Structure of the Nucleon: Pions and Quarks
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 centre 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:
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.
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.
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.
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.
The following summarises 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 colour are indistinguishable except by their colour charge.

                         Quark          Electric charge        Mass (MeV/c^2)

                            u                       2/3                        1.5-4
                            d                      -1/3                        4-8

                            c                        2/3                       1150 – 1350
                            s                       -1/3                       80-130

                            t                        2/3                       169100-172700
                            b                      -1/3                        4100-4400

Note the range in mass values due to uncertainties. Also note that mass is given in units of MeV/c^ (mega
electronvolts divided by the speed of light squared). 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/c^2 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/c^2 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 = mc^2 (energy equals mass times the speed of light squared) and tells us that energy
divided by the speed of light squared (c^2) is equivalent to mass, hence the units MeV/c^2.

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/c^2)

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, and we shall mention these some other time.

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/c^2)

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) due to switch on this year at CERN, is 27 kilometres in
circumference. 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 = mc^2). 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.
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.
Nucleons
Nucleon charge distributions
Nucleon core
Pion exchange
Pion exchange
Pion exchange
Pion exchange
Nucleons exchanging pion
See also:

  1. QED, fundamental forces and Feynman
    diagrams.
  2. The atomic nucleus.
  3. QCD.
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