Definitions

# Atomic nucleus

The nucleus of an atom is the very dense region, consisting of nucleons (protons and neutrons), at the center of an atom. Although the size of the nucleus varies considerably according to the mass of the atom, the size of the entire atom is comparatively constant. Almost all of the mass in an atom is made up from the protons and neutrons in the nucleus with a very small contribution from the orbiting electrons.

The diameter of the nucleus is in the range of 1.6 fm (10−15 m) (for a proton in light hydrogen) to about 15 fm (for the heaviest atoms, such as uranium). These dimensions are much smaller than the size of the atom itself by a factor of about 23,000 (uranium) to about 145,000 (hydrogen).

The branch of physics concerned with studying and understanding the atomic nucleus, including its composition and the forces which bind it together, is called nuclear physics.

## Introduction

### Etymology

The term nucleus dates to from 800b.c, and means “kernel of a nut”. 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 , that “the atom is composed of the kernel and an outer atom or shell”.

### Nuclear makeup

The nucleus of an atom consists of protons and neutrons (two types of baryons) bound by the nuclear force (also known as the residual strong force). These baryons are further composed of subatomic fundamental particles known as quarks bound by the strong interaction. Which chemical element an atom represents,is determined by the number of protons in the nucleus.

## Protons and neutrons

Protons and neutrons are fermions, with different values of the isospin quantum number, so two protons and two neutrons can share the same space wave function. In the rare case of a hypernucleus, a third baryon called a hyperon, with a different value of the strangeness quantum number can also share the wave function.

## Forces

Nuclei are bound together by the residual strong force. The residual strong force is minor residuum of the strong force which binds quarks together to form protons and neutrons. This force is much weaker between neutrons and protons because it is mostly neutalized within them, in the same way that electromagnetic forces between neutral atoms (van der Waals forces) are much weaker than the electromagnetic forces that hold the atoms internally together.

The strong force is so named because it is significantly larger in magnitude than the other fundamental forces (electroweak, electromagnetic and gravitational). The strong force is highly attractive at very small distances, and this overwhelms the repulsion between protons due to the electromagnetic force, thus allowing nuclei to exist. However, because the residual strong force has a limited range, only nuclei smaller than a certain size can be completely stable. The largest known complete stable nucleus is lead-208 which contains 208 neutrons and protons. Nuclei larger than this maximal size of 208 particles generally become increasingly short-lived as the number of neutrons and protons which compose them increases beyond this number.

The residual strong force usually acts over a very short range (a few fermis, roughly one or two nucleon diameters) and causes an attraction between nucleons (protons and neutrons). However there are also halo nuclei such as lithium-11 or boron-14, in which dineutrons, or other collections of nucleons, orbit at distances of about ten fermis (similar to the size of lead-208). Such nuclei are always short-lived; for example, lithium-11 has a half-life of less than 8.6 milliseconds.

## Nuclear models

Nuclear radius is a basic experimentally measurable fact that any rational model simply has to explain. It is proportional to the cube root of the nuclear mass

$R propto A^\left\{1/3\right\}$

This very important experimental fact implies that spherical nuclei have radii directly proportional to the cube root of their respective volumes (volume of a sphere = $4/3 pi R^3$). It says that nuclear volumes are generally equal to the sum of the respective volumes of constituent nucleons, like oranges packed together in a string bag, exactly as assumed in meson theory. This single experimental fact shows that protons and neutrons behave in some ways like spheres with fixed volumes that are packed together in a nucleus with a volume which approximates that which would result if the spheres were touching.

### Liquid drop models

Early models of the nucleus viewed the nucleus as a rotating liquid drop. In this model, the trade-off of long-range electromagnetic forces and relatively short-range nuclear forces, together caused behavior which resembled surface tension forces in liquid drops of different sizes. This formula is successful at explaining many important phenomena of nuclei, such as their changing amounts of binding energy as their size changes, but it does not explain the special stability which occurs when nucleii have special "magic numbers" of protons or neutrons.

### Shell models and other quantum models

A number of models for the nucleus have also been proposed in which nucleons occupy orbitals, much like the atomic orbitals in atomic physics theory. These wave models imagine nucleons to be either sizeless point particles in potential wells, or else probability waves as in the "optical model", frictionlessly orbiting at high speed in potential wells.

In these models, the nucleons occupy orbitals in pairs, due to being fermions, but the exact nature and capacity of nuclear shells differs somewhat from those of elections in atomic orbitals, primarily because the potential well in which the nucleons move (especially in larger nucleii) is quite different from the central electromagnetic potential well which binds electrons in atoms. Nevertheless, the resemblance to atomic orbital models may be seen in a small atomic nucleus like that of helium-4, in which the two protons and two neutrons separately occupy 1s orbitals analagous to the 1s orbitals for the two electrons in the helium atom, and achieve unusual stability for the same reason. This stability also underlies the fact that nuclei with 5 nucleons are all extremely unstable and short-lived.

For larger nuclei, the shells occupied by nucleons begin to differ signifficantly from electron shells, but nevertheless, present nuclear theory does predict the "magic numbers" of filled nuclear shells for both protons and neutrons. The closure of the stable shells predicts unusually stable configurations, something like inert gases in chemistry. An example is the stability of the closed shell of 50 protons, which allows tin to have 10 stable isotopes, more than any other element.

### Consistency between models

As with the case of superfluid liquid helium, atomic nuclei are an example of a state in which both (1) "ordinary" particle physical rules for volume and (2) non-intuitive quantum mechanical rules for a wave-like nature apply. In superfluid helium, the helium atoms have volume, and essentially "touch" each other, yet at the same time exhibit strange bulk properties, consistent with a Bose-Einstein condensation. The latter reveals that they also have a wave-like nature and do not exhibit standard fluid properties, such as friction. For nuclei made of hadrons which are fermions, the same type of condensation does not occur, yet nevertheless, many nuclear properties can only be explained similarly by a combination of properties of particles with volume, in addition to the frictionless motion characteristic of the wave-like behavior of objects trapped in Schroedinger quantum orbitals.