General Information

The working group for Nuclear Physics and Nuclear Astrophysics at the Atomic Institute deals with the fundamental interactions. In the domain of nuclear physics this is mainly the strong interaction. Connected with this is the research on the strongly interacting particles, the hadrons. The internal structure of the hadrons, which are built up of quarks, is described by quantum chromodynamics (QCD). Members of the group are working in one of the most active branches of this theory, Lattice QCD.
Another focus of interest is the investigation of a special type of wave phenomena, the so-called solitons. These phenomena throw new light on the wave-particle dualism and may lead to a deeper understanding of the wave character of elementary particles.

Experimentally, the strong interaction manifests itself as the interaction between nucleons. The nucleon-nucleon interaction is characterized by high strength and short range. It is caused by the virtual emission and absorption of field quanta, in which process energy conservation is temporarily violated. However, this is permissible within the bounds set by Heisenberg's uncertainty relation. A finite range of the force indicates a finite rest mass of the exchange particles. The quanta of the electromagnetic field, the photons, have rest mass zero. Therefore, the range of the electromagnetic interaction is infinite. After estimating the rest mass based on the range, the pions were identified as the quanta of the strong interaction.

In 1938, Hideki YUKAWA (Japanese Nobel prize laureate, 1907 - 1981) suggested a differential equation for the field of the nuclear force, in analogy to the electromagnetic field. In contrast, the nucleon-nucleon-(Yukawa-)potential falls off more rapidly than the electromagnetic one, and acts repulsively at short distances, which explains the finite density of atomic nuclei.

Figure: Schematic drawing of the potential between two nucleons

The complex character of the nuclear force at separations below 1.2 fm gives a hint that the internal quark structure of the hadrons cannot be neglected anymore when the nucleons begin to overlap. A more fundamental force enters the scene, namely the color force between quarks, the actual origin of the strong interaction.

The strongly interacting particles, the hadrons, vary in their physical properties. These "inner" qualities are determined by the mass (rest energy) and the following quantum numbers: spin angular momentum, and electric charge Q. Particles with nearly equal mass are grouped together and one assignes to them an additional property, the hypercharge Y, which is calculated from the double charge center (average of the charges within a group). Finally, one introduces the isospin I₃ = Q - 2Y. Like particles, which differn only in their charge, belong to so-called isospin multiplets. For example, the nucleons - neutron and proton - form an isospin doublet (n,p). Among the mesons we find the triplet consisting of the pions ((π^-,π⁰,π⁺). If the particle multiplets are plotted in a I₃-Y-coordinate system, one obtains geometric figures of remarkable shape.

The origin of these symmetric patterns can be understood with the help of the SU(3) algebra. All multiplet shapes are built up from fundamental cells, the SU(3) triplets. These contain those three quarks which are the constituents of the hadrons in the multiplets: The up, down and strange quark can be combined to a quark triplet, while their antiparticles form an antitriplet.

According to the quark model, the baryons are bound states of three quarks, whereas mesons are bound states of a quark and an antiquark. One can verify that these combinations yield the required properties by adding the quark charges and hypercharges, as given in quark-antiquark-table, and comparing the results with the corresponding baryon and meson quantum numbers.

Quantum Chromodynamics (QCD) describes the dynamics of the quarks, which interact via the gluon field. QCD is based on the notion that quarks possess a charge-like property, the "color". Color charges and color currents serve as sources of electric and magnetic color fields, the gluon fields. These ideas are described by the Maxwell equations of QCD. Contrary to electrodynamics, they are nonlinear equations since the gluons themselves also carry a color charge and hence interact with each other.

QCD is new theory based on the mentioned assumptions and cannot be derived from an underlying theory. One can only construct it in such that it is compatible with phsical experiments. QCD was first formulated in a paper of Fritzsch, Gell-Mann and Leutwyler in 1973.

QCD is the widely accepted theory for the strong interaction. It is formulated in the framework of quantum field theory, which describes the fundamental interactions by exchange particles. Predictive calculations are possible for phenomena at high energies, or equivalently, very short distances. Here the coupling constant is weak and perturbation theory is a useful tool. How the quarks are bound in the hadrons, however, is controlled by the large-scale behaviour of the coupling, which increases with distance. For such questions, lattice QCD is an indispensable technique, for example to compute the hadron spectrum.

Lattice QCD is QCD formulated on a discrete Euclidean spacetime lattice. LQCD preserves the fundamental character of QCD but realizes important improvements: first, the discrete spacetime lattice serves as a "regulator". A general feature of quantum field theories, and also QCD, is the occurrence of singularities. On the lattice, as long as the lattice constant a is finite, these singular quantities are rendered finite. Furthermore, the limit a → 0 is well-defined and leads to finite, so-called renormalized physical quantities. In contrast to the continuum, calculations can be performed even for high values of the coupling constant. Another advantage is that LQCD can be simulated numerically on the computer, using methods similar to those used in statistical mechanics.

A soliton is a wave package which travels through a dispersive, non-linear medium and yet preserves its shape while propagating. Two solitons which cross can even survive their collision unscathed.
A wave packet is composed of several, or a range of, frequencies. If the velocity of the wave in the medium is different at different frequencies (so-called dispersion), the package will be deformed and broaden in the course of time. Non-linear effects convert the individual frequencies, of which the wave package consists, in each other. If this happens in such a way that fast frequencies are transformed in slower ones and vice versa, then both effects can be in equilibrium and the wave shape remains unaltered: a soliton.
Solitons were first described in 1834 by the young engineer John Scott Russell. Russell rode several kilometers side by side to water wave, about 10 meters long and half a meter high, which propagated in a narrow scottish channel. He observed that the shape of the wave hardly changed. → Picture