This section describes the most basic facts about nuclei. These facts will be taken for granted in the rest of this chapter.
Nuclei consist of protons and neutrons. Protons and neutrons are
therefore called “nucleons.” Neutrons are electrically neutral, but protons are
positively charged. In particular, the electric charge of a proton
has the same magnitude as the charge of an electron, but has opposite
sign. Since opposite charges attract, the protons in a nucleus
attract electrons. Despite that, the electrons do not end up inside
the nucleus. They have much larger quantum mechanical uncertainty in
position than the much heavier nucleons. So the electrons form a
cloud
around the tiny nucleus, producing an atom.
Since charges of the same sign repel, protons mutually repel each
other. That is due to the same electric Coulomb
force
that allows them to attract electrons. By itself, the Coulomb force
between the protons in a nucleus would cause the nucleus to fly apart
immediately. But nucleons, both protons and neutrons, also attract
each other through another force, the “nuclear force.” It is this force that keeps a nucleus together.
The nuclear force is very strong, which allows it to dominate
electromagnetic forces like the repulsive Coulomb force in stable
nuclei. But the nuclear force is also very short range, extending
over no more than a few femtometers. (A femtometer, or fm, equals
1
The strength of the nuclear force is about the same regardless of the type of nucleons involved, protons or neutrons. That is called “charge independence.”
More restrictively, but even more accurately, the nuclear force is the same if you swap the nucleon types. In other words, the nuclear force is the same if you replace all protons by neutrons and vice-versa. That is called “charge symmetry.” For example, if you swap the nucleon type of a pair of protons, you get a pair of neutrons. Therefore the nuclear force between a pair of protons is very accurately the same as the one between a pair of neutrons, all else being equal. (The already mentioned Coulomb repulsion between the protons is additional and not the same.) But if you swap the nucleon type of a pair of protons, or of a pair of neutrons, you do not get a proton and a neutron. So the nuclear force between a proton and a neutron is less accurately the same as that between two protons or two neutrons.
The nuclear force is not a fundamental one. It is just an effect of the “color force” or “strong force” between the “quarks” of which protons and neutrons consist. That is why the nuclear force is also often called the “residual strong force.” It is much like how the Van der Waals force between molecules is not a fundamental one; that force is a residual of the electromagnetic force between the electrons and nuclei of which molecules exist, {A.33}.
However, the theory of the color force,“quantum chromedynamics,” is well beyond the scope of this book. It is also not really important for nanotechnology. In fact, it is not all that important for nuclear engineering either because the details of the theory are uncertain, and numerical solution is intractable, [19].
Despite the fact that the nuclear force is poorly understood, physicists can say some things with confidence. First of all,
Nuclei are normally in the ground state.The
ground stateis the quantum state of lowest energy
excitedstates of higher energy. However, a bit of thermal energy is not going to excite a nucleus. Differences between nuclear energy levels are extremely large on a microscopic scale. That is why nuclear bombs and nuclear reactors can create so much energy. Still, nuclear reactions will typically leave nuclei in excited states. Usually such states decay back to the ground state very quickly. (In special cases, it may take forever.)
It should be noted that if a nuclear state is not stable, it implies
that it has a very slight uncertainty in energy, compare chapter
7.4.1. This uncertainty in energy is commonly called the
“width”
A second general property of nuclei is:
Nuclear states have definite nuclear massYou may be surprised by this statement. It seems trivial. You would expect that the nuclear mass is simply the sum of the masses of the protons and neutrons that make up the nucleus. But Einstein’s famous relation.
(Similarly, a hydrogen atom has less mass than a free proton and a free electron. But here the difference, a few eV, is far too small to note. Since nuclear binding energies are millions of times bigger, in nuclei the effect is much more important.)
It may be noted that binding energies are almost never expressed in
mass units in nuclear physics. Instead masses are expressed in energy
units! And not in Joule either. The energy units used are almost
invariably electron volts
(eV). Never use an SI unit
when talking to nuclear physicists. They will immediately know that
you are one of those despised nonexperts. Just call it a
blah.
In the unlikely case that they ask, tell them
That is what Fermi called it.
Next,
Nuclear states have definite nuclear spinHere the “nuclear spin”.
The name nuclear spin
may seem inappropriate since net
nuclear angular momentum includes not just the spin of the nucleons
but also their orbital angular momentum. But since nuclear energies
are so large, in many cases nuclei act much like elementary particles
do. Externally applied electromagnetic fields are not by far strong
enough to break up the internal nuclear structure. And the angular
momentum of an elementary particle is appropriately called spin.
However, the fact that nuclear spin
is two words and
“azimuthal quantum number of the net nuclear angular
momentum” is nine might conceivably also have something to do
with the terminology.
According to quantum mechanics,
The fact that nuclei have definite angular momentum does not depend on
the details of the nuclear force. It is a consequence of the very
fundamental observation that empty space has no build-in
preferred direction. That issue was explored in more detail in chapter
7.3.
(Many references use the symbol
Consider also the component
Nuclear states have definite parity.Here
parityis what happens to the wave function when the nucleus is mirrored and then rotated 18
Or actually, there is one force of nature, the still unmentioned
so-called weak force
that does not behave the
same way when seen in the mirror. But the weak force is, like it
says, weak. On nuclear scales, it is many orders of magnitude smaller
than the nuclear and electromagnetic forces. So, while the weak force
introduces some quantum-mechanical uncertainty in the parity of
nuclei, this uncertainty is usually negligibly small. The chances of
finding a nucleus in a given energy state with the
wrong
parity can be ballparked at 1
Parity is commonly indicated by p
and is not used for anything else in science.
And physicists usually list the spin and parity of a nucleus together
in the form
Key Points
- Nuclei form the centers of atoms.
- Nuclei consist of protons and neutrons. Therefore protons and neutrons are called nucleons.
- Protons and neutrons themselves consist of quarks. But for practical purposes, you may as well forget about that.
- Neutrons are electrically neutral. Protons are positively charged.
- Nucleons are held together by the so-called nuclear force.
- The nuclear force is approximately independent of whether the nucleons are protons or neutrons. That is called charge independence. Charge symmetry is a more accurate, but also more limited version of charge independence.
- Nuclear states, including the ground state, have definite nuclear energy
. The differences in energy between nuclear states are so large that they produce small but measurable differences in the nuclear mass.
- Nuclear states also have definite nuclear spin
. Nuclear spin is the azimuthal quantum number of the net angular momentum of the nucleus. Many references indicate it byor .
- Nuclear states have definite parity
. At least they do if the so-called weak force is ignored.
- Never use an SI unit when talking to a nuclear physicist.