Category: Particle Physics

Exploring the Subatomic World : Electrons and Nuclei

Exploring the Subatomic World : Electrons and Nuclei

Reading Time: 6 minutes

Atoms were once thought to be indivisible and fundamental. Nineteenth century chemistry was based around atoms, culminating in Dmitry Mendeleev’s extraordinary Periodic Table. The discovery of the electron in 1897 led to a subatomic revolution, and the twentieth century has revealed the rich internal structure of the atom, culminating in the Standard Model, the subatomic counterpart of Mendeleev’s Table. In this series of brief articles, The Nerd Druid traces the wonderful history of the subatomic.

Subatomic particles

Protons, neutrons and electrons are the three most well-known subatomic particles. Earth has an abundance of free protons and electrons. All you need for the former is to somehow make electricity happen. An easy way to do that is to rub amber with fur 1. For the latter, water works pretty well, since it has plenty of free protons roaming about. Of course, it helps to keep in mind that protons are simply ionised hydrogen atoms.

The Electron

The ancient Greeks noticed that if you rub amber with fur, the amber tended to attract small light objects. This, along with lightning strikes, was the only connection humans had with electricity until modern times.

Image of Garfield (the cartoon cat character) rubbing his fur against Jon's pants. This creates static electricity. The charged fur repels each other.
Garfield rubbing his fur against Jon’s pants creates static electricity. The charged fur repels each other.

Cathode Rays

In the latter half of the nineteenth century, German and English physicists found that if you pull air out of sealed container and insert a cathode 2 into it, you see a glowing discharge. Pump out more air, lower the air pressure further, and this cathode discharge glows brighter. The pioneers of cathode ray physics were Johann Hittorf (Germany) and Eugen Goldstein (Germany); they did their work in 1869 and 1876 respectively.

William Crookes (England) created the first cathode ray tube in the 1870s by creating a high vacuum. He observed that the glow had now become a sort of a ray, moving from the cathode to the anode 3. Reckon we’d have to thank Crookes for all the televisions and older computer monitors.

Crookes also applied a magnetic field to the cathode rays and made them deflect. This showed that the rays were charged. Arthur Schuster (Germany-England) modified Crookes’ setup. He sandwiched the cathode ray between two parallel plates, one positive and one negative. The electric potential between the plates made the rays bend and strike the positive plate. This proved that the rays were negatively charged.

Discovery of the electron

Schuster didn’t stop there. By varying the current fed into his parallel capacitor, Schuster was able to vary the degree by which the cathode rays were deflected. He measured and tabulated these results, and was thus able to calculate the charge-to-mass (Q/m) ratio of the cathode rays. His results were astonishing–the Q/m ratio of the cathode rays seemed to be more than a thousand times what was expected!

Unfortunately, Schuster’s results were ignored, probably because they didn’t quite conform to what people knew about atoms. The prevalent idea at that time was that cathode rays were some sort of atoms or molecules, and thus they were expected to have a mass at least equal to the hydrogen ion.

Image of J.J. Thomson, English physicist. Experimentally obtained evidence for the existence of electrons. Thus showed that cathode rays are independent particles. Showed that these negatively charged particles are the same as the ones produced by radioactivity, by heated materials, and by illuminated materials. Suggested the plum pudding model for the distribution of positive charges and electrons within the atom. Discovery of the electron threw open the subatomic realm.
J.J. Thomson, English physicist

In 1897, J.J. Thomson (England), working with colleagues John Townsend (Ireland) and H.A. Wilson (England), showed that cathode rays were, indeed, individual charged particles. A few years later, Millikan and Fletcher performed the famous oil-drop experiment and accurately measured the charge of this new particle, the electron 4. Since the charge-to-mass ratio of the electron had already been measured, it was now simple to calculate the mass of the electron. Simply put, the electron has the same magnitude but opposite sign of the charge of a hydrogen ion. However, it had almost two thousandth its mass.

The Atomic Nucleus

Thanks to Thomson and his fellow cathode ray physicists, the atom was no longer a black box. Negatively charged cathode rays were actually particles called electrons, and they lived inside an atom. Sometimes some of these electrons would get knocked off the atom. The charged atom would then be a positive ion, a cation. At all other times, the atom would be strictly neutral. Clearly, the atom within contained an amount of positive charge equal to the negative charge it contained due to the electrons. The question was, where did the positive charge reside, and where were the electrons in relation to this?

Thomson had an answer to this. He envisaged electrons embedded within a uniform diffuse distribution of positive charge within the atom, much like plums in a pudding. The Geiger-Marsden experiment (1909) put paid to this plum pudding model soon enough.

Image of Thomson's plum pudding model (above) and Rutherford's Gold Foil experiment (below, aka the Geiger-Marsden expt.).
Thomson’s plum pudding model (above) and Rutherford’s Gold Foil experiment (below, aka the Geiger-Marsden experiment)

Hans Geiger 5 (England) and Ernest Marsden (England-New Zealand), working under the direction of Ernest Rutherford (New Zealand-England), fired positively charged alpha particles 6 at a metal foil. While most of the alpha particles whizzed through without any change in momentum, a tiny fraction (1-in-20000) deflected by almost 90 degrees. Rutherford concluded (in 1911) that this must be because all the positive charge in the atom is tightly packed inside a tiny volume at its centre. This, of course, is the atomic nucleus.

There were quite a few experiments performed by Geiger and Marsden. The most famous one is also referred to as Rutherford’s Gold foil experiment.

Nationalities

A quick aside about the nationalities of the people involved. A majority seem to be from England and Germany. The only two scientists from the US are Millikan and Fletcher, and they did their work in the 20th century. This seems to suggest that the nerve-centre of cutting edge physics in the nineteenth century was very much a few nations in Europe.

Nuclear density and pressure

The atom is mostly empty space 7 Atomic diameters are usually of ångström order (1 Å = 10-10 m). Nuclear diameters are a hundred thousand times smaller, usually of femtometer order (1 fm = 10-15 m). However, nuclei carry most of the atom’s mass. Due to their small sizes, they are incredibly dense objects.

A quick back-of-the-envelope calculation for carbon (C-12 isotope) shows that its nuclear density is approximately 1.25×1015 gm/cc. To put that into perspective, the density of ordinary water, under normal atmospheric pressure and standard room temperature, is approximately 1 gm/cc. Atomic nuclei are hundreds of trillion times denser than tap water.

Before we proceed, I’m going to presume that you are aware that atomic nuclei contain protons and neutrons. I’ll get to them in the next part of this series.

You’d think that such high densities would mean that the pressure inside the nucleus would be immense. You’d be correct, but there are places in this universe which make nuclear pressures seem like cotton candy. I’m talking about the interior of neutron stars, where pressures reach absurd values of 1034 pascal. In comparison, standard atmospheric pressure is about a hundred thousand pascal, 105. This of course makes neutron star cores very very hot. The story of how they cool down is quite interesting.

Up until a few days ago, this was the highest pressure found in the universe. Recently however, scientists at Jefferson Lab (the USA) have found that proton pressure is ten times that inside neutron stars. That is a mind-boggling million trillion trillion times that of standard Earth sea-level pressure.

Yes. A million trillion trillion times. 10 followed by 30 zeros.

In the next article, we encounter nucleons.


References

List of People : Who Did What

  1. Dmitry Mendeleev : Russian chemist
    • Designed the Periodic Table of Elements
  2. Johann Wilhelm Hittorf : German physicist
    • Discovered that a cathode within an evacuated chamber emitted a glow
    • Found that the intensity of the glow increased as pressure is lowered
  3. Eugen Goldstein : German physicist
    • Showed that the rays from Hittorf’s glow cast a shadow
    • Named the rays cathode rays
  4. Sir William Crookes : English chemist and physicist
    • Invented the extreme low pressure cathode ray tube
    • Showed that cathode rays travel as a straight beam between a cathode and anode
    • Showed that cathode rays deviate in a magnetic field, proving that they are charged
  5. Arthur Schuster : German-British physicist
    • Placed the cathode ray between the plates of a parallel plate capacitor
    • Showed that the beam deviated towards the positive plate
    • Thus showed that cathode rays are negatively charged
  6. J.J. Thomson : English physicist
    • Experimentally obtained evidence for the existence of electrons
    • Thus showed that cathode rays are independent particles
    • Showed that these negatively charged particles are the same as the ones produced by radioactivity, by heated materials, and by illuminated materials
    • Suggested the plum pudding model for the distribution of positive charges and electrons within the atom
    • Discovery of the electron enabled the subatomic world to be probed
  7. George Johnstone Stoney : Irish physicist
    • Introduced the term electron for units of electricity
  8. Robert Millikan : American physicist
    • Performed the famous oil-drop experiment and measured the charge of the electron
  9. Harvey Fletcher : American physicist
    • Performed the famous oil-drop experiment and measured the charge of the electron
  10. Ernest Rutherford : New Zealand-British physicist
    • The father of subatomic and nuclear physics
    • Called the greatest experimentalist since Faraday
    • Supervised the Geiger-Marsden experiment or the Gold foil experiment that disproved the plum-pudding model and discovered the atomic nucleus
    • Discovered the proton
    • Suggested that protons within the nucleus have a neutral partner
    • Named them neutrons
  11. Hans Geiger : German physicist
    • Performed the Geiger-Marsden experiment that disproved the plum-pudding model and discovered the atomic nucleus
    • Invented the Geiger counter, a detector of radioactivity
  12. Ernest Marsden : New Zealand-English physicist
    • Performed the Geiger-Marsden experiment that disproved the plum-pudding model and discovered the atomic nucleus

Original papers

  1. Thomson, J.J. : Cathode Rays, Philosophical Magazine (1897)
  2. Rutherford, Ernest : The scattering of α and β particles by matter and the structure of the atom, Philosophical Magazine (1911)
  3. Millikan, R.A. : On the Elementary Electrical Charge and the Avogadro Constant
Proton Pressure : How do Quarks Tackle Stress?

Proton Pressure : How do Quarks Tackle Stress?

Reading Time: 9 minutes

Proton pressure, theoretically estimated to be higher than even neutron stars, has been notoriously difficult to measure experimentally. Recently, however, particle physicists have used a nice trick to measure proton pressure. The Nerd Druid delves deeper.


Subnucleonic particles

Quarks

Particle physics is the study of extremely small particles. In the nineteenth century, atoms were thought to be indivisible and fundamental. Then, in 1897, J.J. Thompson discovered the electron. Following the Geiger-Marsden experiment in 1909, Ernest Rutherford in 1911 postulated the existence of the proton. The now-familiar subatomic trio was completed when James Chadwick discovered the neutron in 1932.

Image of a comparison of various physical properties of the three most familiar subatomic particles.
Comparison of various physical properties of the three most familiar subatomic particles.

In the three decades following 1932, the use of higher and higher energies in particle accelerators led to the discovery of a veritable particle zoo. In 1964, Murray Gell-Mann and George Zweig attempted to simplify matters. They proposed that protons, neutrons and all the other hadrons were not as fundamental as once thought. Instead, they suggested that smaller particles called quarks are the true fundamental particles that make up hadrons.

Image of Murray Gell-Mann (left) and George Zweig (right) were the first to propose the existence of quarks. 10 years after their proposal, the discovery of the charm quark in 1974 definitively proved Gell-Mann and Zweig to be correct. Gell-Mann received the Nobel Prize in physics in 1969.
Murray Gell-Mann (left) and George Zweig (right) were the first to propose the existence of quarks. 10 years after their proposal, the discovery of the charm quark in 1974 definitively proved Gell-Mann and Zweig to be correct. Gell-Mann received the Nobel Prize in physics in 1969.

The naming of quarks

Quarks are possibly one of the first particles named without reference to a Greek or Latin dictionary. Murray Gell-Mann, the man responsible for the name, had borrowed the word from the novel Finnegan’s Wake by James Joyce. At one point in the novel, a character, presumably drunk, exclaims

Three quarks for Muster Mark!

the words quarks and Muster possibly drunk modifications of quarts and Mister.

The Nerd Druid has once attempted to read Finnegan’s Wake. In his opinion, had Joyce not written Ulysses, Finnegan’s Wake would have been, without doubt, one of the most difficult books to read in the English language.

The discovery of the quarks

According to Gell-Mann and Zweig, there were three types or flavours of quarks. These were the up, down and the strange quarks. In 1970, Glashow, Iliopoulus and Maiani (GIM) proposed that a fourth flavour, the charm quark, should also exist. Three years later, Kobayashi and Maskawa’s proposal of top and bottom quarks increased the number of quark flavours to six.

Despite such stunning theoretical success, particle physicists were initially unwilling to accept the quark model. Richard Feynman proposed an alternative and called them partons. However, increasingly complex and beautiful experiments in the decade since Gell-Mann and Zweig seemed to weigh evidence in favour of quarks. Deep inelastic scattering experiments at the Stanford Linear Accelerator Centre (SLAC) found particles that would later be identified with the up and the down quark. The SLAC experiment also indirectly suggested that strange quarks should exist.

The November Revolution

The final breakthrough came in the November of 1974. Unlike its more illustrious and political Russian cousin, the particle physics November Revolution took place at SLAC and at Brookhaven National Laboratory, both in the USA. The two teams almost simultaneously discovered the charm quark and its antiparticle, bound together to form a meson. Burton Richter, who led the SLAC team, named it the ψ (psi) meson. Samuel Ting, who led the Brookhaven team, preferred to call it the J meson. Due to the joint announcement of their discovery, the J/ψ meson is the only particle with a two letter name.

Images of Samuel Ting (left) and Burton Richter (right), discoverers of the J/psi meson. They received the 1976 Nobel Prize in Physics for their work.
Samuel Ting (left) and Burton Richter (right), discoverers of the J/ψ meson. They received the 1976 Nobel Prize in Physics for their work.

The J/ψ discovery validated the quark model and led to rapid changes in high-energy particle physics. One of the major innovations to come out of this incredible time is what is known as the Standard Model of particle physics. To put it in a nutshell, the Standard Model puts the entire workings of the universe–sans gravity–in a nutshell. Thus, the name November Revolution.

The Standard Model

The standard model did to high-energy particle physics what Dmitry Mendeleev’s periodic table had done for chemistry almost exactly a hundred years earlier. It cut through all the noise and gave a beautiful tabular representation of all the fundamental particles that interact among each other via the four fundamental forces 1.

Image of a schematic depiction of the Standard Model of elementary particles. Shown are the six quark flavours, the three leptons and their corresponding neutrinos, the four force-carrying vector gauge bosons, and the solitary mass-carrying scalar gauge boson, the Higgs.
A schematic depiction of the Standard Model of elementary particles. Shown are the six quark flavours, the three leptons and their corresponding neutrinos, the four force-carrying vector gauge bosons, and the solitary mass-carrying scalar gauge boson, the Higgs. (Image Credit : Wikipedia).

The Fermions

In the image above, the six purple boxes represent the six flavours of quarks, while the six green boxes represents the three leptons and their neutrino counterparts. These twelve particles are fermions : particles that follow Fermi-Dirac statistics and have half-integer spins.

The Bosons

The particles on the right half of the image are bosons. These follow Bose-Einstein statistics and have integer spins. The four red boxes represent vector gauge bosons. These carry and mediate three of the four fundamental forces of nature; the fourth, gravity and its mediating gravitons, are still out of the standard model’s grasp. The yellow box on the very right represents the solitary scalar gauge boson, the Higgs, which carries and mediates mass.

Thus, all in all, 17 particles (and their antiparticles) are involved in almost everything that happens in the universe. The Nerd Druid will, hopefully, expand on the standard model in a later post.

Proton Constituents

Quarks are the building blocks of protons, neutrons, and a host of other particles. Together, these quark-based particles are called hadrons. For instance, the J/ψ meson is a hadron. There are two types of hadrons:

  1. Baryons : Composed of three quarks. These can be any flavour.
  2. Mesons : Composed of a quark and its antiquark.

The J/ψ is a meson because it comprises the charm (c) quark and its antiquark. Protons are composed to two up quarks and a down quark (uud), while neutrons have two down and one up quark.

Image of the quark composition of protons and neutrons. On the left, two up and one down quark make up a proton. On the right, two down and one up quark make up a neutron. The quarks have different "colour charges" that add up to "white", and are joined by gluon flux tubes.
On the left, two up and one down quark make up a proton. On the right, two down and one up quark make up a neutron. The quarks have different “colour charges” that add up to “white”, and are joined by gluon flux tubes. Do note that the flux tubes as shown here are wrong. They do not act along the sides of the triangle making up the quarks, but rather form a Y-shape, much like the flux capacitor in the movie Back to the Future.

Why does a proton not break up?

An up quark has charge +2/3, a down quark has charge -1/3. This makes the interior of nucleons a very interesting place. Take the proton, for instance. It has two positively charged up quarks within it, each of which is attracted towards, and attracts, the third negatively charged down quark. However, since they are both positive, they repel each other. How in the world does the proton not break up?

{Atomic nuclei have a similar problem. Going by common sense, the positive protons should never be confined to such a small region.}

If conditions are energetically favourable, bound protons transmute into neutrons. Free protons, one of the stablest objects in the universe, only do so if bombarded with high energy particles. The quarks within them never fly apart on their own, although, electromagnetically speaking, they should be flying apart. What the proton needs is an attractive force that keeps the various quarks together. One candidate is gravitation. However, that is approximately 1040 times weaker than the EM force. So that’s no help.

The Strong Force

Luckily, there is a force stronger than even the EM force. This is the imaginatively named strong force. While the EM force is mediated by photons, the strong force is mediated via gluons.

Take a quick peek at the standard model diagram. The topmost red box on the right half is the gluon. It is a vector gauge boson, and functions as a force-carrier. The strong force holding the quarks together manifests as constant exchanges of gluons between the quarks. From a quantum field theoretic viewpoint, the three quarks within the proton live in a sea of frothing bubbling gluon field.

{The strong force is, of course, also responsible for holding the nucleus together, and manifests itself via constant exchange of gluons between protons and neutrons.}

Proton Mass

The mass of an atom is approximately the same as the mass of its nucleus, since electrons are 1839 times lighter than neutrons, and 1836 times lighter than protons. Adding the masses (the rest masses) of the nucleons is the mass of the atom minus the binding energy needed to keep the nucleus together. However, this is still a small percentage of the nucleonic rest masses.

Inside a proton, the situation is rather different. The total rest mass of the three quarks (2u+1d) is only about 10% of the total mass of the proton. The rest 90% of the mass is provided by the highly energetic gluon field. Since it has energy, and by Einstein’s Mass-Energy equivalence, E = mc2, the gluon field has relativistic mass.

Image of a schematic of the masses of the six different quark flavours. The larger the balls, the higher the mass. The mass of the proton (grey) and electron (red) are shown in the southwest corner. Note that the total mass of 2u+1d would be quite a bit lesser than that of the proton.
A schematic of the masses of the six different quark flavours. The larger the balls, the higher the mass. The mass of the proton (grey) and electron (red) are shown in the southwest corner. Note that the total mass of 2u+1d would be quite a bit lesser than that of the proton.

Proton Pressure

Probing the inside of a proton is not easy. While it is possible to build up a three-dimensional image of the proton using the EM force, probing the mechanical properties of the proton is another matter entirely.

The Energy-Momentum Tensor

The energy-momentum tensor provides a complete classical dynamical description of a particle. It encodes information such as its mass and its momentum, and the shear stresses and pressures on it. Einstein’s Field Equations, which form the backbone of general relativity, relates this tensor with the curvature of spacetime. In the image, the E-M tensor is represented as a 4-by-4 matrix. The energy density, shown in the red box on the top left corner, is equivalent to the mass. The rest of the diagonal, the green band, represents pressure.

Image of the energy-momentum tensor, represented as a 4-by-4 matrix. The northwest corner (red) is mass. The northern and western walls (yellow-orange) are momentum. The elements along the diagonal (green) are pressure acting along the three space axes.
The energy-momentum tensor, represented as a 4-by-4 matrix. The northwest corner (red) is mass. The northern and western walls (yellow-orange) are momentum. The elements along the diagonal (green) are pressure acting along the three space axes.

Gravitational Form Factors

To obtain information about the mechanical structure of a proton, you’d need to prod it with a gravity probe. However, a gravity probe will not directly measure the matrix elements of the E-M tensor. Instead, what it can do it measure what are called gravitational form factors. In 1966, Heinz Pagels developed the concept of these GFFs and also analytically calculated them. Pagels, however, was not very confident that it would ever be possible to measure the detailed structure of a particle using the GFFs, since there was

…very little hope of learning anything about the detailed mechanical structure of a particle, because of the extreme weakness of the gravitational interaction.

And therein lies the rub. Gravity is just too weak a force at the scale of subnucleonic particles.

Image of Heinz Pagels, who constructed the gravitation form factors for nucleons in 1966, at the age of 27. He was extremely capable of explaining science in a simple way. Pagel's work in chaos theory provided the inspiration for the character of Ian Malcolm in Michael Crichton's Jurassic Park.
Heinz Pagels constructed the gravitation form factors for nucleons in 1966, at the age of 27. He was extremely capable of explaining science in a simple way. Pagel’s work in chaos theory provided the inspiration for the character of Ian Malcolm in Michael Crichton’s Jurassic Park.

Generalised Parton Distributions

If restricted to EM probes, then, using something called generalised parton distributions, researches can build up a 3D model of the proton. The word parton here is not quite used in the sense Feynman envisioned it; the term parton nowadays collectively refer to quarks, antiquarks, and gluons. GPDs were introduced around the year 1994. In the quarter century till then, they have emerged as an extremely valuable tool for probing hadrons.

However, the puzzle was still incomplete. GPDs are electromagnetic objects, while GFFs are gravitational. Proton investigations required a bridge between these two.

Measuring Proton Pressure

Deeply Virtual Compton Scattering

The bridge was finally proposed in 1997, when the Xiandong Ji suggested that a method called deep virtual compton scattering (DVCS) could be used to map GFFs onto GPDs. In this process, a beam of electrons is fired into atomic nuclei. Some of these electrons shoot through protons. In doing so, they transfer some of their energy to one of the quarks inside the proton. This is mediated by a virtual photon. The proton, thus energised, doesn’t hold on to this excess energy for long. It soon emits another photon and drops down to its original state.

Magnitude of Proton Pressure

By analysing these photons, Jefferson Lab scientists Volker Burkert, Latifa Elouadrhiri, and Francois-Xavier Girod (BEG) have built up a mechanical picture of the interior of the proton. In particular, they have calculated proton pressure for the very first time. BEG have found that quarks near the centre of the proton feel pressures of the order of 1035 pascal.

To put that into perspective, standard atmospheric pressure at sea level on Earth is slightly more than a million pascal. That is 106.

The centres of neutron stars used to be the undisputed champions of the universe when it came to ultrahigh pressures. They’ve been dethroned, for proton pressure is about 10 times the pressure found within neutron stars.

Distribution of Proton Pressure

Image of the proton pressure distribution. The y-axis is in units of force (positive outward), while the x-axis shows distance from proton centre (in femtometer, 10^-15 m). The repulsive proton pressure near the centre, directed outwards, is balanced by the confining proton pressure from the outer edges of the proton, directed inwards.
Pressure distribution within a proton. The y-axis is in units of force (positive outward), while the x-axis shows the distance from proton centre (in femtometer, 10^-15 m). The repulsive pressure near the centre, directed outwards, is balanced by the confining pressure from the outer edges of the proton, directed inwards.

According the BEG analysis, the proton pressure at the centre of the proton is highest. It is also repulsive, threatening to push the three quarks apart. However, proton pressure near its edge, though less in magnitude, is compressive in nature. This confines the quarks to within the interior of the proton, within a diameter of about 2 fm (1 fm = 10-15 m).

BEG are not done yet, though. They are waiting for better and precise data that they hope to obtain soon. This will help them polish some of their current results on the distribution of proton pressure. BEG are confident that their method of DVCS-GPD-GFF will reveal more about the interior of the proton, such as internal shear forces and the its mechanical radius.


References

Original Paper

Burkert, V. and Elouadrhiri, L. and Girod, F-X. : The pressure distribution inside the proton, Nature (2018).

Reference papers

  1. Pagels, Heinz : Energy-Momentum Structure Form Factors of Particles, Physical Review (1966)
  2. Maxim V. Polyakov, Maxim V. and Schweitzer, Peter : Forces inside hadrons: pressure, surface tension, mechanical radius, and all that, arXiv (2018)
  3. Ji, Xiangdong : Gauge-Invariant Decomposition of Nucleon Spin, Physical Review Letters (1997)
  4. Ji, Xiangdong : Deeply virtual Compton scattering, Physical Review D (1997)
  5. Rutherford, Ernest : The scattering of α and β particles by matter and the structure of the atom (2011)
  6. Chadwick, James : Possible Existence of a Neutron, Nature (1932)
  7. Belitsky, A.V. and Radyushkin, A.V. : Unraveling hadron structure with generalized parton distributions, Physics Reports (2005)

Other resources

  1. Perdrisat, Charles and Punjabi, Vina : Nucleon Form Factors, Scholarpedia (2010)
  2. Wikipedia
    1. Atoms#Subatomic Particles
    2. Proton#History
    3. Neutron#Discovery

Articles

  1. Press Release : First measurement of subatomic particle’s mechanical property reveals distribution of pressure inside proton
  2. Press Release : Quarks feel the pressure in the proton
    1. EurekaAlert (2018)
    2. Jefferson Lab (2018)
  3. Mandelbaum, Ryan F. : Scientists Calculate the Pressure Inside a Proton and It’s Higher Than in a Neutron Star, Gizmodo.com (2018)
  4. Micu, Alexandru : Pressure in protons’ cores is over ten times greater that that in neutron stars
  5. News Staff : Physicists Measure Pressure Distribution inside Proton, Sci-News.com (2018)
  6. Yirka, Bob : Best of Last Week – Measuring pressure inside a proton, flying wireless robot insects and yogurt may treat inflammation, ScienceX.com (2018)
  7. McRae, Mike : Protons Contain 10 Times More Pressure Than a Neutron Star, According to First-Ever Measurement, Science Alert (2018)
  8. Grossman, David : Pressures Inside a Proton Are More Extreme Than Inside a Neutron Star, Popular Mechanics (2018).
  9. Williams, Matt : The Pressure Inside Every Photon is 10x That Inside Neutron Stars, Universe Today (2018)