Proton

In quantum chromodynamics, the modern theory of the nuclear force, most of the mass of protons and neutrons is explained by special relativity. The mass of a proton is about 80–100 times greater than the sum of the rest masses of its three valence quarks, while the gluons have zero rest mass. The extra energy of the quarks and gluons in a proton, as compared to the rest energy of the quarks alone in the QCD vacuum, accounts for almost 99% of the proton's mass. The rest mass of a proton is, thus, the invariant mass of the system of moving quarks and gluons that make up the particle, and, in such systems, even the energy of massless particles confined to a system is still measured as part of the rest mass of the system.

Two terms are used in referring to the mass of the quarks that make up protons: current quark mass refers to the mass of a quark by itself, while constituent quark mass refers to the current quark mass plus the mass of the gluon particle field surrounding the quark.^{: 285–286  : 150–151} These masses typically have very different values. The kinetic energy of the quarks that is a consequence of confinement is a contribution (see Mass in special relativity). Using lattice QCD calculations, the contributions to the mass of the proton are the quark condensate (~9%, comprising the up and down quarks and a sea of virtual strange quarks), the quark kinetic energy (~32%), the gluon kinetic energy (~37%), and the anomalous gluonic contribution (~23%, comprising contributions from condensates of all quark flavors).

The constituent quark model wavefunction for the proton is

$${\displaystyle \mathrm {|p_{\uparrow }\rangle ={\tfrac {1}{\sqrt {18}}}\left(2|u_{\uparrow }d_{\downarrow }u_{\uparrow }\rangle +2|u_{\uparrow }u_{\uparrow }d_{\downarrow }\rangle +2|d_{\downarrow }u_{\uparrow }u_{\uparrow }\rangle -|u_{\uparrow }u_{\downarrow }d_{\uparrow }\rangle -|u_{\uparrow }d_{\uparrow }u_{\downarrow }\rangle -|u_{\downarrow }d_{\uparrow }u_{\uparrow }\rangle -|d_{\uparrow }u_{\downarrow }u_{\uparrow }\rangle -|d_{\uparrow }u_{\uparrow }u_{\downarrow }\rangle -|u_{\downarrow }u_{\uparrow }d_{\uparrow }\rangle \right)} .}$$

 

The internal dynamics of protons are complicated, because they are determined by the quarks' exchanging gluons, and interacting with various vacuum condensates. Lattice QCD provides a way of calculating the mass of a proton directly from the theory to any accuracy, in principle. The most recent calculations claim that the mass is determined to better than 4% accuracy, even to 1% accuracy (see Figure S5 in Dürr et al.). These claims are still controversial, because the calculations cannot yet be done with quarks as light as they are in the real world. This means that the predictions are found by a process of extrapolation, which can introduce systematic errors. It is hard to tell whether these errors are controlled properly, because the quantities that are compared to experiment are the masses of the hadrons, which are known in advance.

These recent calculations are performed by massive supercomputers, and, as noted by Boffi and Pasquini: "a detailed description of the nucleon structure is still missing because ... long-distance behavior requires a nonperturbative and/or numerical treatment ..." More conceptual approaches to the structure of protons are: the topological soliton approach originally due to Tony Skyrme and the more accurate AdS/QCD approach that extends it to include a string theory of gluons, various QCD-inspired models like the bag model and the constituent quark model, which were popular in the 1980s, and the SVZ sum rules, which allow for rough approximate mass calculations. These methods do not have the same accuracy as the more brute-force lattice QCD methods, at least not yet.

The internationally accepted value of a proton's charge radius is 0.8414 fm. The radius of the proton defined by a formula which can be calculated by quantum electrodynamics and be derived from either atomic spectroscopy or by electron-proton scattering. The formula involves a form-factor related to the two-dimensional parton diameter of the proton.

Before 2010 value is based on scattering electrons from protons followed by complex calculation involving scattering cross section based on Rosenbluth equation for momentum-transfer cross section), and based on studies of the atomic energy levels of hydrogen and deuterium. In 2010 an international research team published a proton charge radius measurement via the Lamb shift in muonic hydrogen (an exotic atom made of a proton and a negatively charged muon). As a muon is 200 times heavier than an electron, resulting in a smaller atomic orbital, much more sensitive to the proton's charge radius and thus allowing a more precise measurement. Subsequent improved scattering and electron-spectroscopy measurements agree with the new small radius. Work continues to refine and check this new value.

Pressure inside the proton

Since the proton is composed of quarks confined by gluons, an equivalent pressure that acts on the quarks can be defined. The size of that pressure and other details about it are controversial.

In 2018 this pressure was reported to be on the order 10³⁵ Pa, which is greater than the pressure inside a neutron star. It was said to be maximum at the centre, positive (repulsive) to a radial distance of about 0.6 fm, negative (attractive) at greater distances, and very weak beyond about 2 fm. These numbers were derived by a combination of a theoretical model and experimental Compton scattering of high-energy electrons. However, these results have been challenged as also being consistent with zero pressure and as effectively providing the pressure profile shape by selection of the model.

Charge radius in solvated proton, hydronium

The radius of the hydrated proton appears in the Born equation for calculating the hydration enthalpy of hydronium.

Although protons have affinity for oppositely charged electrons, this is a relatively low-energy interaction and so free protons must lose sufficient velocity (and kinetic energy) in order to become closely associated and bound to electrons. High energy protons, in traversing ordinary matter, lose energy by collisions with atomic nuclei, and by ionization of atoms (removing electrons) until they are slowed sufficiently to be captured by the electron cloud in a normal atom.

However, in such an association with an electron, the character of the bound proton is not changed, and it remains a proton. The attraction of low-energy free protons to any electrons present in normal matter (such as the electrons in normal atoms) causes free protons to stop and to form a new chemical bond with an atom. Such a bond happens at any sufficiently "cold" temperature (that is, comparable to temperatures at the surface of the Sun) and with any type of atom. Thus, in interaction with any type of normal (non-plasma) matter, low-velocity free protons do not remain free but are attracted to electrons in any atom or molecule with which they come into contact, causing the proton and molecule to combine. Such molecules are then said to be "protonated", and chemically they are simply compounds of hydrogen, often positively charged. Often, as a result, they become so-called Brønsted acids. For example, a proton captured by a water molecule in water becomes hydronium, the aqueous cation H₃O⁺.

Atomic number

In chemistry, the number of protons in the nucleus of an atom is known as the atomic number, which determines the chemical element to which the atom belongs. For example, the atomic number of chlorine is 17; this means that each chlorine atom has 17 protons and that all atoms with 17 protons are chlorine atoms. The chemical properties of each atom are determined by the number of (negatively charged) electrons, which for neutral atoms is equal to the number of (positive) protons so that the total charge is zero. For example, a neutral chlorine atom has 17 protons and 17 electrons, whereas a Cl⁻ anion has 17 protons and 18 electrons for a total charge of −1.

All atoms of a given element are not necessarily identical, however. The number of neutrons may vary to form different isotopes, and energy levels may differ, resulting in different nuclear isomers. For example, there are two stable isotopes of chlorine: ³⁵
₁₇Cl
with 35 − 17 = 18 neutrons and ³⁷
₁₇Cl
with 37 − 17 = 20 neutrons.

Hydrogen ion

 

In chemistry, the term proton refers to the hydrogen ion, H⁺
. Since the atomic number of hydrogen is 1, a hydrogen ion has no electrons and corresponds to a bare nucleus, consisting of a proton (and 0 neutrons for the most abundant isotope protium ¹
₁H
). The proton is a "bare charge" with only about 1/64,000 of the radius of a hydrogen atom, and so is extremely reactive chemically. The free proton, thus, has an extremely short lifetime in chemical systems such as liquids and it reacts immediately with the electron cloud of any available molecule. In aqueous solution, it forms the hydronium ion, H₃O⁺, which in turn is further solvated by water molecules in clusters such as [H₅O₂]⁺ and [H₉O₄]⁺.

The transfer of H⁺
in an acid–base reaction is usually referred to as "proton transfer". The acid is referred to as a proton donor and the base as a proton acceptor. Likewise, biochemical terms such as proton pump and proton channel refer to the movement of hydrated H⁺
ions.

The ion produced by removing the electron from a deuterium atom is known as a deuteron, not a proton. Likewise, removing an electron from a tritium atom produces a triton.

Proton nuclear magnetic resonance (NMR)

Also in chemistry, the term "proton NMR" refers to the observation of hydrogen-1 nuclei in (mostly organic) molecules by nuclear magnetic resonance. This method uses the quantized spin magnetic moment of the proton, which is due to its angular momentum (or spin), which in turn has a magnitude of one-half the reduced Planck constant. (${\displaystyle \hbar /2}$ ). The name refers to examination of protons as they occur in protium (hydrogen-1 atoms) in compounds, and does not imply that free protons exist in the compound being studied.

The Apollo Lunar Surface Experiments Packages (ALSEP) determined that more than 95% of the particles in the solar wind are electrons and protons, in approximately equal numbers.

Because the Solar Wind Spectrometer made continuous measurements, it was possible to measure how the Earth's magnetic field affects arriving solar wind particles. For about two-thirds of each orbit, the Moon is outside of the Earth's magnetic field. At these times, a typical proton density was 10 to 20 per cubic centimeter, with most protons having velocities between 400 and 650 kilometers per second. For about five days of each month, the Moon is inside the Earth's geomagnetic tail, and typically no solar wind particles were detectable. For the remainder of each lunar orbit, the Moon is in a transitional region known as the magnetosheath, where the Earth's magnetic field affects the solar wind, but does not completely exclude it. In this region, the particle flux is reduced, with typical proton velocities of 250 to 450 kilometers per second. During the lunar night, the spectrometer was shielded from the solar wind by the Moon and no solar wind particles were measured.

Protons also have extrasolar origin from galactic cosmic rays, where they make up about 90% of the total particle flux. These protons often have higher energy than solar wind protons, and their intensity is far more uniform and less variable than protons coming from the Sun, the production of which is heavily affected by solar proton events such as coronal mass ejections.

Research has been performed on the dose-rate effects of protons, as typically found in space travel, on human health. To be more specific, there are hopes to identify what specific chromosomes are damaged, and to define the damage, during cancer development from proton exposure. Another study looks into determining "the effects of exposure to proton irradiation on neurochemical and behavioral endpoints, including dopaminergic functioning, amphetamine-induced conditioned taste aversion learning, and spatial learning and memory as measured by the Morris water maze. Electrical charging of a spacecraft due to interplanetary proton bombardment has also been proposed for study. There are many more studies that pertain to space travel, including galactic cosmic rays and their possible health effects, and solar proton event exposure.

The American Biostack and Soviet Biorack space travel experiments have demonstrated the severity of molecular damage induced by heavy ions on microorganisms including Artemia cysts.

CPT-symmetry puts strong constraints on the relative properties of particles and antiparticles and, therefore, is open to stringent tests. For example, the charges of a proton and antiproton must sum to exactly zero. This equality has been tested to one part in 10⁸. The equality of their masses has also been tested to better than one part in 10⁸. By holding antiprotons in a Penning trap, the equality of the charge-to-mass ratio of protons and antiprotons has been tested to one part in 6×10⁹. The magnetic moment of antiprotons has been measured with an error of 8×10⁻³ nuclear Bohr magnetons, and is found to be equal and opposite to that of a proton.