Those working outside theoretical nuclear physics might be surprised to discover that, to this day, there remains no unified model of the atomic nucleus. Instead, a variety of techniques and models exist, each having some utility, but each becoming invalid when pushed outside its comfort zone.
For example, the Liquid Drop Model, first developed in the 1930s, provides an excellent explanation of nuclear fission by treating the neutrons and protons in a nucleus as a collective entity. The Liquid Drop Model, however, fails to explain why nuclei containing certain numbers of protons and neutrons are particularly stable. The Nuclear Shell Model, developed in 1949, provides an explanation for the latter by treating each neutron and proton as if it were an individual entity residing in a mean field created by all the other neutrons and protons in the nucleus.
The neutrons and protons in an atomic nucleus consist of quarks interacting with each other via the strong nuclear force. Hence, in principle, the fundamental theory of an atomic nucleus should be Quantum Chromodynamics, the application of quantum field theory to strong force interactions. Quantum field theory, however, is beset with difficulties when tasked with the representation of interactions, and whilst so-called perturbative renormalization provides the computational recipes to paper over these problems in Quantum Electrodynamics, (the application of quantum field theory to electromagnetic interactions), Quantum Chromodynamics becomes quite intractable when faced with nuclear structure.
A variety of nuclear models have been developed in lieu of a tractable fundamental theory, one of which is the so-called MIT Bag Model. This represents a neutron or proton as consisting of three non-interacting quarks, confined within a fixed spherical volume. The mass of a neutron or proton is then determined by summing the kinetic energies of the quarks and the potential energy of the whole bag. Each quark in the MIT Bag Model is represented as a Dirac spinor field which satisfies the relativistic Dirac equation. The quarks are therefore represented in the style of what's called first-quantized relativistic quantum theory, rather than the second quantized theory, quantum field theory proper.
Now, the standard model of particle physics considers the only possible bound states of quarks to consist of quark-antiquark pairs (mesons), and quark triplets (baryons) such as the neutrons and protons in an atomic nucleus. However, an application of the MIT Bag Model by Robert Jaffe in 1977 suggested that there may be more exotic bound quark states, such as tetraquarks and hexaquarks.
Intriguingly, physicists in Germany and Pakistan now suggest that data collected by the KEK particle collider in Japan in 2008 can best be explained by postulating that the collider created a tetraquark called Yb(10890). If so, it would demonstrate once more that a lack of fundamental understanding is not necessarily a barrier to achieving progress in physics.