Physics & Politics

Nuclear Theory

Constituents of the nucleus

We now know that atoms are made of electron clouds surrounding a densely packed center called the atomic nucleus. Almost all of the mass of the atom is in its nucleus. In neutral atoms (as opposed to ions) the nucleus  has a positive electric charge equal to the negative charge of surrounding electron cloud. So, if we were to "rip off" from the atom all of its electrons we would be left with a matter that is as massive as it were originally, but positively charged. In fact, the amount of its charge determines what species it belong to. So, if its charge is +1 (in electronic unit), then it is the nucleus of hydrogen, +2, helium, etc. By examining the nucleus in more detail we have learned that its charge is directly related to how many protons  it has. But its mass is dependent on both the number of protons as well as the number of neutrons  that make it up. There appears to be very little difference between a proton and a neutron, except for their electric charge: protons are positive and neutrons, as suggested by their names, have no net charge. Because of this similarity of protons and neutrons they are also referred to as nucleons. So, a nucleon can mean either a proton or a neutron.

If two different nuclei have the same number of protons, but different number of neutrons they are called to be different isotopes. This is because, as was mentioned above, it is the proton number alone that determines the species. Hydrogen for example, has three stable isotopes. All three have one proton; but one isotope has no neutrons, the second has one neutron, and the third isotope has two neutrons. Notice that these three different isotopes have different masses, because of the difference in their neutron numbers. In fact, the deuterium, which is the isotope with one neutron, is twice as heavy as the more common isotope that has no neutrons. (Water molecules that have  deuterium isotope of hydrogen are thus referred to as heavy water.)

It is important to note that in most of our every day lives we are dealing with processes that involve interactions of atoms and molecules (from cooking, which is chemistry, to breathing, which is biology, to touching, which is physics). All of these interactions are electromagnetic in origin. So, it should not be surprising that what distinguishes one atomic element from another is its electric charge number, which is the same as its proton number. The famous periodic table is therefore arranged in terms of increasing proton (charge) number. Check out the table of isotopes at the Lawrence Berkeley Laboratories.

Forces in the nucleus and Nuclear Binding Energy

Nucleons (protons and neutrons) interact with each other by two types of forces. One of these is the same familiar electromagnetic force that binds electrons to the nucleus. But here this force is purely repulsive because the only nucleons that are charged are the protons. Because all protons are positively charged, they repel each other. In addition to electromagnetic force there is a force that is the same for all nucleons. So both protons and neutrons interact equally as far as this force is concerned. It is called the strong force, or the hadronic force. The nature of this force is very different from the electromagnetic force. In the case of electric force when two protons interact they always repel each other. The closer they get the stronger this force gets. Also, this force tends to remain non-zero for relatively large separation distances of the protons (because of this, it is called a "long-range" force).  In contrast, the hadronic force is very strongly repulsive when the two nucleons are near each other, then as they get a little further away it gets to be strongly attractive. In addition, its value drops rapidly as the nucleons get further and further apart. So, this force wants to keep the nucleons near each other, but not too near! When they are near each other they hold on very strongly, but as they get a bit apart they sort of let go. In  this way, then, the hadronic force is said to have a repulsive hard core and a very short range, but strong, attractive part. (The hard core could be thought of as if the nucleons are "solid" objects that cannot penetrate each other, and the short range part can be thought of as if these solid objects are held together with very strong, but stiff, springs. As if once these "springs" are stretched a little too far, they lose their elasticity.)

Binding energy  of a system is basically the energy that holds it together. Equivalently, it can be thought of as the energy that is needed in order to separate its constituents. Deuteron, for example, has a nuclear binding energy of 2.2 million electron volts (MeV). What this means is that in order to separate the proton and the neutron that make up the nucleus of the deuterium atom we need to supply it an equivalent of 2.2 MeV. (1 MeV is the energy that an electron would gain were it to be accelerated though one million volts.) In the case of deuteron it seems to be little difference to think of its binding energy versus to think of the force that the proton and the neutron exert on one another. But thinking of forces gets to be rather complicated when we are dealing with, say, iron which has 56 nucleons! So, instead of trying to figure out what is the forces that the 56 nucleons exert on one another, it is easier to think of the binding energy of the nucleus as a whole, or the average binding energy per nucleon.

Check out this site for Nuclear Binding Energy Curve.

Nuclear Reactions and Nuclear Decay

When a nucleus changes from one species or one isotope into another it is said to decay. The simplest of all nuclei, is of course a single proton - nucleus of hydrogen atom.  Fortunately for us protons are the most stable of all elementary particles. Up to this date there have been no measurements to show that protons decay. Neutron, on the other hand, tends to change into a proton, when in isolation and some times as a member of a nucleus, by emitting an electron and a neutrino. Nuclear decay, however, is further complicated due to the interactions of the nucleons with one another. Because the electromagnetic force between protons is purely repulsive, nuclei with large number of protons are not very stable. In fact, experiments examining stable nuclei have discovered that stable nuclei that appear in nature favor an excess of neutrons to that of protons. So, isotopes that differ from this favorable arrangement tend to decay to generate by products that have proton and neutron numbers that better match this natural tendency. Beside this feature of proton versus neutron excess and stability, the over all nucleon-nucleon interaction that we can summarize with the notion of binding energy also plays a major role in the stability or decay of the nucleus. 

Experiments that have measured nuclear binding energies for stable nuclei have shown that the average binding energy per nucleon tends to increase, from its minimum of 2.2 MeV for deuteron, to slightly over 8 MeV for more massive nuclei. But then it begins to decrease and fall below this 8 MeV value as the nuclei get more and more massive. It is this feature of stable nuclei that also "encourages" nuclear decay.

The most common by products of nuclear decays, aside from the residual nucleus, nucleons, or nuclei, are electrons (or beta  particles), positrons, alpha "particles", and gamma "particles". Strictly speaking, alpha particles (a) are not particles. They are two protons and two neutrons bound together, the same as the nucleus of helium atom. This arrangement tends to be very tightly bound - it has an unusually large binding energy. Because of this "tightness" it behaves nearly like a particle. Gamma (g) particles are just photons (electromagnetic waves, if you like). Their only difference from visible photons is that gamma particles (or gamma rays) are far more energetic. Positrons are identical to electrons, but have, instead, a positive charge. For historic reasons, electrons and positrons are often called beta particles (b- for electrons and b+ for positrons).

Also, check out the Lawrence Berkeley Laboratory's Web site on ABC of nuclear physics.

Fission & Fusion - source of energy

Fission is a nuclear reaction that results in the separation of the original nucleus (mother) into less massive daughter nuclei. When fission occurs it releases energy. This is because, as we discussed above, for heavier nuclei the binding energy per nucleons tends to decrease from its most common 8 MeV. So the daughters have a net binding energy that is higher than their mother's. The difference in energy is often released in the form of a fast moving particle (a neutron, for example). It is the energy of these fast particles, generated in a fission reaction, that is used to generate other forms of energy (heat and then electricity). This is the standard reaction in today's nuclear power plants. In addition to the energy released in fission the power plant reactions rely on the process of chain reaction , in which some of the by products help initiate the reaction. In a uranium 235 chain reaction (see one example to the right of this page), for example, one slow neutron initiates the fission. Aside from the two daughter nuclei this reaction produces three neutrons, each of which can be slowed down to initiate new reactions, etc.

Fusion is the reverse process. Two lighter nuclei fuse to form a heavier one. In this case too, the binding energy per nucleon increases and results in release of extra energy. It is this type of nuclear reaction that is responsible for the "burning" or stars.  Here, similar to a chain reaction the process is a fusion cycle (see an example of this to the right) in which some of the by products are necessary components of the reaction itself. There are two separate ways that laboratories are trying to generate fusion. One is by using strong electromagnetic fields to bring nuclei close enough together for fusion to take hold. Another is to use laser light to accomplish the same. Recently there are attempts to generate fusion using sound waves, in sono-luminescence experiments. To date, none of these schemes has resulted in efficient production of energy. However, because in fusion reactions the source is cheap and readily available and that the reaction produces no radioactive by products, fusion has become a very attractive alternative to all other methods of energy generations.

Questions on Nuclear Theory

Last Modified April 28, 2010 malekis@union.edu

 A uranium Chain Reaction & its beta decay products

n + 235 92U --------->236 92U* --------> 144 56Ba + 89 36Kr + 3 n

both Ba and Kr undergo a series of beta decays, as follows:

144 56Ba  -------->144 57La ------->144 58Ce------->144 59Pr-------->144 60Nd

89 36Kr -------->89 37Rb --------> 89 38Sr --------> 89 39Y

In all of the above the superscript gives the nucleon (mass) number, A, and the subscript indicates the proton (charge) number, Z. The actual beta decays are of the type that results in increasing the proton number, i.e.:        n (in parent nucleus) ----------> p (in daughter) + b- + ne , without changing the mass number.

For an animation of this reaction check out the appelet: Nuclear Decay Animation!

Proto-proton Fusion Cycle

p + p -----------> 2H + b+ + n

p + 2H -----------> 3He + g

3He + 3He -----------> 4He + 2 p

Here, most of the released energy is in the form of the emitted gamma. Please note that cycle uses three protons and one helium (isotope of mass three) to generate two protons and a stable helium (mass four). It is not a self sufficient cycle, but it is efficient and does not result in any radioactive by products, so it is clean.