Structure of the Nucleon - Pions, Quarks & Gluons

Nucleons

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Above: models of the proton (left) and neutron (right). These particles are the nucleons that are the building blocks of the atomic nucleus. The diagrams illustrate the charge density. In the center is the nucleon core, the region of highest charge density, which is the nucleon proper. This is surrounded by a shell of electric charge due to the formation of virtual pions. The middle shell illustrates the radius at which this pion charge density is a maximum, it then drops to zero at the outer radius of each nucleon. This is further illustrated in the diagram below:

Nucleon charge distributions

Above: Beneath each model is given the corresponding plot of electrical charge density (given as radial probability, referring to the likelihood of finding a pion at any given point - this concept is similar to the probability shells of electrical charge due to electrons in the atom). On the horizontal axis is given distance from the nucleon centre in femtometres. Notice that for both the proton and neutron the electrical charge is densest in the cores and positive. This core charge is due to the nucleon proper, though in both the proton and neutron this core can fluctuate between being a neutron and a proton, as we shall see below! In the region of the middle shell, where the pion charge density is greatest, this gives a hump of positive charge in the case of the proton and a dip of negative charge for the neutron. This indicates that the proton core is surrounded by electric charge due to positively charged pions whilst the neutron core is surrounded by negatively charged pions. Thus, the proton is overall positively charged, whilst the neutron is overall neutral (the positive and negative charges cancel).

Notice also that the charge density gradually drops to zero at a radius of about 2 fm for the proton and 1.5 fm for the neutron - the proton is lightly larger, probably because the like charges of the proton core and positive pion repel one another slightly (though not enough to overcome the strong forces that bind them).

What are these pions and where do they come from?

The pions are actually virtual pions. This means that individual pions cannot be observed as definite and 'real' particles. A proton or neutron constantly creates and emits pions without losing any energy or mass itself. Thus, energy is being created, which would be a violation of the laws of physics - since the law of >energy conservation says that energy can neither be created nor destroyed. However, an uncertainty principle states that in principle it is impossible to measure both the energy and time of existence of a particle with complete precision - the more accurately one (energy or time) is measured the less accurate the other one becomes. Thus, a large amount of energy can be borrowed from nothing (from the vacuum) for a period of time that is so short that this energy cannot be directly measured, so long as at the end of its time this energy is destroyed again - so things even out and nobody really notices the energy-conservation violation! Notice that the uncertainty principle is a principle - it has nothing to do with how accurately our instruments can measure things, rather it is a fundamental property of the system being measured.

Thus a proton or a neutron can constantly create these ephemeral unmeasurable virtual pions and reabsorb them a short time later. Thus, pions are constantly emitted and reabsorbed by nucleons, causing a pion charge cloud to surround each nucleon.

These pions do have real and observable consequences, however, even if they cannot be directly captured and observed. If the pion charge clouds of two neighbouring nucleons (two protons, two neutrons or a proton and a neutron) overlap, as they will do when they are packed close together in the very dense nucleus of an atom, a pion emitted by one may be absorbed by the other nucleon instead of by the emitting nucleon. This still does not violate energy conservation in the long run as this satisfies the requirements of the uncertainty principle. Now if one nucleon transfers a virtual pion to a neighbouring nucleon in this way then energy and momentum have also been transferred. The effect of this exchange of virtual pions is to produce a force between the nucleons. This force binds the nucleons together in the nucleus and is called the nuclear force. It is this force that stops the protons repelling one another (like charges repel) and stops the nucleus disintegrating.

This nuclear force is similar in some ways to the force that keeps the electrons bound to the atom. The electrons are electrically negatively charged and so are attracted to the positively charged proton (opposite charges attract) - this is the Coulomb (electromagnetic) force. This force is also due to the exchange of virtual particles, but not pions, rather virtual photons. Photons are particles of light (electromagnetic radiation) and the exchange of virtual photons between electrically charged particles produces an attractive force if the particles have opposite charge (positive and negative) or a repulsive force if the particles have like charges (both positive or both negative).

Thus protons will exchange both virtual photons and virtual pions with one another. Virtual photons will also be exchanged between a charged core and the pion cloud within the nucleon. The force due to pion exchange is the stronger of the two, however it is very short range. When two protons are far apart the Coulomb force dominates and they repel one another, but when they are close together within the nucleus, the nuclear force dominates and the protons are bound together. The range of such forces depends upon the mass of the virtual particle exchanged, lighter particles produce longer range forces, - the photon is massless and so is very long range, whilst the pion is heavy and so the nuclear force is very short range (of the order of the nuclear diameter. Thus, we are familiar with the Coulomb force in every day life - such as the electrostatic attraction between hair and a charged comb. However, the nuclear force is only experienced at ranges shorter than the atom, on the size-scale of the atomic nucleus!

Structure of the nucleon core

The core of the nucleon (or the nucleon proper if one considers the pion cloud to surround the nucleon rather than to be a part of it) consists of particles called quarks. Quarks come in a variety of flavours, or types. The proton and neutron are composed of three quarks of two different flavours. The proton is composed of two up-quarks and one down-quark and so can be written: uud. The neutron is composed of one up-quark and two down-quarks and so can be written udd. Up-ness and down-ness  are two quark flavours carried bu the up-quark (u) and the down-quark (d) respectively. The other quark flavours are strangeness (strange or s-quark), charm (charmed or c-quark), beauty (bottom or b-quark) and truth (top or t-quark). Of course quark 'flavours' are not flavours in the gustatory sense of the word (!), they are simply types of quarks characterised by different quantum numbers (i.e. they are quarks in different quantum states).

Quarks also come in one of three colours - red, blue and green. Again this is not colour that we can see (quarks are much smaller than the wavelength of light and so are invisible to light and hence have no colour in the usual sense). However, they possess a colour charge, analogous to electric charge except that it isn't electricity and because there are three 'signs' of these charges (rather than two - positive and negative, in electricity) the term colour charge seems appropriate since colour schemes are based on three primary colours. Thus a quark has one unit of either red, green or blue charge. Thus, we have 6 flavours and 3 colours, giving 18 different types of quarks (each flavour comes in three different colours). There are also 18 antiquarks, the antimatter equivalent of quarks (yes, antimatter is real!), each of six anti-flavours (anti-up, anti-down, anti-strange, anti-charm, anti-top and anti-bottom) and of three anti-colours (antired, antiblue and antigreen, sometimes called cyan, yellow and magenta. This gives us 36 types of quark in all (18 quarks plus 18 anti-quarks).

Colour confinement

Quarks have never been definitely observed as single particles, rather they only occur as either quark/anti-quark pairs (mesons) or in groups of three as in the nucleon. Furthermore, they must combine in such a way that their colours cancel. So, in the nucleon, we must have a red quark, a green quark and a blue quark since these three primary colours cancel to give white (in terms of light). A red quark can also achieve colour confinement by pairing up with an anti-red anti-quark. Colour confinement is an apt name, since the colour cannot be detected as it is confined to a mixture that gives white.

Quarks also carry electric charge, so that they will exchange virtual photons with one another when close enough, as in a nucleon. However, quarks also exchange another type of virtual particle with one another, this virtual particle is called the gluon. Quarks carry either + 2/3 electric charge units (u, c and t quarks) or - 1/3 electric charge (d, s and b quarks). In the proton we have + 4/3 electric charge from two u quarks and - 1/3 from one d quark, giving (4/3 - 1/3 = 3/3/ = 1) +1 electric charge overall, the electric charge of the proton. In the neutron we have udd, giving +2/3 -1/3 -1/3 = 0 electric charge, so overall the neutron is electrically neutral.

The model below shows a nucleon core consisting of three quarks of opposite colour charge (shown as red, green and blue for illustrative purposes) embedded in a sphere of virtual photons and gluons that the quarks constantly emit and reabsorb and exchange with one another. Since the photons may move further than the gluons (gluons have mass and so give rise to a short-range force) some virtual photons will also be exchanged with other nucleons (if they are both protons) and with any electrons orbiting the nucleus of an atom that the proton may belong to. In contrast, the short-range force produced by gluon exchange only has effect over the diameter of the nucleon core.

Nucleon core

The force generated by gluon exchange between the quarks is called the strong force. It is very strong, but also very short range.

What is the difference between the nuclear force and the strong force?

Some of you may have heard about the strong nuclear force binding nucleons together and that the strong force is conveyed by gluons. It might have confused you, therefore, to read about pion exchange accounting for the nuclear force. Pions are mesons and so they are made up of a quark and an anti-quark bound together by gluon exchange and the strong force. (Though the constituent quarks will also exchange virtual photons giving rise to a Coulomb (electric) force). When a nucleon emits a virtual pion, the pion conveys its internal quark and anti-quark to the absorbing nucleon. Remember that the pion is created 'from nothing' and so its quark and anti-quark are newly created and when they are absorbed by the recipient nucleon they are  destroyed again (avoiding energy conservation violation).

The force that gives rise to the pion is actually the strong force mediated by gluons (presumably a gluon turns into a quark plus an antiquark, which can later annihilate back into gluons). In an analogous way, photons (via the electromagnetic force) can give rise to an electron (negatively charged) and an anti-electron (positron - positively charged) which can also annihilate back into photons. In essence, then, gluons are indirectly responsible for the nuclear force - they are converted into pions enabling them to traverse distances that are greater than the nucleon diameter and equivalent to the nuclear diameter. Upon arrival the pion is unpackaged by quark/anti-quark annihilation. The nuclear force is strong, but it is the indirect result of the true strong force that acts between quarks and is mediated by gluons. Colour is to the true strong interaction what electric charge is to the electromagnetic interaction.

Three types of pions

There are three types of pions, all of which are involved in the nuclear force. A neutron can emit a negatively charged pion, turning into a proton as it does so (forming a neutron with a positively charged proton core surrounded by a negatively charged pion field or cloud). A recipient proton may then absorb this negative pion and turn into a neutron. The end result is that the proton and neutron have switched identities - the proton has become a neutron and vice versa! This reaction is shown below, both using the symbols: p for proton, n for neutron and Greek pi for pion (plus charge sign) and as the quark constituents: udd = p, uud = n and the negative pion is a down quark paired with an anti-down quark. A bar above a quark symbol indicates an anti-quark.

Pion exchange

Above a neutron becomes a proton and negative pion, and a nearby proton absorbs this pion to become a neutron. Notice that the net result is the creation of an up-quark and an anti-up quark pair, the up-quark (u) swaps for a down quark (d) in the neutron, turning the neutron into a proton. The down and anti-up quarks form a negative pion which is absorbed by a nearby proton and then the anti-up quark annihilates with an up-quark in the recipient proton, which then absorbs the remaining d-quark, converting the proton from uud to udd, i.e. into a neutron.

The equation below shows a similar process, in which a proton emits a positive pion, turning itself into a neutron, and then the pion is absorbed by a recipient neutron, turning it into a proton. Essentially a down anti-down quark/antiquark pair has been produced near the donor proton and annihilated near the recipient neutron. This is quark/anti-quark pair production and annihilation. Quarks can only be produced from nothing as such pairs.

Pion exchange

Note that a proton cannot emit a negative pion and a neutron cannot emit a positive pion - indeed such pions are destroyed near to such nucleons.

Both neutrons and protons can emit a neutrally charged pion, however, which consists of a down and anti-down quark pair. The pion does not necessarily swap its quark with the emitting nucleon in this case (though if it did we couldn't tell anyway!) and so this corresponds to d/anti-d pair production and annihilation. These two processes are shown below, for a donor neutron and a donor proton. Notice that the recipient nucleon could be either a proton or a neutron in either case (though only one example of these two possibilities is shown) - it makes no difference since the recipient is not changes and neutral pions can be emitted and destroyed by either nucleon type.

Pion exchange

Pion exchange

Nucleons exchanging pion

The model above shows a proton and neutron with overlapping pion fields, allowing the proton to donate a pion to the neutron, contributing to the nuclear force holding the two nucleons together.

The following summarizes some of the properties of the particles mentioned in this section.

Summary of quark types

The table below lists some key properties of the different quark flavours. Quarks of the same flavour but with different color are indistinguishable except by their color charge.

Quark Electric Charge Mass (MeV/c2)
up (u) 2.3
down (d) -⅓ 4.8
charm (c) 1 275
strange (s) -⅓ 95
top (t) 173 210
bottom (b) -⅓ 4 180

Note that mass is given in units of MeV/c2 (mega electronvolts divided by the speed of light squared; in units with c = 1 the values will be in MeV). This mass is sometimes called the 'rest mass' (since the apparent mass of an object increases as its velocity increases) though this term is seldom used these days. To put this in perspective, the proton has a mass of 938.3 MeV/c2 or 1.67 x 10-27 kg (0. 000 000 000 000 000 000 000 000 00167 kg) with such tiny masses the units of MeV/c2 are clearly more convenient! The electronvolt is actually a unit of energy, and the mega-electronvolt is one million electronvolts. (The electronvolt is the amount of kinetic energy gained by a single free electron when it passes through an electrostatic potential difference of one volt, in a vacuum. Equivalently, it is equal to one volt times the (unsigned) charge of a single electron). However, Eisntein's famous equation of special relativity is: E = mc2 (energy equals mass times the speed of light squared; note this equation is not as simple as it seems since we need to use relativistic mass in this equation) and tells us that energy divided by the speed of light squared (c2) is equivalent to mass, hence the units MeV/c2.

Notice also the pattern of electric charges. This arises because the u and d quarks form a related pair, the first generation of quarks. Quarks c and s form the second generation, which is similar to the first except the quarks are heavier and t and b form the third generation which is the most massive. Being massive means that top quarks are only formed in very energetic reactions between particles, i.e. high-energy particle-particle collisions. It also means they are unstable, typical enduring for a tiny fraction of a second before decaying into lighter particles. Since a top quark is apparently an elementary particle we should not think of this decay as the particle falling apart into its constituents, rather the mass/energy of the top quark is converted into lighter particles. The first generation are the lightest and the most stable and consequently the most abundant quarks making up normal matter.


Baryons

Nucleons belong to a group of particles called baryons. Each baryon is made of three quarks. The nucleons and some of their properties are given in the table below:

Baryon Electric Charge Stability Quark Constituents Mass (MeV/c2)
p +1 stable
uud
938.3
n 0 unstable
udd
939.6

Surprisingly the neutron is unstable, and decays after about ten minutes, but only when free. Inside an atomic nucleus it is quite stable (maybe because it doesn't exist for long before turning into a proton?). There are other baryons which are very unstable. For example, the Δ0 baryon is an excited state of the neutron (udd) and the Δ+ baryon an excited state (resonance) of the proton (uud). They decay (de-excite by emitting a pion) as follows:


Δ0 p+ + π

Δ0 n + π+


Δ+ p+ + π0

Δ+ n + π+


Mesons

Pions belong to a class of particles called mesons. Mesons are all quark / anti-quark pairs.

Meson Electric Charge Stability Quark constituents Mass (MeV/c2)
neutral-pion 0 unstable d + anti-d 135.0
positive-pion +1 unstable u + anti-d 139.6
negative-pion -1 unstable d + anti-u 139.6


Again, there are other mesons. Mesons and baryons are together known as hadrons.

Leptons

The electron and its anti-matter equivalent the positron belong to a class of particles called leptons. The tauon, muon and three types of neutrino are the other members of the lepton group. leptons, like quarks, are fundamental particles - that is they appear to be indivisible - they do not consist of smaller constituents as far as we can tell, but are fundamental building blocks or elementary particles. Hadrons, in contrast, are made up of smaller constituents - quarks.

Gluons

Gluons mediate the strong force, rather as photons mediate the electromagnetic force, but whereas photons carry no electric charge, gluons do carry colour charge. This complicates matters considerably (it makes the governing mathematical equations nonlinear and nonlinear equations are difficult to solve and can have complicated solutions). Gluons also carry anti-colour, so there are eight possible gluon types:

1. Red / anti-green
2. Red / anti-blue
3. Green / anti-red
4. Green / anti-blue
5. Blue / anti-red
6. Blue / anti-green

7,8. Instead of the remaining three obvious combinations: red / anti-red, green / anti-green and blue / anti- blue there are two more gluon types which are combinations of these three. This is often the case in quantum mechanics and arises because of mathematical reasons. Indeed it is also a physical principle of quantum mechanics that particles can exist in a combination of states and arises simply because each state behaves like a wave and as it is possible to combine waves, so it is possible to combine certain quantum states.

Probing Nucleon Structure - a deeper look

To see living cells one would use a light microscope, which can detect structures of one thousandth of a millimetre (one micrometre) comfortably. For higher magnification, necessary to see the details of organelles within cells, one would use an electron microscope. Electron microscopes can comfortably be used to observe structures of a little less than 10 millionths of a millimetre (10 nanometres). This is still 100 times larger than a typical atom (atomic diameter around 0.1 nanometres). Individual atoms just become detectable with ultra-hi-resolution electron microscopes. Electron microscopes contains large columns several metres tall and require a bank of computer controls. They use electron beams instead of light beams. However, an atom is still some 100 000 times larger than an atomic nucleus! To probe such structures and even individual nucleons and quarks, particle physicists use particle accelerators.

State of the art particle accelerators are huge constructions underground. Linacs are linear particle accelerators - they fire a beam of particles in a straight line from one end to the other. The beam consists of charged particles, such as protons or electrons, which can be accelerated by powerful magnets. However, this beam can be used to generate a secondary beam of other particle types, including non- charges particles which cannot be easily accelerated but continue with the momentum generated by the primary charged beam.  Synchrotons are circular structures, allowing the charged primary beam to travel further under acceleration as it is accelerated for several circuits (until the energy it loses going around the bends at high speed cancels out any further possible gain and the beam hits its maximum energy). Building larger diameter synchrotons reduces the energy loss and allows beams to be accelerated to higher energies. The Large Hadron Collider (LHC) at CERN, is 27 kilometres in circumference and conducted its first proper experiment in 2009. The LHC is a collider, meaning that it is used in experiments in which two beams collide into one another, as opposed to a fixed-target machine, which fires abeam at a stationary target. Colliders are the more efficient in breaking up particles into their constituent particles. The LHC will be the most powerful particle accelerator in the World.

When a highly energetic high-speed electron collides with a nucleus, such as the nucleus of deuteron (heavy hydrogen) which consists of a single neutron and a single proton bound together, the proton captures a virtual photon emitted by the electron. This virtual photon conveys momentum, and possibly energy, to the nucleus. The electron, having lost some of its momentum in the photon emitted, gets deflected and hits a detector. Measuring the angle of deflection, and knowing the energies involved, it is possible to work out what exactly the electron collided with. This allows us to determine the number of particles that make up a nucleus or nucleon. For the electron colliding with a deuterium nucleus (a deuteron) we detect two constituents - the proton and the neutron. However, when we probe an individual nucleon more closely, the electron can hit any one of three primary valence quarks, these are the three quarks that account for many of the observable properties of the nucleon, such as its electric charge, and are the uud quarks in the proton, and udd in the neutron. However, it is also possible to detect collisions with other multiple targets, these are the quarks and antiquarks emitted by the nucleons and constitute the sea quarks - they form a kind of 'sea' bathing the valence quarks. Most of these are low mass quark/antiquark pairs, such as the u and d quarks that form the pion fields around the valence quarks. Strange, s, quarks and their antiquarks may also be produced by the nucleon core and these may collide with the electron.

Less frequent (at lower energies) are collisions with the more massive c, b and t quarks. These massive quarks need to 'borrow' more energy and so do not emit spontaneously as often as u,d or s quarks (or they travel a shorter distance before being reabsorbed, so as to avoid violation of energy conservation - remember mass and energy are related by E = mc2). These collisions become more distinguishable at higher energies, where the electron may collide with a quark with such force that the quark releases a gluon with enough energy to produce a heavy quark/antiquark pair, such as b/anti-b. In short all flavours of quarks and antiquarks make a contribution to nucleon structure, though lighter quarks make the bigger contribution. All these quarks and antiquarks are collectively called partons, since they form part of the nucleon.

There are other targets too. About 50% of the momentum of a nucleon is locked up in a sea of gluons that the quarks and antiquarks constantly emit and reabsorb. These gluons seem too innumerable to count, as are the sea quarks (and their number presumably fluctuates as they come and go).

Rather than using electrons (and their virtual photons) as probes of nucleon structure, further information is obtained by using a secondary beam of particles called neutrinos. Neutrinos have no electric charge and very little (if any) mass. Neutrinos have the useful property of being able to collide with d quarks but not u quarks, whilst antineutrinos can collide with u quarks but not d quarks. This has allowed the electric charge of u and d quarks to be determined and allows the gluon constituents to be probed.

Proton and Neutron Form Factors

Colliding high-energy electrons, and other particles, with protons and neutrons thus gives us insight into the structure of neutrons and protons. Below a certain energy the electrons have a wave-length too large to 'probe' the internal structure of the nucleon and elastic collisions (like those between billiard balls) occur. Elastic collisions are those in which both the total momentum and kinetic energy of the electron and nucleon are conserved. In such collisions the nucleon essentially behaves like a point particle with no internal structure. At higher energies, however, the electron can probe finer structure within the nucleon by undergoing an elastic collision with a constituent quark within the nucleon. At still higher energies, the quark/anti-quark pairs generated by gluons emitted by the quarks can be detected (gluons themselves are uncharged and so do not interact with the electric field of the electron). Such collision experiments give insight into the nucleon form factors - mathematical expressions that modify the collision equations to account for the nucleon no longer behaving like a point particle.

The electric form factor describes the distribution of electric charge within the nucleon, the magnetic form factor describes the distribution of the nucleon's internal magnetic field (these two are not identical but they are connected as we would expect through electromagnetism, the unification of electric and magnetic forces). On the other hand, the gravitational form factor describes the distribution of mass within the nucleon and reveals a super-dense core (within about 0.6 fm) whose matter is about ten times as dense as the matter making up the outer layers of a neutron star. A teaspoonful of neutron star matter may weigh as much as 10 billion tonnes and yet the core of a proton is ten times more dense! This realization may help in understanding the core of neutron stars and perhaps denser 'quark stars' (if this 

Feynman diagram for electron-proton scattering

Above: electron-proton elastic scattering

Feynman diagram for electron-quark scattering

Above: electron-quark elastic scattering


Nucleons exchanging pion

Article updated: 21 Aug 2020