Walter Greiner

Induced radiative transitions of intermediate molecules in heavy ion collisions

Abstract Three types of transitions exists in intermediate molecules occuring in heavy ion scattering: spontaneous radiative, induced non-radiative, and induced radiative decay. The latter ones yield an asymmetric angular distribution for molecular X-rays with respect to the ion-beam axis. The experimental verification of this effect would furnish an experimentum crucis for both, the existence of molecular X-rays and the induced radiative transitions.

Limiting charge for point nuclei

Abstract We investigated the behavior of the vacuum charge around a supercritical nucleus h Z > 137 in dependence of the nuclear radius. The screening effects are considered in an effective potential approximation. We show that in the point nucleus limit the nuclear charge is screened by the vacuum charge up to Z = 137. This means that the coupling strength of a point charge in QED cannot be larger than 1. The influence of heavier leptons is also discussed briefly.

Aspects of supercritical heavy ion collisions

In collisions of very heavy ions “supercritically” strong electric fields can be created transiently. In the presence of a supercritical field the neutral vacuum state of QED becomes unstable and decays into a charged vacuum, signalled by the spontaneous emission of positrons. Consequently the emission of positrons is strongly enhanced in high-Z collisions. Clear experimental signals for spontaneous positron creation are still missing and could only be expected from collisions with a prolonged time scale. We discuss possible scenarios for this to happen and indirect methods to perform a spectroscopy of superheavy quasimolecules.

Spin-1 Fields: The Maxwell and Proca Equations

In field theory, particles of spin 1 are described as the quanta of vector fields. Such vector bosons play a central role as the mediators of interactions in particle physics. The important examples are the gauge fields of the electromagnetic (massless photons), the weak (massive W ± and Z 0 bosons), and the strong (massless gluons) interactions. On a somewhat less fundamental level vector fields can also be used to describe spin-1 mesons, for example the ρ and the ω meson.

Mathematical Excursion. Group Characters

In this chapter a special group theoretical concept is introduced which has many applications. It describes the main properties of representations and is therefore called “group character”. It solves the problem of how to describe the invariant properties of a group Ĝa , representation in a simple way. If we denote an element of a group G by Ĝ a representation Ď(Ĝ a) is not unambiguous, because every similarity transformation ÂĎ(Ĝa)Â-1, Â ∈ D(G) yields an equivalent form. One possibility for the description of the invariant properties would be to use the eigenvalues of the representation matrix, which do not change under a similarity transformation. This leads to the construction of the Casimir operators, the eigenvalues of which classify the representations. The construction of the Casimir operators and their eigenvalues is in general a very difficult nonlinear problem. Fortunately, in many cases it is sufficient to use a simpler invariant, namely the trace of the representation matrix n n n n(10.1) n nwhere d is the dimension of the matrix representation. Equation (10.1) is in fact invariant under similarity transformations, because n n n n(10.2) n nX(Ĝa) is called the “grup character” of the representation.

Quantization of the Photon Field

When quantizing the massive spin-1 field within the canonical formalism, we encountered the problem that the 0 component of the potential, A 0 (x), does not possess a conjugate field π 0(x) since the Lagrangian L does not depend on the time derivative of A 0. This did not have harmful consequences, however, since according to the Proca equation the time-like component of the field can be expressed as a dependent quantity: n n

Spin-0 Fields: The Klein-Gordon Equation

{A_0} = - frac{1}{{{m^2}}}nabla cdot E

The Reduction Formalism

n n(7.1) n n. Therefore it was sufficient to quantize the three space-like components of the vector field, in agreement with the three physical polarization states of a massive vector particle. Contrary to superficial evidence this quantization procedure proved to be relativistically covariant (see (6.98)).