Nuclear force

(PD) Image: John R. Brews
A neutron and proton trade identities by exchange of a π⁻ in the Yukawa model.

In physics, the nuclear force is the force holding assemblies of protons and neutrons together.

History

In 1935 Yukawa invented the meson theory for explaining the forces holding an assemblage of neutrons and protons together. The mesons were postulated to exist in three forms: π⁺, π⁰, and π^– , all of spin zero, today called pions. The behavior of nuclear forces was explained as an exchange of pions. An example is shown in the figure, where the neutron (lower right) emits a pion of negative electric charge to become a positive proton (upper right), while the proton (lower left) absorbs the pion to become a neutron (upper left).

Incidental experimental observation of the muon or μ-meson in 1936 appeared to provide the π^– meson needed by the theory, but soon it was found that the muon did not interact with the nucleus and had spin 1/2 (it is a lepton). Later, in 1947, the actual π-meson or pion was discovered, and the pion did interact with the nucleus. Today all three pions have been observed, π⁺, π^–, and π⁰, the last being the neutral pion found in 1950.

Pion properties

The main pion properties are tabulated below (overscores indicate antiparticles). Symbols u and d refer to the up-quark and the down-quark.

Pion properties

Symbol	Quark structure	Electric charge (units e)	Spin	Mass (MeV/c02)	Lifetime (s)	Main decay mode
$\pi ^{+}$	$u{\overline {d}}$	+1	0	139.5708	2.6033 × 10−8	$\pi ^{+}\rightarrow \mu ^{+}+\nu _{\mu }$
$\pi ^{-}$	${\overline {u}}d$	−1	0	139.5708	2.6033 × 10−8	$\pi ^{-}\rightarrow \mu ^{-}+{\overline {\nu }}_{\mu }$
$\pi ^{0}$	$u{\overline {u}}$	0	0	134.9766	0.84 × 10−16	$\pi ^{0}\rightarrow \gamma +\gamma$

In the Standard Model the pions are colorless: the antiquark of the quark-antiquark pair must possess the anticolor of the quark.

Modern formulation

See also the articles Quark and Standard Model

Today a more refined theory of nuclear interactions is based upon the Standard Model. In that model, pions are considered to be quark-antiquark pairs. As indicated in the table above, the π^– is a d-quark combined with a ū-antiquark, and a π⁺ is the other way around, making each the antiparticle of the other. The π⁰ is a u-quark combined with a ū-antiquark, and therefore its own antiparticle. Because the pions are colorless (the anti-quark in a pion always has the anti-color to the quark, regardless of its flavor), their exchange between nucleons is not a simple color exchange, but a residual color force sometimes referred to as a color van der Waals force, an analogy to the weak electromagnetic attraction between electric charge-neutral atomic complexes. In any event, nuclear forces are not considered fundamental today, but are a consequence of the underlying strong forces between quarks, also called chromodynamic forces or color forces. On that basis, nuclear forces are fundamentally based upon color, and only approximated by the Yukawa theory.