Nuclear Physics/Nuclear Fusion and Fission

Introduction

Nuclear fusion and fission are the processes by which the nucleus of an atom gains (fusion) or loses (fission) protons, transforming into a different type of atom. Both processes release energy. Nuclear fusion and fission occur in nature, for example, within a star, and artificially, for example in a nuclear reactor.

Energy is released from the nucleus if the Nuclear Binding Energies of the nucleus is increased.

Where Does the Energy Come From?

Everyone has heard of the equation $E=mc^{2}$ but surprisingly few know what it actually means. As well as having heavy implications in electrodynamics and other fields, it says that energy and mass are like beasts, and you can convert one to the other. The Binding Energy, also known as the mass defect, is where this energy comes from. Mass is lost from the nucleus, and energy is released.

Fusion

Fusion is the process of combining the nuclei of smaller atoms(less protons & neutrons and hence, a smaller atomic number) to create a larger atom. In many stars, the process starts with hydrogen (H) atoms combining to form helium atoms (He) then combining again to form Beryllium (Be) atoms and so on... The process stops when all the atoms are converted to Iron (Fe) and the star is thus dead. The reason for this is that once the atoms reach Iron and higher, the energy required to fuse the atoms becomes greater than the energy released by the atoms.

More precisely, fusion is only favourable up to Iron since it is only up to this point that the energy per nucleon (proton and neutron) continues to decrease. The most efficient energy/nucleon reactions that can occur in the process of fusion are Hydrogen-Hydrogen reactions, or between various isotopes of hydrogen. For nuclei heavier than Iron, the tendency is for fission (see other section) to become more viable in terms of liberating energy, i.e. to reduce stored energy/nucleon.

Fusion occurs naturally in environments where a sufficiently large amount of matter is collapsed under gravitational pressure that atoms are stripped of their electrons and nuclei have a sufficiently low mean free path (i.e. their density is fairly high). The aggregate of matter forming such an object is then usually referred to as a star.

Fusion Power

Since the yield from hydrogen fusion is actually higher than for uranium fission, the byproducts are largely benign (with the exception of high energy neutrons), and the materials can be readily obtained by electrolysis from a plentiful resource (water), it is natural to consider trying to build fusion power plants. Since the nuclei are charged, it is possible to control them using powerful magnetic fields, and this is the standard idea in trying to control hydrogen plasma in order to produce a sustained and controlled nuclear reaction. Although progress has been steady, considerable engineering obstacles still need to be overcome.

Wikipedia's entry on Fusion Power

Fission

This is the breakdown of large, heavy nuclei, to make smaller, lighter, more stable nuclei with a lower energy state and release energy at the same time, this is the process used in creating nuclear weapons. A nucleus may split in many different ways, in fact it is very rare for an even split to occur, one "half" being larger than the other in most cases. the mechanism maybe something like this an unstable (large Neutron rich isotope)is held together by the strong nuclear force because it is unstable it distorts allowing the coulomb repulsion between the positive protons to over come the strong nuclear attraction and separate them this forms two highly energetic halves. these may increase their stability by emitting neutrons, these are known as prompt neutrons. Other neutrons maybe emitted later these are known as not surprisingly delayed neutrons. There are two types of fission, the first is spontaneous(this happens without first absorbing a neutron)and more common neutron induced fission which is as its name implies.

For power generation only nuclear fission occurring in a chain reaction is of interest. It is performed controlled in a reactor and uncontrolled in a nuclear bomb. For running a chain reaction the absence of neutron captures and materials with fissionables nuclei are required. The only natural nuclei, which can be used for reactor operation is uranium235. Others like plutonium239 have to be created artificially, however also in a reactor, which requires a fuel like uranium235 or plutonium239. Interestingly a few billion years ago, building a reactor would have been much easier, as there was a much higher concentration of uranium235 in natural uranium! You can read the exact content therefore under Change of isotope composition of natural uranium.

Driving a Star

The Proton-Proton Chain

This is the main fusion process in stars with masses similar to our Sun. The core temperature reached in such stars is in the order of 15 million Kelvin. For larger stars, with higher core temperatures, the Carbon-Nitrogen-Oxygen cycle fusion process becomes the dominant mechanism. Basically the Branch I reactions are as follows, with the ultimate generation of 26.72 MeV of energy. These reactions generate approximately 85% of the Sun's solar energy production.

p + p = d + e⁺ + ν_e
p + d = ³He + γ
³He + ³He = ⁴He +2p

Branch II and III of main sequence hydrogen burning produce much less energy.

Branch II

³He + ⁴He = ⁷Be + γ
e^- + ⁷Be = ⁷Li + ν_e
p + ⁷Li = ⁴He + ⁴He

Branch III

p + ⁷Be = ⁸B + γ
⁸B = ⁸Be^* + e⁺ + ν_e
⁸Be^* = ⁴He + ⁴He

The Carbon-Nitrogen-Oxygen Cycle

This reaction takes place in stars 1.3 times more massive than our own, it is almost exactly the same as the proton-proton chain except that it uses carbon as catalyst. The carbon in the reaction is not used up and is recycled at the end of the reaction. The CNO process generates 26.72 MeV of energy, this is the main branch.

p + ¹²C = ¹³N + γ + 1.95 MeV

¹³N = ¹³C + e⁺ + v_e + 2.22 MeV

¹³C + p = ¹⁴N + γ + 7.54 MeV

¹⁴N + p = ¹⁵O + γ + 7.35 MeV

¹⁵O = ¹⁵N + e⁺ + v_e + 2.75 MeV

¹⁵N + p = ¹²C + ⁴He + 4.96 MeV

Branch ||

There is a small chance that the last reaction in the branch above will not happen and that instead this reaction will.

¹⁵N + p = ¹⁶O + γ + 12.13 MeV

¹⁶O + p = ¹⁷F + γ + 0.60 MeV

¹⁷F = ¹⁷O + e⁺ + v_e + 2.76 MeV

¹⁷O + p = ¹⁴N + ⁴He + 1.19 MeV

¹⁴N + p = ¹⁵O + γ + 7.35 MeV

¹⁵O = ¹⁵N + e⁺ + v_e + 2.75 MeV

However the nitrogen produced in the last reaction will eventually take part in the last reaction of the first branch.

Branch |||

The last branch only takes place in particularly very massive stars where the ¹⁷O + p in the third reaction of the second branch produces a ¹⁸F + γ instead. This can also be called the OF cycle as the oxygen and fluorine used in the reaction are recycled.

¹⁷O + p = ¹⁸F + γ + 5.61 MeV

¹⁸F = ¹⁸O + e⁺ + v_e + 1.65 MeV

¹⁸O + p = ¹⁹F + γ + 7.99 MeV

¹⁹F + p = ¹⁶O + ⁴He + 8.11 MeV

¹⁶O + p = ¹⁷F + γ + 0.60 MeV

¹⁷F = ¹⁷O + e⁺ + v_e

It is important to note that all of the cycles can be simplified into one reaction because all branches will use the same reactants and produce the products.

4p = ⁴He + 2e⁺ + 2v_e + 3γ + 26.72 MeV

The positrons released in the reaction will annihilate with the electrons and produce more energy in the form of gamma rays.