by Frank Close
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We have described how the discovery a century ago of atomic structure and of the proton came about as a result of scattering beams of high-energy particles from them. However, in both the case of atoms and protons, the first hints that they had a substructure came earlier, from the discovery of spectra.
The first clue to the existence of electrons within atoms was the discovery that atomic elements emit light with discrete wavelengths manifested, for example, as discrete colours rather than the full spread of the rainbow, so-called spectral lines. We now know that quantum mechanics restricts the states of motion of electrons within atoms to a discrete set, each member of which has a specific magnitude of energy. The configuration where an atom has the lowest total energy is known as the ‘ground state’; all other configurations have larger energies and are known as excited states. Atomic spectra are due to light radiated or absorbed when their electrons jump between excited states, or between an excited state and the ground state. Energy is conserved overall; the difference in energy of the two atomic states is equal to the energy of the photon that has been emitted or absorbed in the process. It was the spectra of these photons that revealed the differences in these energy levels of the atom, and from the rich set of such data a picture of the energy levels could be deduced. Subsequently the development of quantum mechanics explained how the pattern of energy levels emerges: it is determined by the nature of the electric and magnetic forces binding the electrons around the central nucleus – in particular for the simplest atom, hydrogen, being intimately linked to the fact that the strength of the electrical force between its electron and proton falls as the square of the distance between them.
An analogous set of circumstances occurred in the case of the proton. When experiments with the first ‘atom smashers’ took place in the 1950s to 1960s, many short-lived heavier siblings of the proton and neutron, known as ‘resonances’, were discovered. A panoply of states emerged and with hindsight it is obvious, though it was not so at the time, that here was evidence that the proton and neutron are composite systems made, as we now know, from quarks. It is the motion of these quarks that gives size to the proton and neutron, analogous to the way that the motion of electrons determines the size of atoms. It is the quarks that provide the electric charge and the magnetic properties of a proton or neutron. Although the electric charges of the quarks that form a neutron add up to zero, their individual magnetism does not cancel out, which leads to the magnetic moment of the neutron. It is when the quarks are in the state of lowest energy that the configurations that we call proton and neutron arise; excite one or more quarks to a higher energy level in the potential that binds them and one forms a short-lived resonance with a correspondingly larger rest-energy, or mass. Thus the spectroscopy of short-lived resonance states is due to the excitation of the constituent quarks.
This far is akin to the case of atoms. However, there are some important differences. When more and more energy is given to the electrons in an atom, they are raised to ever higher energy levels, until eventually they are ejected from the atom; in this type of scenario we say that the atom is ‘ionized’. In Chapter 2 we saw how a temperature of 104K provides enough energy to ionize atoms, as happens in the Sun. In the case of the proton, as it is hit with ever higher energies, its quarks are elevated to higher levels, and short-lived resonances are seen. This energy is rapidly released, by emitting photons or, as we shall see, other particles, and the resonance state decays back to the proton or neutron once more. No-one has ever ionized a proton and liberated one of its constituent quarks in isolation: the quarks appear to be permanently confined within a region of about 10–15 m – the ‘size’ of the proton. Apart from this, which is a consequence of the nature of the forces between the quarks, the story is qualitatively similar to that of electrons within atoms. The excited levels are short lived, and release excess energy, typically by radiating energy in the form of gamma-ray photons, and fall back to the ground state (proton or neutron). Conversely one can excite these resonance states by scattering electrons from protons and neutrons.
The final piece to the analogy came around 1970. Beams of electrons, which had been accelerated to energies of over 20 GeV, were scattered from protons at Stanford in California. Similar to what had occurred for Rutherford half a century earlier, the electrons were observed to scatter through large angles. This was a direct consequence of the electrons colliding with quarks, the pointlike fundamental particles that comprise the proton.
In the subsequent 30 years these experiments have been extended to higher energies, most recently at the HERA accelerator in Hamburg, Germany. The resulting high-resolution images of the proton have given fundamental insights into the nature of the forces binding the quarks to one another. This has given rise to the theory of quarks known as quantum chromodynamics, of which we shall learn more in Chapter 7. Its ability to describe the interactions of quarks and gluons at distance scales below 10–16 m has passed every experimental test.
Quarks with flavour
Three quarks clustered together are sufficient to make a proton or a neutron. There are two different varieties (or ‘flavours’) of quark needed to make a proton and neutron, known as the up and down (traditionally summarized by their first letters, u and d respectively). Two ups and one down make a proton; two downs and one up make a neutron.
7. Properties of up and down quarks.
The quarks are electrically charged. An up quark carries a fraction 2/3 of the (positive) charge of a proton, while a down quark carries a fraction –1/3 (that is, negative). Thus as the total electric charge of a collection is the sum of the individual pieces, we have for the charge of a proton p(uud) = 2/3 + 2/3 – 1/3 = +1, and of a neutron n(ddu) = –1/3 – 1/3 + 2/3 = 0.
Particles have an intrinsic angular momentum, or ‘spin’. The amount of spin is measured in units of Planck’s quantum, h divided by 2π; as this combination occurs throughout atomic and particle physics it is denoted by the symbol . The proton, neutron, and the quarks each have an amount /2, or in the usual shorthand, ‘spin 1/2’.
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One quark can point its spin axis up or down q ↑ or q ↓
Two quarks with net spin 1 ↑↑ or 0↑↓
Three quarks with net spin 3/2 ↑↑↑ or 1/2 ↑↓↑
Examples
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8. Quark spins and how they combine
Spins add or subtract so long as the total is not negative. So combining two particles each having spin 1/2 gives either 0 or 1. Adding three together gives a total of either 1/2 or 3/2. The proton and neutron have spin 1/2 resulting from the three quarks having coupled their individual spins to the former possibility. When the quarks combine to a total of 3/2, they have slightly greater total energy, and this forms the short-lived particles known as the ‘Δ resonances’, which have some 30% more mass than do the proton or neutron, and they survive less than 10–23 s before decaying back to the more stable neutron or proton. (10–23 s is a time too short to imagine, but roughly is similar to the time that it takes light to travel across a single atomic nucleus.) Rules of quantum theory (the ‘Pauli exclusion principle’) allow only certain correlations to occur among the spins and flavours of the quarks, and it is this that ultimately forbids three ‘identical’ up quarks (or three down) to combine into a net spin 1/2; thus there are no siblings of the proton and neutron with charge +2 or –1 made respectively of uuu and ddd. By contrast, when the three quarks have coupled their spins to a total of 3/2, three identical ‘flavours’ of quark are allowed to cluster together. Thus there exist examples such as the Δ++(uuu) and Δ–(ddd) (with superscripts denoting their electric charges). The full details of how these correlations emerge involve properties of the quarks that govern the strong interquark forces (see Chapter 7), but go beyond the scope of this short introduction.
The individual quarks have masses that are about ten times larger than that of an electron. As a proton or neutron have similar masses to one
another, and nearly 2,000 times greater than that of an electron, there are two questions to face. One is: how do the proton and neutron get such large masses; the other is: are the masses of these quarks perhaps to be regarded as similar to that of the electron, hinting at some deeper unity among the fundamental constituents of matter?
Quarks grip one another so tightly that they are forever imprisoned in groups, such as the threesome that forms the entity that we call the proton. No quark has ever been isolated from such a family; their universe extends only for the 10–15 m that is the extent of the proton’s size and it is this confinement within the 10–15 m ‘femtouniverse’ that we call the proton that gives them collectively an energy of ~ 938 MeV, which is the mass of the proton. We saw how length and energy are related, and that distances of the order of 10–15 m correspond to an energy of around 1 GeV. The precise correspondence of relevance here involves factors of 2 and π which go beyond this Very Short Introduction, with the result that an up or down quark, which were it free would have a mass of only a few MeV, when restricted to a femtouniverse of 10–15 m has an energy of some 200–300 MeV. The quarks are interacting strongly with one another (which must be so as they do not escape!) and the full details of how the mass of the proton turns out to be precisely 938.4 MeV is beyond our ability to derive from theory at present.
The down quark is a few MeV more massive than the up quark. We don’t know why this is (indeed, we don’t know why these fundamental particles, along with the electron, have the masses they do), but this does explain why the neutron is slightly more massive than the proton. A trio as in uud (proton) and ddu (neutron) each have mass of around 1 GeV due to their common entrapment in a 10–15 m region. There will be differences at the order of an MeV as a result of two features: (i) the neutron has an extra down quark at the expense of an up quark relative to the proton, and the greater mass of this down quark gives the total in forming the neutron a greater mass than the corresponding trio for a proton; (ii) the electrostatic forces among two ups and a down (as in a proton) will differ from those between two downs and an up (as in a neutron). These also contribute to the total energy at the MeV scale. So the mass difference between a neutron and proton (experimentally 1.3 MeV) is due to the electrostatic forces between their constituent quarks and the greater intrinsic mass of a down quark relative to the up quark.
Up and down are siblings in the quark family. The electron is not made of quarks, and as far as we know is itself fundamental, like the quarks. As such it belongs to a different family, known as leptons. As up and down quarks are paired, with a difference of one unit between their respective electric charges (in the sense that +2/3 – (–1/3) = 1), so does the electron have a sibling whose electric charge differs from the electron’s by one unit. This entity, with no electric charge, is known as the neutrino.
Neutrinos are produced in radioactive decays of many atomic nuclei. In these processes they appear along with their sibling, the electron. For example, so long as it is not trapped in a nucleus, a neutron turns into a proton by emitting an electron and neutrino in the process. This is called beta decay, where the instability of the neutron is due to it having a slightly greater mass than does a proton. Nature seeks the state of lowest energy, which translates in this case to the state of lowest mass. It is the small excess mass of a neutron that makes it (slightly) unstable when left in isolation. If you had a large sample of neutrons, each of them free of the others, then after about ten minutes, half will have decayed by beta radioactivity. If we denote the neutron and proton by the symbols n, p, and the electron and neutrino by e–, ν, then beta decay of the neutron is summarized by the expression
n → p + e– + ν
9. Beta decay of neutron.
The neutron has no electrical charge overall; this is preserved in the beta decay as the proton has one unit positive, counterbalancing the negative electron. The proton, being the lightest state made of three quarks, is stable (or, at least, if protons are unstable, their mean lifetime is greater than 1032 years!)
The neutrino
Along with no electric charge, the neutrino has almost no mass and goes through almost everything. Oblivious to the normal electrical forces that act within bulk matter, neutrinos are hard to detect. It is figuratively the most nugatory of the particles.
The neutrino is the first ‘fossil’ relic of the Big Bang, and a messenger from the earliest processes in the universe. Neutrinos determine how fast the universe is expanding, and may determine its ultimate destiny. In stars like the Sun, they are essential in helping to cook the heavy elements that are necessary for life. The Sun is powered by the fusion of protons near its centre bumping into one another, joining and building up the nuclei of helium. In doing so some protons turn into neutrons by a form of beta radioactivity, and neutrinos are emitted as this happens. The effect is enormous: neutrinos are produced in the Sun at a rate of 2 × 1038 each second. That’s two followed by 38 zeroes; I cannot even imagine how to give an idea of how huge that number is – it’s like the relative size of the whole universe to the size of a single atom. These neutrinos fly out into space and many hit Earth. About 400 billion neutrinos from the Sun pass through each one of us each second.
Natural radioactivity of the elements in the ground, such as uranium, also liberate neutrinos: about 50 billion of them hit us each second. So the Sun is indeed putting out a lot: eight times as many arrive from the Sun each second after spreading out over 100 million km of space than come from beneath our feet here at home. And we ourselves are radioactive (mainly from the decays of potassium in our bones) and emit some 400 neutrinos a second.
All in all, neutrinos are the commonest particles of all. There are even more of them flying around the cosmos than there are photons, the basic particles of light.
As they are so common, their mass could affect the gravity of the universe. If they have any mass, it is so small that to date no-one has managed to measure it, but there are emerging hints that they might manage this (described in Chapter 10).
Neutrinos from the Sun fly through matter almost unchecked, so as many fly up through our beds at night as shine down on our heads by day. One of these neutrinos could fly through a light year of lead without hitting anything. This property of the neutrino is frequently mentioned in popular articles, and begs an obvious question: how do we detect them? Two things come to our aid.
The first is to use very intense sources of neutrinos so that the lottery of chance means that one or two will bump into atoms in some detector and be recorded. Although a single neutrino might only interact once in a blue moon (or a light year), the Sun is putting out so many that chance comes to our aid. You or I have almost no chance of winning the lottery, but enough people enter that someone does. With enough neutrinos shining down on us, a few will hit atoms en route. So with a big enough tank of material – maybe water, or iron, or even cleaning fluid (the chlorine is particularly useful in detecting neutrinos) – it has been possible to detect occasional neutrinos coming from the Sun. A new science, called neutrino astronomy, is now beginning. This has already revealed that fewer neutrinos arrive from the Sun than our understanding of the Sun would have led us to expect. It isn’t the Sun that is the problem, however; it seems that something is happening to the neutrinos en route, as Chapter 10 will describe.
The second property that comes to our aid is that their ‘shyness’ is only true for neutrinos with low energies, such as those emitted by the Sun. By contrast, neutrinos with high energy (as produced in some cosmic processes or in high-energy particle accelerators) have much greater propensity to reveal themselves. So it is in high-energy accelerators that we have produced neutrinos and studied them in detail. And it is here that we are getting our first hints that neutrinos do have a small, but non-zero, mass. This could make us rethink some of our ideas about cosmology.
Antiparticles
The quarks and the electron are the basic seeds of atoms, and of matter as we know it. But they are not the
full story; they also occur in a sort of mirror image form, known as antiparticles, the seeds of antimatter. Every variety of particle has as its ‘anti’ version: an entity with the same mass, spin, size, and amount of electric charge as itself, but with the sign of that charge reversed. So, for example, the negatively charged electron has as its anti-electron a positively charged entity, which is known as the positron, not to be confused with the proton. A proton is nearly 2,000 times more massive than a positron, and has its own anti-version, the antiproton, which has negative charge. The forces that enable an electron and proton to combine to form an atom of hydrogen also enable a positron and antiproton to form an atom of antihydrogen.
We can summarize the charges of the basic particles and antiparticles that we have met so far in the table in Figure 10.
10. Fundamental particles of matter and their antiparticles.
As a proton is made of uud, so is the antiproton made of the corresponding antiquarks, . It is traditional to denote an antiparticle by the symbol of the corresponding particle but with a line over the top. This is so unless the charge is specified, in which case the antiparticle is of the opposite charge (for example the positron, which is uniformly denoted e+ for historical reasons). Similarly for the neutron ddu, the antineutron is made of . So although a neutron and antineutron have the same electrical charge, their inner structure distinguishes them. A neutrino and antineutrino also have the same charge, but their distinguishing property is more subtle. When neutrinos interact with a particle of matter, a neutron say, they will turn into electrons and the neutron is converted into a proton, thereby preserving over all the electric charge: