Atomic nucleus

The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford at the University of Manchester based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg. An atom is composed of a positively charged nucleus, with a cloud of negatively charged electrons surrounding it, bound together by electrostatic force. Almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud. Protons and neutrons are bound together to form a nucleus by the nuclear force.
The diameter of the nucleus is in the range of for hydrogen to about for uranium. These dimensions are much smaller than the diameter of the atom itself, by a factor of about 26,634 ) to about 60,250.
The branch of physics involved with the study and understanding of the atomic nucleus, including its composition and the forces that bind it together, is called nuclear physics.

History

The nucleus was discovered in 1911, as a result of Ernest Rutherford's efforts to test Thomson's "plum pudding model" of the atom. The electron had already been discovered by J. J. Thomson. Knowing that atoms are electrically neutral, J. J. Thomson postulated that there must be a positive charge as well. In his plum pudding model, Thomson suggested that an atom consisted of negative electrons randomly scattered within a sphere of positive charge. Ernest Rutherford later devised an experiment with his research partner Hans Geiger and with help of Ernest Marsden, that involved the deflection of alpha particles directed at a thin sheet of metal foil. He reasoned that if J. J. Thomson's model were correct, the positively charged alpha particles would easily pass through the foil with very little deviation in their paths, as the foil should act as electrically neutral if the negative and positive charges are so intimately mixed as to make it appear neutral. To his surprise, many of the particles were deflected at very large angles. Because the mass of an alpha particle is about 8,000 times that of an electron, it became apparent that a very strong force must be present if it could deflect the massive and fast moving alpha particles. He realized that the plum pudding model could not be accurate and that the deflections of the alpha particles could only be explained if the positive and negative charges were separated from each other and that the mass of the atom was a concentrated point of positive charge. This justified the idea of a nuclear atom with a dense center of positive charge and mass.

Etymology

The term nucleus is from the Latin word nucleus, a diminutive of , meaning 'the kernel' inside a watery type of fruit. In 1844, Michael Faraday used the term to refer to the "central point of an atom". The modern atomic meaning was proposed by Ernest Rutherford in 1912. The adoption of the term "nucleus" to atomic theory, however, was not immediate. In 1916, for example, Gilbert N. Lewis stated, in his famous article The Atom and the Molecule, that "the atom is composed of the kernel and an outer atom or shell."
Similarly, the term kern meaning kernel is used for nucleus in German and Dutch.

Principles

The nucleus of an atom consists of neutrons and protons, which in turn are the manifestation of more elementary particles, called quarks, that are held in association by the nuclear strong force in certain stable combinations of hadrons, called baryons. The nuclear strong force extends far enough from each baryon so as to bind the neutrons and protons together against the repulsive electrical force between the positively charged protons. The nuclear strong force has a very short range, and essentially drops to zero just beyond the edge of the nucleus. The collective action of the positively charged nucleus is to hold the electrically negative charged electrons in their orbits about the nucleus. The collection of negatively charged electrons orbiting the nucleus display an affinity for certain configurations and numbers of electrons that make their orbits stable. Which chemical element an atom represents is determined by the number of protons in the nucleus; the neutral atom will have an equal number of electrons orbiting that nucleus. Individual chemical elements can create more stable electron configurations by combining to share their electrons. It is that sharing of electrons to create stable electronic orbits about the nuclei that appears to us as the chemistry of our macro world.
Protons define the entire charge of a nucleus, and hence its chemical identity. Neutrons are electrically neutral, but contribute to the mass of a nucleus to nearly the same extent as the protons. Neutrons can explain the phenomenon of isotopes. The main role of neutrons is to reduce electrostatic repulsion inside the nucleus.

Composition and shape

Protons and neutrons are fermions, with different values of the strong isospin quantum number, so two protons and two neutrons can share the same space wave function since they are not identical quantum entities. They are sometimes viewed as two different quantum states of the same particle, the nucleon. Two fermions, such as two protons, or two neutrons, or a proton + neutron can exhibit bosonic behavior when they become loosely bound in pairs, which have integer spin.
In the rare case of a hypernucleus, a third baryon called a hyperon, containing one or more strange quarks and/or other unusual quark, can also share the wave function. However, this type of nucleus is extremely unstable and not found on Earth except in high-energy physics experiments.
The neutron has a positively charged core of radius ≈ 0.3 fm surrounded by a compensating negative charge of radius between 0.3 fm and 2 fm. The proton has an approximately exponentially decaying positive charge distribution with a mean square radius of about 0.8 fm.
The shape of the atomic nucleus can be spherical, rugby ball-shaped, discus-shaped, triaxial or pear-shaped.

Forces

Nuclei are bound together by the residual strong force. The residual strong force is a minor residuum of the strong interaction, which binds quarks together to form protons and neutrons. This force is much weaker between neutrons and protons because it is mostly neutralized within them, in the same way that electromagnetic forces between neutral atoms are much weaker than the electromagnetic forces that hold the parts of the atoms together internally.
The nuclear force is highly attractive at the distance of typical nucleon separation, and this overwhelms the repulsion between protons due to the electromagnetic force, thus allowing nuclei to exist. However, the residual strong force has a limited range because it decays quickly with distance ; thus only nuclei smaller than a certain size can be completely stable. The largest known completely stable nucleus is lead-208 which contains a total of 208 nucleons. Nuclei larger than this maximum are unstable and tend to be increasingly short-lived with larger numbers of nucleons. However, bismuth-209 is also stable to beta decay and has the longest half-life to alpha decay of any known isotope, estimated at a billion times longer than the age of the universe.
The residual strong force is effective over a very short range and causes an attraction between any pair of nucleons. For example, between a proton and a neutron to form a deuteron , and also between protons and protons, and neutrons and neutrons.

Halo nuclei and nuclear force range limits

The effective absolute limit of the range of the nuclear force is represented by halo nuclei such as lithium-11 or boron-14, in which dineutrons, or other collections of neutrons, orbit at distances of about . These nuclei are not maximally dense. Halo nuclei form at the extreme edges of the chart of the nuclides—the neutron drip line and proton drip line—and are all unstable with short half-lives, measured in milliseconds; for example, lithium-11 has a half-life of.
Halos in effect represent an excited state with nucleons in an outer quantum shell which has unfilled energy levels "below" it. The halo may be made of either neutrons or protons . Nuclei which have a single neutron halo include ¹¹Be and ¹⁹C. A two-neutron halo is exhibited by ⁶He, ¹¹Li, ¹⁷B, ¹⁹B and ²²C. Two-neutron halo nuclei break into three fragments, never two, and are called Borromean nuclei because of this behavior. ⁸He and ¹⁴Be both exhibit a four-neutron halo. Nuclei which have a proton halo include ⁸B and ²⁶P. A two-proton halo is exhibited by ¹⁷Ne and ²⁷S. Proton halos are expected to be more rare and unstable than the neutron examples, because of the repulsive electromagnetic forces of the halo proton.

Nuclear models

Although the Standard Model of physics is widely believed to completely describe the composition and behavior of the nucleus, generating predictions from theory is much more difficult than for most other areas of particle physics. This is due to two reasons:

In principle, the physics within a nucleus can be derived entirely from quantum chromodynamics. In practice however, current computational and mathematical approaches for solving QCD in low-energy systems such as the nuclei are extremely limited. This is due to the phase transition that occurs between high-energy quark matter and low-energy hadronic matter, which renders perturbative techniques unusable, making it difficult to construct an accurate QCD-derived model of the forces between nucleons. Current approaches are limited to either phenomenological models such as the Argonne v18 potential or chiral effective field theory.
Even if the nuclear force is well constrained, a significant amount of computational power is required to accurately compute the properties of nuclei ab initio. Developments in many-body theory have made this possible for many low mass and relatively stable nuclei, but further improvements in both computational power and mathematical approaches are required before heavy nuclei or highly unstable nuclei can be tackled.

Historically, experiments have been compared to relatively crude models that are necessarily imperfect. None of these models can completely explain experimental data on nuclear structure.
The nuclear radius is considered to be one of the basic quantities that any model must predict. For stable nuclei the nuclear radius is roughly proportional to the cube root of the mass number of the nucleus, and particularly in nuclei containing many nucleons, as they arrange in more spherical configurations:
The stable nucleus has approximately a constant density and therefore the nuclear radius R can be approximated by the following formula,
where A = Atomic mass number and r₀ = = . In this equation, the "constant" r₀ varies by 0.2 fm, depending on the nucleus in question, but this is less than 20% change from a constant.
In other words, packing protons and neutrons in the nucleus gives approximately the same total size result as packing hard spheres of a constant size into a tight spherical or almost spherical bag.
Models of nuclear structure include: