Strong Coulomb Coupling of Charged Particles

Abstract

According to our present understanding of Quantum Electrodynamics of strong fields, we expect spontaneous pair production of electron positron pairs to occur in the external Coulomb field of a nucleus of charge Z when Z exceeds a critical value Zc ≈ 170.1 The corresponding critical value Z\(Z_{c}^{0}\) above which spontaneous creation of pion pairs (π−, π+) occurs is Z\(Z_{c}^{0}\approx {{10}^{4}}\), so that the interest for such phenomenon would seem quite academical. Nevertheless the study of scalar boson “condensation” is of theoretical interest for (at least) two reasons. First, boson condensation of charged scalar particles in a strong Coulomb field may give us some insight into the structure of the QCD vacuum and its gluon condensate.2 Second, it provides us with a simple model for the “restructuring” of the vacuum in a high density medium3 that may exist, for instance, in the collision of two heavy ions, inducing a state of matter under “extreme conditions”. Sections 2–3 are devoted to the discussion of this subject within classical electromagnetic field theory. We shall discuss in Sec. 4 a related topic which is being currently investigated in great detail in lattice QED,4 i.e. the much more complicated problem of two spin one-half charged particles in mutual strong Coulomb interaction. Our interest for such a problem stems from recent heavy-ion experiments at Darmstadt and the conjecture of a new phase of QED.5 We shall see that a reasonable non perturbative approach to the relativistic two-body problem leads to an equation whose eigenvalue spectrum is very different from the spectrum of the Klein-Gordon (or Dirac) equation and does not lead to the existence of a critical coupling strength above which spontaneous pair production may occur. Thus, a simple extrapolation of external field results to the problem of two mutually interacting particles may be quite misleading, at least if one trusts some reasonable two-body relativistic wave equations.