1. Review of Fundamentals
Nuclear Reactions
Let’s discuss various kinds of nuclear reactions and their health physics significance.
Day 1 – Lecture 6

2. Objective To learn various kinds of nuclear reactions
To discuss health physics significance and energy considerations of nuclear reactions

3. Content Properties of neutrons Nuclear decay processes Cross section
Neutron interactions
Charged particle reactions
Spallation
Fission
Fusion

4. Chadwick, 1932, alpha bombardment
Properties of Neutrons
Neutron Discovery
Chadwick, 1932, alpha bombardment
He + Be  C + n + Q
Thermal ( eV)
Slow ( eV)
Epithermal (100 eV – 100 keV)
Fast (100 keV – 1 MeV)
Ultrafast (>1 MeV)
Neutron Classification
James Chadwick discovered the neutron in 1932 by bombarding the element beryllium with alpha particles. Many of the nuclear reactions important to health physicists involve neutrons.
Neutrons are classified into several different energy categories, as shown in this slide.

5. Properties of Neutrons
Neutron Characteristics
symbol - n
no charge
rest energy MeV
has a magnetic moment
it is a fermion
Neutron Interaction with matter
Scattering (2 mechanisms)
Absorption (>4 mechanisms)
The neutron has no electrical charge and has essentially the same mass as a proton.
More will be said later about mechanisms for neutron interaction with matter, but they basically involve either scattering or absorption of the neutron.

6. Nuclear Reactions Nuclear Decay
Chemical reactions all involve the exchange or sharing of electrons, they never have an influence on the nucleus of the atom. Nuclear reactions involve a change in the nucleus. There are forces in the nucleus that oppose each other; the "Strong" force holding Protons and Neutrons to each other and the electrostatic force of protons repelling other protons. Under certain arrangements of protons and neutrons the electrostatic force can cause instability in the nucleus causing it to decay. It will continue to decay until it reaches a stable combination.
This graph shows the stable nuclei in red. There are several things to notice:
There are no stable nuclei with an atomic number higher than 83 or a neutron number higher than 126.
The more protons in the nuclei, the more neutrons are needed for stability. Notice how the stability band pulls away from the P=N line. Stability is favored by even numbers of protons and even numbers of neutrons of the stable nuclei are even-even while only 4 of the stable nuclei are odd-odd.

7. Nuclear Reactions Alpha Decay
Alpha decay happens to nuclei with Z>83
The 2 p+ 2n loss brings the atom down and to the left toward the belt of stable nuclei.

8. Nuclear Reactions Beta Decay
Beta decay happens to nuclei with high neutron:proton ratio.
A neutron becomes a proton causing a shift down and to the right on the stability graph.
Generally gamma emission accompanies other radioactive radiation because it is the energy lost from settling (i.e. de-excitation) within the nucleus after a change. Since gamma rays do not affect the atomic number or mass number, they are generally not shown in the nuclear equation.

9. Positron Decay or Electron Capture
Nuclear Reactions
Positron Decay or Electron Capture
Positron Emission
Electron Capture
Positron Emission:
Happens to nuclei with a low neutron:proton ratio.
A proton becomes a neutron causing a shift up and to the left.
Electron Capture:
A proton becomes a neutron causing a shift up and to the left. Always results in gamma radiation.

10. Summary of Major Decay Mechanisms
Nuclear Reactions
Summary of Major Decay Mechanisms
This graph shows all the trends of decay and the band of stable nuclei.
There are some exceptions to the trends but generally a nucleus will decay following the trends (in multiple steps) until it becomes stable.
For example 92U238 will go through 8 alpha emissions and 6 beta emissions (not all in order) before becoming 82Pb206. The steps nuclei follow in becoming stable are called a radioactive series.

11. Cross Section  =  = cross section R I where
 = R I
where
 = cross section
R = number of reactions per unit time per nucleus
I = number of incident particles per unit time per unit area
To characterize the probability that a certain nuclear reaction will take place, it is customary to define an effective size of the nucleus for that reaction, called a cross section.
The cross section has the units of area and is on the order of the square of the nuclear radius. A commonly used unit is the barn, which is equal to cm2.
A standard old story was that in the early days, a particular cross section turned out to be much bigger than expected. An experimenter exclaimed "Why, that's as big as a barn!" and a unit name was born.

12. Nuclear Reactions Fast Neutron Interactions
Elastic scattering - neutrons interact with particles of approximately the same mass such as protons (billiard ball analogy)
Occurs in materials rich in hydrogen such as water, wax, concrete
Accounts for about 80% of fast neutron dose to tissue
Some of the most important nuclear reactions involve fast neutron interactions.
Elastic scattering is the most likely interaction between fast neutrons and low-atomic numbered absorbers. This interaction is a “billiard ball” type collision, in which kinetic energy and momentum are conserved.
Up to neutron energies of the order of 10 MeV, the most important interaction of fast neutrons with matter is elastic scattering.

13. Nuclear Reactions Fast Neutron Interactions
Inelastic scattering – neutrons interact with particles of much greater mass, for example, iron (table tennis ball vs bowling ball analogy)
In inelastic scattering, kinetic energy and momentum are not conserved. Rather, some of the kinetic energy is transferred to the target nucleus which excites the nucleus. The excitation energy is then emitted as a gamma-ray photon.
Inelastic scattering occurs primarily with high-Z absorbers.
For fast neutrons of energies of about 1 MeV, inelastic scattering can become appreciable.
In human tissue, and for fast neutron energies in excess of 10 MeV, inelastic scattering and nuclear reactions (frequently with the emission of several particles) become comparable in frequency with elastic scattering.

14. Elastic Scattering of Neutrons
Nuclear Reactions
Elastic Scattering of Neutrons
In collision with protons, neutrons lose half their energy on average. This reaction makes hydrogenous materials (materials rich in protons) good shields (e.g. concrete, wax, water, and various plastics).
This reaction is very important from a health physics standpoint, since it is responsible for most of the tissue dose from fast neutrons.

15. Inelastic Scattering of Neutrons
Nuclear Reactions
Inelastic Scattering of Neutrons
This interaction is best described by the compound nucleus model, in which the neutron is captured, then re-emitted by that target nucleus together with the gamma photon.
This is a threshold phenomenon; the neutron energy threshold varies from infinity for hydrogen (i.e. inelastic scattering cannot occur with H) to about 7 MeV for oxygen to less than 1 MeV for U.
This reaction is not very significant from a tissue dose standpoint, since tissue is composed of relatively low-Z materials.
Iron has a particularly strong probability of fast neutron inelastic scattering.

16. Neutron Reactions (n, CP) (n, gamma) (n, fission)
An example of each type of nuclear reaction is shown in this slide.
the most important neutron reactions with matter include:
Charged particle emission or (n, CP) reactions - shown by neutron capture in boron
Radiative capture or (n, gamma) reactions - shown by neutron capture in stable Co and
Fission - in this example, the fission products are Mo-95 and Li-139 but in general many different fission products will be produced, in accordance with the fission yield probability. 95 and 139 add up to only 234, not 236, since in general two or more neutrons (average of 2.5) are emitted from each fission event.
Note that Co-60 emits two rather energetic gamma rays (1.17 and 1.33 MeV ), which are of concern from a radiation exposure and shielding standpoint.

17. Nuclear Reactions Neutron Absorption, Charged Particle
n B  7Li(*) + 
It should be noted that although the products of neutron capture in boron are charged particles which do not travel very far in matter, the Li product is left in an excited energy state after this reaction occurs.
It gets rid of this excess energy by emitting a gamma ray photon of energy MeV. This is of concern in neutron shielding and in potential radiation exposure to people.
7Li(*)  7Li + soft gamma (480 KeV)

18. Fission
The theoretical basis for fission is the massive energy release which occurs when a heavy nucleus divides into two smaller ones. Only a few very heavy nuclei undergo fission spontaneously, while others can be encouraged to undergo fission by the addition of energy when a neutron is absorbed. Such fissile materials (as they are known) include 235U and 239Pu.
During the fission process, a number of neutrons are released, and if these go on to induce new fission events, a chain reaction results. The use of a controlled chain reaction is the basis for all nuclear power stations.
The process of nuclear fission was discovered in 1938 by Otto Hahn and Fritz Strassmann and was explained in early 1939 by Lise Meitner and Otto Frisch. The fissionable isotope of uranium, U-235, can be split by bombarding it with a slow, or thermal, neutron. (Slow neutrons are called “thermal” because their average kinetic energies are about the same as those of the molecules of air at ordinary temperatures.) The atomic numbers of the nuclei resulting from the fission add up to 92, which is the atomic number of uranium. A number of pairs of product nuclei are possible, with the most frequently produced fragments being krypton and barium.
Since this reaction also releases an average of 2.5 neutrons, a chain reaction is possible, provided at least one neutron per fission is captured by another nucleus and causes a second fission. In an atomic bomb, the number is greater than 1 and the reaction increases rapidly to an explosion. In a nuclear reactor, where the chain reaction is controlled, the number of neutrons producing additional fission must be exactly 1.0 in order to maintain a steady flow of energy.

19. Breeding 239Pu from 238U Neutron Capture
Uranium-235, which occurs naturally as one part in 140 in a natural mixture of uranium isotopes, is not the only material fissionable by thermal neutrons. Uranium-233 and plutonium-239 can also be used but must be produced artificially. Uranium-233 is produced from thorium-232, which absorbs a neutron and then undergoes beta decay (the loss of an electron).
Plutonium-239 is produced in a similar manner from uranium-238, which is the most common isotope of natural uranium.
The average energy released by the fission of uranium-235 is 200 million electron volts, and that released by uranium-233 and plutonium-239 is comparable. Fission can also occur spontaneously, but the time required for a heavy nucleus to decay spontaneously by fission (10 million billion years in the case of uranium-238) is so long that induced fission by thermal neutrons is the only practical application of nuclear fission.

20. Details of 239U Decay to 239Pu 
239U (23.5 min)  239Np (2.3 d)  239Pu 
U-239 is produced when a neutron is captured in U U-239 then decays by two successive beta decays to Pu-239, which has a half-life of 24,390 years.
The U-239 half-life is 23.5 min and the Np-239 half-life is 2.3 days.

21. Charged Particle Bombardment
Nuclear Reactions
Charged Particle Bombardment
p Zn  67Ga + 2n
 O  18F p + n
Many radionuclides can be produced through charged particle (protons, deuterons, alpha particles, 3He+2 ) bombardment of nuclei of stable atoms. Two such nuclear reactions are shown in this slide.
The charged particles must have enough kinetic energy to overcome the repulsive effects of a positively charged nucleus (1-100 MeV per nucleon). Such energies are produced by accelerating particles using a linear accelerator or cyclotron.
The desired isotope almost always has a different atomic number (Z) with respect to the target material. Charged particle reactions yield radionuclides that are predominantly neutron deficient and therefore decay via positron emission or EC (electron capture).

22. Nuclear Fusion Reactions Utilize Isotopes of Hydrogen
Controlled thermonuclear fusion utilizes hydrogen and its two isotopes, deuterium and tritium, for fuel. Hydrogen is found in water (H20) and consists of one proton in the atomic nucleus and one electron orbiting the nucleus.
Deuterium is one of the isotopes of hydrogen and consists of one proton and one neutron in the nucleus and one orbiting electron. One out of approximately 6500 hydrogen atoms in ordinary water is a deuterium atom. Tritium is the other isotope of hydrogen and consists of one proton and two neutrons in the nucleus and one orbiting electron.
This figure shows the three isotopes of hydrogen. Each isotope has one positively charged proton (blue) and one negatively charged electron (small yellow). What makes the isotopes different is that they have a different number of uncharged neutrons (yellow).

23. Nuclear Reactions Fusion
The first generation of fusion power plants will use the D-T fusion reaction, shown schematically in the above animation. Nuclei of two isotopes of hydrogen, deuterium (D) and tritium (T) react to produce a helium (He) nucleus and a neutron (n).
In each reaction, 17.6 MeV of energy (2.8 pJ) is liberated:
D T  4He (3.5 MeV) n (14.1 MeV)
The first generation fusion reactors will use deuterium and tritium for fuel because they will fuse at lower temperature. Deuterium can be easily extracted from seawater, where 1 in 6500 hydrogen atoms is deuterium. Tritium can be bred from lithium, which is abundant in the earth's crust. In the fusion reaction a deuterium and tritium atom combine together, or fuse, to form an atom of helium and an energetic neutron.
This figure shows a deuterium ion (deuteron) combining with a tritium ion (triton) to form an unstable compound nucleus which relaxes into a helium ion and an energetic neutron. The "D-T" reaction has the highest reaction rate at the plasma temperatures which are currently achievable; it also has a very high energy release. These properties make it the easiest reaction to use in a man-made fusion reactor. As the figure shows, the products of this reaction include an alpha particle (Helium-4 nucleus) with 3.5 MeV energy, and a neutron with 14.1 MeV energy. The neutron escapes from the plasma (it has no charge and is not confined) and can be trapped in a surrounding "blanket" structure, where the n + Li-6 => He-4 + T reaction can be used to "convert" the neutrons back into tritium fuel.
Additional notes:
1 eV = E-19 joules;
Average particle thermal kinetic energy is 1 eV per 11,600 K.

24. Deuteron – Deuteron Fusion
We shall briefly consider the deuteron-deuteron reaction to form an alpha particle (helium nucleus). A deuteron is the name that has been given to an atom of hydrogen that contains one neutron (besides the one proton, which makes the atom a hydrogen atom) in the nucleus. The neutron possesses a net charge of zero, while the proton possesses a net charge of plus one (+1). To fuse, two deuterons must bind together at the nuclear level creating a single atomic nucleus which contains two protons and two neutrons. This new nucleus is now a helium nucleus which only requires the acquisition of two free electrons to become an atom of helium.
Prior to the capture of the two electrons, the nucleus is properly referred to as an alpha particle and possesses a net charge of plus two (+2). Whenever two deuterium nuclei fuse into an alpha particle, there is a net decrease in mass. For example: A single deuteron nucleus has a mass of Atomic Mass Units (amu), where 1 amu is equal to x kg. The fusion of two such particles yields a particle (an alpha particle) whose mass is amu instead of amu. There has been a disappearance of amu!
This loss of mass, called a mass decrement, is the binding energy of the alpha particle from the two deuterium nuclei. Put another way, to split an alpha particle into two deuterium nuclei would require that the alpha particle absorb MeV (million electron volts), which is the energy evolved from the conversion of amu into energy. This mass does not simply disappear, in the sense that it has vanished into nothingness, but is converted into the kinetic energy of the newly created nucleus. Thus, the alpha particle leaves the point of fusion at over 11% of the velocity of light!
One deuteron has a mass of amu (Atomic Mass Units) 1 amu = MeV. Also 1 amu = x kg.
Thus the combined amu of 2 deuterons should be 2( ) = amu
The mass of the resultant helium nucleus of alpha particle = amu
The mass loss or mass decrement or binding energy = amu
This decrement will be grams per gram of reactant. This mass converted into energy is equal to x 1018 ergs which is equal to 159,996 kilowatt hours.

25. Production from Fusion
Tritium – Proton
Production from Fusion
Since two like charged particles repel each other (according to Coulomb's Law), why does fusion take place at all?
Current concepts hold that if two like charged nuclei (such as our previously-mentioned deuterium nuclei) can be brought close enough together (approx. one nuclear diameter-about 5 x cm), that a short range nuclear 'strong force' will take over and bind the two nuclei into a single new nucleus. Enough energy must be supplied to the interacting nuclei to enable or allow them to come close enough together so that fusion can take place. According to the classical theory, the energy which must be supplied to the interacting nuclei to overcome the force of electrostatic repulsion (known as the Coulomb barrier) so that the nuclei can fuse, is given by:
Energy required to surmount the Coulomb barrier = Zl Z2e2/R0
where Zl and Z2 are the respective charges (or atomic numbers) of the interacting nuclei, 'e' is the unit (or electronic) charge, and Ro is the distance between the centers of the nuclei at which the attractive 'strong force' can dominate or overcome the repulsive Coulomb force.
This figure shows how the deuterium and tritium fuel weighs more than the resulting helium and neutron products. This mass is converted into energy via Einstein's E=mc2 equation. The fusion energy released from just a 1 gram of deuterium and tritium mixture equals the energy from about 2400 gallons of oil.

26. 3He with Neutron Production
from Fusion
For light nuclei, which are of interest in controlled nuclear fusion research Ro may be taken to be approximately equal to a nuclear diameter (5 x cm), and since 'e' is 4.8 x esu (statcoulomb) it follows from the equation that the energy required to surmount the Coulomb barrier is:
= 4.6 x 10-7 Zl Z2 erg = .28 Zl Z2 MeV (million electron volts)
Where 1 MeV = 1.6 x 10-6 erg.
It can be seen that the energy which must be acquired by the nuclei before they can undergo fusion increases with the atomic numbers Zl and Z2 . For reactions among hydrogen isotope nuclei (deuterium, for example) for which Zl=Z2=l, the minimum energy according to classical theory is about .28 MeV. Larger energies would be required for reactions involving nuclei of higher atomic numbers because of the increased electrostatic repulsion.
During the fusion reaction, a small amount of mass appears to be lost, about 38 parts out of 10,000. But the matter has not been destroyed but instead has been converted to energy following Einstein's famous equation E=mc2. This equation states that the energy (E) is equal to the lost mass (m) times the square of the velocity of light (c). Even a very small mass can yield a considerable amount of energy. For example, if a 1 gram raisin were completely converted to energy it would equal about 10,000 tons of TNT!

27. Fusion - Tokamak
The tokamak is presently the leading candidate design for a future "working" magnetic fusion device.
The word tokamak means "toroidal chamber" in Russian. It is a magnetic fusion device that is in a shape of a torus (e.g. a doughnut), and which depends on external windings for generating a strong toroidal magnetic field (i.e. in the direction along the doughnut).
Poloidal magnetic fields (in the direction of the doughnut's cross-section) are created primarily by a toroidal current inside the plasma itself. This combination of toroidal and poloidal magnetic fields generates an overall nested helical structure which is necessary to keep the plasma stable.

28. Energy Production Reactions in Stars
The Proton-Proton Chain is the principal set of reactions for solar-type stars to transform hydrogen to helium:
1H + 1H --> 2H + e+ + neutrino: Two protons (p+) react to form Deuterium (2H = 1p+ 1n) plus a positron (e+) and a neutrino. In the highly ionized stellar interior the positron will quickly "annihilate" with an electron (e+ + e- --> 2 gamma-rays); the gamma-rays will be absorbed and re-emitted by the dense matter in the stellar interior, gradually diffusing outward and being "degraded" into photons of lower energy. When the gamma-ray energy reaches the photosphere each gamma-ray will have been transformed into about 200,000 visible photons. The neutrino, which only interacts through the Weak Force, streams straight out of the sun.
2H + 1H --> 3He + gamma-ray: The Deuterium reacts with another proton to form 3He (2p+ 1n) plus another gamma-ray. The first two reactions must happen twice to form two 3He nuclei.
3He + 3He --> 4He + 2 1H: The two 3He nuclei react to form 4He (2p+ 2n) giving two protons "change“ plus a bit of added kinetic energy to the product nuclei. Note that the 3He nuclei repel each other more strongly because they contain two positively charged protons. The initial reaction above can occur at temperatures as low as 1 million K, but the last reaction can only occur at temperatures greater than about 10 million K.
The individual nuclear reactions proceed rather slowly, and it is a very small fraction of nuclei in the core of the sun with enough energy to overcome the electrical repulsion. Even so, every second the sun turns 600 million tons of hydrogen into 596 million tons of helium (with 4 million tons transformed into luminous energy via E=mc2).

29. Summary Various examples of nuclear reactions were discussed
Students learned about properties of neutrons, nuclear decay processes, cross section, neutron interactions, and various kinds of nuclear reactions including charged particle reactions, spallation, fission and fusion

30. Where to Get More Information
Cember, H., Johnson, T. E, Introduction to Health Physics, 4th Edition, McGraw-Hill, New York (2009)
International Atomic Energy Agency, Postgraduate Educational Course in Radiation Protection and the Safety of Radiation Sources (PGEC), Training Course Series 18, IAEA, Vienna (2002)