The neutron

There’s a nice potted history of the discovery of the neutron on the Nobel website. It mentions the great Ernie Rutherford who discovered the proton in 1917. He knew all about Prout’s hypothesis wherein the atomic weights of various elements were integer multiples of the atomic weight of hydrogen. However Rutherford also knew that the atomic number, the number of protons, was circa half the atomic weight. So in 1920 he suggested that this disparity was due to neutral particles called neutrons. The evidence of beta decay suggested that there were electrons within the nucleus, so Rutherford thought of the neutron as a close-coupled or paired proton-electron combination.

Problems with the nuclear-electron idea

However Werner Heisenberg said it would take 100MeV to confine an electron within a nucleus, Oskar Klein said it would tunnel out anyway, and Wolfgang Pauli said the nitrogen-14 exchange-theorem spin statistics were false. Nitrogen-14 was an integer-spin atom so it couldn’t be made up of fourteen spin ½ protons and seven spin ½ electrons. So the neutron couldn’t be made up of a proton plus an electron. The sentiment was that there couldn’t be any electrons inside the nucleus, and that electrons were created during beta decay, like photons are created when an electron drops down an orbital. That sounds fair enough when you think about the wave nature of matter. We can diffract neutrons. Diffraction occurs “when waves encounter obstacles whose size is comparable with the wavelength”. The electron Compton wavelength is 2.426 x 10⁻12 m, whilst the neutron Compton wavelength is 1.321 x 10⁻¹⁵ m. Like Martin van der Mark said in on the nature of stuff, you can’t fit a longer-wavelength particle inside a shorter-wavelength particle. That’s why there’s an issue when you try to fit a 2.3MeV quark inside a 938MeV neutron:

CCASA neutron image by Arpad Horvath, see Wikipedia

But wait a minute. the Copenhagen crew said electrons can’t fit inside neutrons, but we’re told that quarks can? Whilst attempts to model the nuclear force ended in disaster? Surely it’s time we got back to the drawing board. As Bert Schroer said: “perhaps the past, if looked upon with care and hindsight, may teach us where we possibly took a wrong turn”.

True Grit

James Chadwick had been Rutherford’s student in Manchester in 1911. In 1914 he was in Berlin using Hans Geiger’s counter to demonstrate that beta radiation had a continuous spectrum. He was only 23 at the time, and the price of his discovery was high. He spent the next four years in an internment camp where he doggedly conducted experiments with radioactive toothpaste. However the war ended, and in 1919 he followed Rutherford to the Cavendish lab in Cambridge. He became Rutherford’s protégé. He and Rutherford “often discussed neutrons, and suggested ‘silly‘ experiments to discover them”. He tried repeatedly to no avail, and the neutron was scathingly labelled the fewtron. The eventual breakthrough came more than a decade later. In 1931 Herbert Becker and Walter Bothe in Geissen fired alpha particles at beryllium to produce a very strong radiation. This radiation of beryllium was extremely penetrating: “the rays could pierce a brass plate, several centimeters thick, without any noteworthy loss of velocity. When hitting nuclei of atoms, this new radiation caused a disintegration of them, similar to an explosion”. In 1932 Irène and Frédéric Joliot-Curie in Paris demonstrated that when this radiation met paraffin it ejected high-energy protons. They thought they were dealing with 50 MeV gamma radiation, also known as quantum radiation – the word photon wasn’t so common then. Chadwick however suspected heavy neutral particles were involved, and conducted a crucial series of experiments over an intense three-week period. See his brief 1932 Nature paper possible existence of a neutron where he said this: “these results, and others I have obtained in the course of the work, are very difficult to explain on the assumption that the radiation from beryllium is a quantum radiation, if energy and momentum are to be conserved in the collisions. The difficulties disappear, however, if it be assumed that the radiation consists of particles of mass 1 and charge 0, or neutrons”.

The neutron has charge

Chadwick’s 1933 Royal Society Bakerian lecture gives further information. On page 1 he talked about neutrons moving at 3 x 109 cm/s, a tenth the speed of light. On page 12 he talked about neutrinos, though he didn’t use that name. On page 13 he said he obtained a value for the mass of the neutron of 1.0067. On page 14 he said As I shall show later, some suggestion that either the neutron or the proton may be complex can be deduced from the collisions of neutrons with protons”. On page 18 he talked of a collision radius of 4 to 5 x 10-13 cm. What a detective, he even looked like a passable Sherlock Holmes:

James Chadwick image from BBC News

What really caught my eye however was this on page 2: “the collision of a neutron with an atomic nucleus, although much more frequent than with an electron, is also a rare event, for the electric field between a neutron and a nucleus is small except at distances of the order of 10-12 cm”. That’s 10-15 m. The neutron Compton wavelength is 1.319 x 10⁻¹⁵ m. Chadwick was saying that whilst the neutron is neutral, when you get up close and personal, it isn’t. The neutron has zero net charge, but it has both positive charge and negative charge, which is why it has a magnetic moment. This was determined by Otto Stern and others including Isidor Rabi in 1934. So much knowledge was already in place in 1935 when Chadwick received his Nobel prize. So so much.

Early days

Chadwick gave some interesting history in his 1935 Nobel lecture: “the first suggestion of a neutral particle with the properties of the neutron, we now know, was made by Rutherford in 1920. He thought that a proton and an electron might unite in a much more intimate way than they do in the hydrogen atom, and so form a particle of no nett charge and with a mass nearly the same as that of the hydrogen atom. Chadwick said Rutherford’s view was that such a particle was “the first step in the formation of atomic nuclei from the two elementary units in the structure of matter – the proton and the electron”. He also said that with this first step “it would be much easier to picture how heavy complex nuclei can be gradually built up from the simpler ones”. Quite, especially if you know about the alpha particle. Chadwick quotes Rutherford thus: “Under some conditions, however, it may be possible for an electron to combine much more closely with the H nucleus, forming a kind of neutral doublet. Such an atom would have very novel properties. Its external field would be practically zero, except very close to the nucleus, and in consequence it should be able to move freely through matter”. I rather think Rutherford was so far ahead of the curve that some other physicists somehow lost sight of what he was saying, and what the evidence was saying.

Heady days

Chadwick also talked about the alpha particle, saying this: “by a suitable choice of the exchange forces it is possible to obtain a saturation effect, analogous to the saturation of valency bindings between two atoms, when each neutron is bound to two protons and each proton to two neutrons”. He talked of slow neutrons, saying “the calculations of Bethe show that the chance of capture of a neutron may be inversely proportional to its velocity”. He finished up offering great promise: “These ideas thus explain the general features of the structure of atomic nuclei and it can be confidently expected that further work on these lines may reveal the elementary laws which govern the structure of matter”. Physics was making great strides, it was explaining the atom, it was explaining the periodic table. And underlying everything else was the alchemist’s dream. Transmutation. Lead into gold. Those were heady days for particle physics, for physics, for science. The Joliot-Curies missed out on the neutron, and on the positron, but they were awarded the chemistry Nobel prize in 1935. That was “in recognition of their synthesis of new radioactive elements”. Heady days indeed, for science and for the world. Did physics live up to that promise? Sir James Chadwick did. He was the grandfather of the atomic bomb. In 1941 he was on the MAUD committee. In 1944 he was at Los Alamos. He was knighted in 1945. The neutron delivered too. Sadly, it delivered death and destruction in 1945, but it also delivered peace. By 1954 we had nuclear submarines, but we also had nuclear power stations. That was a mere 22 years after Chadwick discovered the neutron.

What happened?

But now it’s 2018. It’s 64 years since the Nautilus and Calder Hall, and contemporary physics doesn’t explain the neutron and it doesn’t explain the nuclear force. What happened? Did physicists persuade themselves that it was a good idea to replace a real wave rotation with abstract mathematical symbolism? Was it because with the mistaken belief that spin is conserved in beta decay, they thought it was a good idea to introduce an abstract isospin that isn’t conserved in beta decay? Was it some kind of disregard for evidence? See the Wikipedia neutron magnetic moment article: “the existence of the neutron’s magnetic moment was puzzling”. Why? Because Pauli gave up on spin? The article goes on to say the neutron magnetic moment “defied a correct explanation until the quark model for particles was developed in the 1960s. But the article also says “the calculation assumes that the quarks behave like pointlike Dirac particles. Pointlike? Contemporary physics “explains” the neutron magnetic moment in terms of pointlike particles that are not explained, and have never been seen? How can the neutron be made up of point particles? It can’t be. It’s the wave nature of matter, not the point-particle nature of matter. It’s the Dirac wave equation, not the Dirac point-particle equation. Annihilate a neutron with an antineutron and you see pions, not pointlike quarks. Those pions are said to consist of quarks and antiquarks, but they don’t even last a microsecond. Circa 26 nanoseconds later you’re left with photons, electrons, and neutrinos, and contemporary physics doesn’t explain any of them. Surely we can do better than that?

Neutron properties

Yes we can do better than that, because we can explain photons, electrons, and neutrinos. And protons. And because we can use the clues from classical electromagnetism and elsewhere to come up with a description of the neutron that makes sense. For starters, the neutron magnetic moment says it has a Poynting vector, and that something is going around and around. See Hans Ohanian’s 1984 paper what is spin? He said this: “the means for filling the gap have been at hand since 1939, when Belinfante established that the spin could be regarded as due to a circulating flow of energy”. The neutron has spin, and spin is real, as evidenced by the Einstein-de Haas effect. The magnetic moment and the g-factor tells us something about it, particularly when we compare with the electron and the proton. The electron magnetic moment is −9284.764 × 10−27 J⋅T−1. The proton magnetic moment is a mere 14.10606 × 10−27 J⋅T−1. That tells us the spin is going the other way around a much smaller radius. Moreover the proton-electron mass ratio is 1836 but the electron-proton magnetic moment ratio is 658, suggesting circa three times as much major-axis rotation in the proton. The electron g-factor of -2.002 suggests a Mobius-style spin ½ rotation of 720°, twice around a twisted loop. The proton g factor of 5.585 suggests a more complex spin ½ rotation of 720°, twice around a near three-loop or trefoil path. The neutron magnetic moment is −9.662364 × 10−27 J⋅T−1, the neutron-electron mass ratio is 1838, and the electron-neutron magnetic moment ratio is 960, suggesting circa twice as much major-axis rotation in the neutron. Hence the neutron g-factor is -3.826 which is nearly twice that of the electron. That would seem to suggest the neutron has a two-loop character as opposed to the one-loop electron and the three-loop proton.

The figure-of-eight knot?

However the neutron can’t be some figure-of-8 thing because it undergoes beta decay to a proton, an electron, and an antineutrino. That magnetic moment has to be net, like the charge is net. It’s like a net rotation, like three minus one equals two. So what else can the neutron be? There is such a thing as the figure-of-eight knot. It’s the next knot in the knot table after the trefoil. It can be depicted like this:

Public domain image by AnonMoos, see Wikipedia

The figure-of-eight knot has a four-loop appearance, akin to a three-loop proton plus a one-loop electron. If you could pull the two larger loops outwards you’d reduce the size of the inner loops. You would have produced something that looked like it was comprised of the two major loops and not much else. This fits with what Chadwick said about one neutron binding with two protons. But he also made it clear that the neutron has charge at close quarters even though it has zero net charge. That would mean the major loops have a negative charge, whilst the interior loops have a positive charge. From what we know about the electron and positron, for this to occur the direction of the associated twist or writhe would have to change from clockwise to anticlockwise. But then surely the clockwise twist would cancel the anticlockwise twist, leaving no twist? Then we wouldn’t have a spin ½ particle. That sounds like an issue. A related issue is that the figure-of-eight knot is said to be achiral, but there is such a thing as the antineutron. The antineutron has the opposite chirality to the neutron. So the figure-of-eight knot doesn’t fit the bill.

The two-loop pion?

Is there anything else that fits the bill? Such as a pion? If a proton is comprised of three quarks and has a three-loop disposition, then surely the two-quark pion has a two-loop disposition? A figure-of-8 disposition? That sounds promising. After all Chadwick said this in his Nobel lecture: “it is assumed, with Heisenberg and Majorana, that the interaction between neutron and proton is of the exchange type – similar to that between the hydrogen atom and the hydrogen ion”. And you can read that the neutron can emit a negative pion to become a proton. John Baez and John Huerta write about this in The Algebra of Grand Unified Theories. They say that in 1932 Heisenberg proposed that the proton and the neutron were two states of the same particle. They say that in 1936 Cassen and Condon employed an analogy between “isospin” and electron spin such that the proton was an isospin-up nucleon and the neutron was an isospin-down nucleon. They say that there must be a mechanism which can convert protons into neutrons and vice versa. They say that any physical process caused by this force should be described by an intertwining operator. It’s all interesting stuff, particularly since you can “intertwine” a trefoil and an 8 to come up with something that looks promising:

Based on a GNUFDL trefoil image by Ylebru

Baez and Huerta also say that “the answer originates in the work of Hideki Yukawa. In the early 1930s, he predicted the existence of a particle that mediates the strong force, much as the photon mediates the electromagnetic force”. The pion was subsequently discovered in 1947 and Yukawa was awarded the 1949 Nobel prize. Yes, the pion sounds promising, particularly since there’s such a thing as pion beta decay. That’s where a negative pion decays into a neutral pion which decays instantly into gamma photons, plus an electron and an antineutrino.

Pion exchange

However there are too many issues to claim that the neutron is some proton+pion combination. Ordinary beta decay results in a proton, an electron, and an antineutrino. Now and then there’s some internal bremsstrahlung which creates a photon, but pions are never produced. Moreover the pion is said to be spinless and described by the Klein–Gordon equation, but π+ and πare charged particles. That doesn’t square with what we know about spin ½ standing waves and charge. The pion is also said to be composite and so not a Yukawa particle. Then there’s a problem with parity, in that pions have a parity of -1, and protons and neutrons both have a parity of +1. On top of that the neutron isn’t 140 MeV heavier than the proton, and the Yukawa interaction is an attractive force whilst the nuclear force is both attractive and repulsive. And for the cherry on top, despite what you can read on some authoritative-looking websites, pion exchange is nothing like ping pong. Pion exchange is likened to the electromagnetic interaction, but hydrogen atoms don’t twinkle and magnets don’t shine. That’s because the virtual photons that are said to mediate the electromagnetic interaction are virtual photons. They only exist in the mathematics of the modelThere are no actual photons flying back and forth between the proton and the electron.

Exchange force

Besides, Chadwick said the exchange force was ”similar to that between the hydrogen atom and the hydrogen ion”. That’s where one electron is shared between two protons. The electron sticks two protons together, but it isn’t being batted back and forth. Matt Strassler said something similar in his blog post neutron stability in atomic nuclei. He said the forces between a proton and a neutron are “similar to the way the electromagnetic force can bind two hydrogen atoms into a hydrogen molecule”. Remember that a neutron can be created via electron capture, where a nucleus absorbs an inner electron. A neutrino is emitted to balance the book of spin. Then this thing that’s been created from a proton and an electron can stick two other protons together. Rather than the exchange force being something that involves messenger particles pinging back and forth, it’s more of a sharing. Two protons are both attracted to an electron. They share it. Two protons are both attracted to a neutron. They share it. Now why might that be?

Neutron charge distribution

The neutron electric dipole moment is evidence of sorts. It’s the dog that didn’t bark in the night sort, because there is no detectable neutron electric dipole moment. The neutron electric dipole moment “can only exist if the centers of the negative and positive charge distribution inside the particle do not coincide”. The magnetic moment means there’s charge in the neutron, but there’s no net charge. So there’s both positive and negative charge in a neutron, and the centers coincide. That’s interesting. As is the structure and geometry of charge distribution section of the Wikipedia neutron article. It says this: “an article published in 2007 featuring a model-independent analysis concluded that the neutron has a negatively charged exterior, a positively charged middle, and a negative core”. It refers to charge densities of the neutron and proton by Gerald Miller, which was published in Physics Review Letters in 2007. There’s an arXiv version too. It says “the results for the neutron contradict the longstanding notion, derived from both gluon-exchange and meson-cloud models [6, 7], that the non-vanishing charge density at the center of the neutron is positive”. That’s because the charge in the center is negative. It’s negative on the outside too. See the 2008 physics focus article journey to the center of the neutron by Don Monroe. It says this: “For decades, such experiments have implied that the neutron is a negatively-charged cloud surrounding a positive central region. But Miller’s re-analysis showed that a negative charge also exists at the core of the neutron, inside the positive region”. So the neutron has a negative exterior. That’s going to stick protons together, surely? And let’s see now. We started with a proton, which doesn’t have a negative-charge centre. Then we perform electron capture and end up with a neutron, which does. And spin is real. Oh what a tangled web we weave. You can trace it all the way back to the 1930s.

The neutron is more like the hydrogen atom than it’s like the proton

It may have been convenient for Heisenberg treat the proton and the neutron as different states of the same particle, but it’s also wrong. The proton and the neutron have a different mass and charge and magnetic moment. They are not different states of the same particle, just as the proton is not a different state of the hydrogen atom. However the difference between a neutron and a proton is one electron and one antineutrino, whilst the difference between a neutron and a hydrogen atom is one antineutrino. So the neutron is more like the hydrogen atom than it’s like the proton. But it was perceived as a different state of the proton rather than a different state of the hydrogen atom. Despite the intertwining operator, which was proposed by Casson and Condon in 1936. Despite the dihydrogen cation, which was the subject of Pauli’s thesis in 1921. Despite electron capture.

Electron capture

Electron capture is “a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, usually from the K or L electron shell. This process thereby changes a nuclear proton to a neutron and simultaneously causes the emission of an electron neutrino”. It was proposed by Gian-Carlo Wick in 1934 and first observed by Luis Alvarez in 1937. Alvarez was a bit of a scientific detective. So, get your thinking cap on, and ask yourself this: how does electron capture actually work? It’s one of those naïve questions for which there’s no satisfactory answer in the literature. You can find answers that say it’s because of the weak interaction. You can find answers that say the electron is converted into a neutrino. But they don’t explain what’s going on at all. In similar vein there’s no satisfactory answer for the creation of a neutron via positron emission. That occurs when the decay energy is at least 1.022 keV, which suggests that an internal pair production occurs to supply an electron which is then captured. So we’re back to the $64,000 question: how does electron capture actually work? Let’s see now. We start with an electron with a magnetic moment of −9284.764 × 10−27 J⋅T−1, and a proton with a magnetic moment of 14.10606 × 10−27 J⋅T−1. We perform electron capture, we emit a neutrino, and we’re left with a neutron with a magnetic moment of −9.662364 × 10−27 J⋅T−1. So what happened? I think there’s a vital clue the Wikipedia neutron article. In fact I think this sentence is gold dust: “This can be reconciled classically with a neutral neutron composed of a charge distribution in which the negative sub-parts of the neutron have a larger average radius of distribution, and therefore contribute more to the particle’s magnetic dipole moment, than do the positive parts that are, on average, nearer the core”. I think that makes gives enough of a clue as to what happens in electron capture:

Based on a GNUFDL trefoil image by Ylebru and S-orbital © Encyclopaedia Britannica

Electron capture does what it says on the tin. The electron is captured. It’s pulled into the proton, like an unfortunate worker in an industrial accident is pulled into a set of rollers. It’s drawn into the region of extreme curvature, reducing the magnetic moment and the angular momentum. Its effective diameter reduces a thousandfold, but the circulating energy can’t go round and round any faster, so the neutrino is emitted to conserve angular momentum. The electron is effectively winched into the proton. It is mangled into the proton. It “intertwines” with it, and the result is a neutron. There’s negative charge and there’s positive charge, and there’s two energy flows. One goes around and around one way. The other goes around and around the other way:

Based on a GNUFDL trefoil image by Ylebru

When the neutron is in a nucleus, an adjacent proton usually keeps the electron captured. It sounds like tension on the rollers, like pulling on a rope to stop a slip-knot slipping. Chadwick was right, the neutron is complex. Rutherford was right too, because the neutron is like a close-coupled hydrogen atom. Not quite the same, but not totally different. Because what we call β or beta-minus decay today used to be called plain old beta decay. And because in that beta decay, the beta particle is always an electron.

Beta decay

Beta decay is the jumping popper of particle physics. In a way it’s the opposite of electron capture. In electron capture the electron is captured by a proton in a proton-rich nucleus, as if they’re going to annihilate but can’t. The result is what we call a neutron. The electron usually stays captured in a proton-rich nucleus. But relocate the neutron into a neutron-rich nucleus, or kick it out of a nucleus altogether, and the surfeit of protons that caused the electron capture are no longer present. The electron is no longer constrained. It eventually works loose and resumes its original larger configuration, with the antineutrino being emitted to again conserve angular momentum. This release is perhaps something like the sudden release of a wound-up spiral mainspring. If you’ve ever toyed with clockwork you will have had a mainspring leap out of its housing and shoot across the room. I think beta decay is something similar. Kick a neutron out of a typical nucleus where it’s no longer tensioned by protons, and in about 15 minutes that neutron has decayed into a proton, an electron, and an antineutrino: n → p + e– + v̄e. The decay energy is 0.782MeV, the electron might have 0.2 MeV of kinetic energy and might be emitted at a relativistic speed of perhaps 0.7c. That electron doesn’t just fall out, it shoots out, in a direction that’s opposite to the spin alignment. The angular momentum conservation of beta decay is the time-reverse of that in electron capture, so the antineutrino truly is the antiparticle of the neutrino. So the standard model was right about something: all neutrinos are left-handed, and all antineutrinos are right-handed.

Excuse me Mr President

However the standard model says there’s a separation of positive and negative charge within the neutron because it’s made up of two down quarks with a charge of -⅓ and an up quark with a charge of +⅔. But there is no detectable electric dipole moment, and no detectable quarks either. And the standard model, as per the Wikipedia neutron article, says the main attraction between neutrons and protons is via the nuclear force, which does not involve charge. I am reminded of Independence Day. Uh, excuse me, Mr President? That’s not entirely accurate. Because we created that neutron via electron capture, and in ordinary hadrons the gluons are virtual. They only exist in the mathematics of the modelThe neutron magnetic moment does not, nor does nuclear magnetic resonance, and nor do atomic nuclei.

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