic diagram of a Gas Filled Detector
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
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.
Gas Multiplication

             –+
             ↓
           –+–+–+
             ↓
     –+–+–+–+–+–+–+–+–+
             ↓
–+–+–+–+–+–+–+–+–+–+–+–+–+–
 +–+–+–+–+–+–+–+–+–+–+–+–+–
    +–+–+–+–+–+–+–+–+–+
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
Mixture of Argon and ethyl alcohol


                                   ANODE




                                    PULSE

Cathode




                   Pulse Counter
Geiger-Muller Counter




α - particle                     Vacuum
                                 tube
                                 amplifier
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
Proportional Counter
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
Scintillation Counter

Incident               Light
Radiation              Pulse   Photomultiplier
            Phosphor
                               tube

                                        Electric
                                        Pulse

                                    Amplifier
                                    scaler and
                                    register
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
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
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
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
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
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
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!
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!

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nuclear physics,unit 6

  • 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).
  • 19.
  • 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
  • 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
  • 56.
  • 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!