Nuclear Physics

• Neutrons and protons are found in the nucleus of an atom, and for this reason are collectively referred to as nucleons.
• A nucleon is defined as a constituent particle of the atomic nucleus, either a neutron or a proton.

• A species of atom characterized by the constitution of its nucleus, which is specified by its atomic mass and atomic number (Z), or by its number of protons (Z), number of neutrons (N), and energy content.
• A listing of all nuclides can be found on the "Chart of the Nuclides."

• Isotopes are defined as nuclides which have the same number of protons but different numbers of neutrons.
• Any nuclides which have the same atomic number but different atomic mass numbers are isotopes.

• Of fundamental concern in nuclear reactions is the question of whether a given reaction is possible and, if so, how much energy is required to initiate the reaction or is released when the reaction occurs.
• The theory that relates the two was proposed by Albert Einstein in 1905.

E = mc²

• This equation expresses the equivalence of mass and energy, meaning that mass may be transformed to energy and vice versa. Because of this equivalence the two are often referred to collectively as mass-energy.
• The mass-energy equivalence theory implies that mass and energy are interchangeable.
• The theory further states that the mass of an object depends on its speed.
• Thus, all matter contains energy by virtue of its mass.
• It is this energy source that is tapped to obtain nuclear energy.
• The Law of Conservation of Energy applies to mass as well as energy, since the two are equivalent.
• In any nuclear reaction the total mass-energy is conserved i.e. mass-energy cannot be created or destroyed.
• This is of importance when it becomes necessary to calculate the energies of the various types of radiation which accompany the radioactive decay of nuclei.

If a nucleus could be disassembled to its constituent parts, i.e., protons and neutrons, it would be found that the total mass of the atom is less than the sum of the masses of the individual protons and neutrons.

This slight difference in mass is known as the mass defect, δ (pronounced "delta"), and can be computed for each nuclide, using the following equation.

Binding energy is the energy equivalent of mass defect.

1 amu = 931.478 MeV

If we multiply the mass defect by this number we can calculate the binding energy.

• If the total binding energy of a nucleus is divided by the total number of nucleons in the nucleus, the binding energy per nucleon is obtained.
• This represents the average energy which must be supplied in order to remove a nucleon from the nucleus.
• If the binding energy per nucleon is plotted as a function of mass number (total number of nucleons) for each element, a curve is obtained.

• The binding energy per nucleon peaks at about 8.5 MeV for mass numbers 40 - 120 and decreases to about 7.6 MeV per nucleon for uranium.
• The binding energy per nucleon decreases with increasing mass number above mass 56 because as more protons are added, the proton-proton repulsion increases faster than the nuclear attraction.
• Since the repulsive forces are increasing, less energy must be supplied, on the average, to remove a nucleon.
• That is why there are no stable nuclides with mass numbers beyond that of 208.

• Using the _z^AX format, equations can be written which depict a transformation that has occurred in a nucleus or nuclei.
• The total mass-energy on the left side of the equation must be equal to the total mass-energy on the right side.
• Any difference in total mass is accounted for as energy released in the transformation.
• This energy release is called the Q value.

For example, the alpha decay of Radium-226 would be shown as:

• 
• The energy release, represented by Q in this case, is the kinetic energy of the high-speed alpha particle, as well as the recoil of the Radon-222 atom.

• When a free neutron strikes a nucleus, one of the processes which occurs is the absorption of the neutron by the nucleus.
• It has been shown that the absorption of a neutron by a nucleus raises the energy of the system by an amount equal to the binding energy of the neutron.
• Under some circumstances, this absorption may result in the splitting of the nucleus into at least two smaller nuclei with an accompanying release of energy.
• This process is called fission.
• Two or three neutrons are usually released during this type of transformation.

• The energy required to drive the nucleus to the point of separation is called the critical energy for fission, Ec.
• The values of Ec for various nuclei can be calculated, based on a knowledge of the forces which act to hold the nucleus together.

An example of a fission is shown below, involving neutron absorption by 235U:

• 
• On the average, approximately 200 MeV of energy is released per fission.

• For 238-U the critical energy for fission is greater than the neutron binding energy.
• Therefore, an additional amount of energy must be supplied in order for fission to occur in these nuclei.
• This additional energy is in the form of neutron kinetic energy, and confirms the observation that fission occurs in these fissionable nuclei only when the neutron has approximately 1 MeV of kinetic energy.

• The situation is quite different for 235-U, 233-U, and 239-Pu.
• In these cases, the neutron binding energy exceeds the critical energy for fission.
• These nuclei may be fissioned by thermal, or very low energy, (0.025 eV) neutrons.
• To attain stability, the fission fragments will undergo various transformations depending on the degree of instability.

• Along with the neutrons immediately released during fission, a highly unstable element may give off several neutrons to try to regain stability.
• This makes more neutrons available to cause more fissions and is the basis for the chain reaction used to produce nuclear power.
• The excited fission product nuclei will also give off other forms of radiation in an attempt to achieve a stable status.
• These include beta and gamma radiation.

• Criticality is the condition in which the neutrons produced by fission are equal to the number of neutrons in the previous generation.
• This means that the neutrons in one generation go on to produce an equal number of fission events, which events in turn produce neutrons that produce another generation of fissions, and so forth.
• This continuation results in a self-sustained chain reaction.

• If the population of neutrons remains constant, the chain reaction will be sustained.
• The system is thus said to be critical.

If too many neutrons escape from the system or are absorbed but do not produce a fission, then the system is said to be subcritical and the chain reaction will eventually stop.

• If the two or three neutrons produced in one fission each go on to produce another fission, the number of fissions and the production of neutrons will increase exponentially.
• In this case the chain reaction is said to be supercritical.

• In nuclear reactors this concept is expressed as the effective multiplication constant or Keff.
• Keff is defined as the ratio of the number of neutrons in the reactor in one generation to the number of neutrons in the previous generation.
• If Keff has a value of greater than 1, the neutron flux is increasing, and conversely, if it has a value of less than 1, the flux is decreasing with time.

• In a subcritical reactor, the neutron flux and power output will die off in time.
• When critical, the reactor operates at a steady neutron and power output.
• A reactor must be supercritical to increase the neutron flux and power level.

• Fusion is the act of combining or "fusing" two or more atomic nuclei.
• The process of fusing nuclei into a larger nucleus with an accompanying release of energy is called fusion.
• Fusion occurs naturally in the sun and is the source of its energy.
• The reaction is initiated under the extremely high temperatures and pressure.

• What occurs in the above equation is the combination of 4 hydrogen atoms, giving a total of 4 protons and 4 electrons.
• 2 protons combine with 2 electrons to form 2 neutrons, which combined with the remaining 2 protons forms a helium nucleus, leaving 2 electrons and a release of energy.