Supercritical fields

Supercritical fields

Static fields that are strong enough to cause the normal vacuum, which is devoid of real particles, to break down into a new vacuum in which real particles exist. This phenomenon has not yet been observed for electric fields, but it is predicted for these fields as well as others such as gravitational fields and the gluon field of quantum chromodynamics.

Vacuum decay in quantum electrodynamics

The original motivation for developing the new concept of a charged vacuum arose in the late 1960s in connection with attempts to understand the atomic structure of superheavy nuclei expected to be produced by heavy-ion linear accelerators. See Particle accelerator

The best starting point for discussing this concept is to consider the binding energy of atomic electrons as the charge Z of a heavy nucleus is increased. If the nucleus is assumed to be a point charge, the total energy E of the 1s1/2 level drops to 0 when Z = 137. This so-called Z = 137 catastrophe had been well known, but it was argued loosely that it disappears when the finite size of the nucleus is taken into account. However, in 1969 it was shown that the problem is not removed but merely postponed, and reappears around Z = 173. Any level E(nj) can be traced down to a binding energy of twice the electronic rest mass if the nuclear charge is further increased. At the corresponding charge number, called Zcr, the state dives into the negative-energy continuum of the Dirac equation (the so-called Dirac sea). The overcritical state acquires a width and is spread over the continuum. See Antimatter, Relativistic quantum theory

When Z exceeds Zcr a K-shell electron is bound by more than twice its rest mass, so that it becomes energetically favorable to create an electron-positron pair. The electron becomes bound in the 1s1/2 orbital and the positron escapes. The overcritical vacuum state is therefore said to be charged. See Positron

Clearly, the charged vacuum is a new ground state of space and matter. The normal, undercritical, electrically neutral vacuum is no longer stable in overcritical fields: it decays spontaneously into the new stable but charged vacuum. Thus the standard definition of the vacuum, as a region of space without real particles, is no longer valid in very strong external fields. The vacuum is better defined as the energetically deepest and most stable state that a region of space can have while being penetrated by certain fields.

Superheavy quasimolecules

Inasmuch as the formation of a superheavy atom of Z > 173 is very unlikely, a new idea is necessary to test these predictions experimentally. That idea, based on the concept of nuclear molecules, was put forward in 1969: a superheavy quasimolecule forms temporarily during the slow collision of two heavy ions. It is sufficient to form the quasimolecule for a very short instant of time, comparable to the time scale for atomic processes to evolve in a heavy atom, which is typically of the order 10-18 to 10-20. Suppose a uranium ion is shot at another uranium ion at an energy corresponding to their Coulomb barrier, and the two, moving slowly (compared to the K-shell electron velocity) on Rutherford hyperbolic trajectories, are close to each other (compared to the K-shell electron orbit radius). Then the atomic electrons move in the combined Coulomb potential of the two nuclei, thereby experiencing a field corresponding to their combined charge of 184. This happens because the ionic velocity (of the order of c/10) is much smaller than the orbital electron velocity (of the order of c), so that there is time for the electronic molecular orbits to be established, that is, to adjust to the varying distance between the charge centers, while the two ions are in the vicinity of each other. See Quasiatom

Giant nuclear systems

The energy spectrum for positrons created in, for example, a uranium-curium collision consists of three components: the induced, the direct, and the spontaneous, which add up to a smooth spectrum. The presence of the spontaneous component leads only to 5–10% deviations for normal nuclear collisions along Rutherford trajectories. This situation raises the question as to whether there is any way to get a clear qualitative signature for spontaneous positron production. Suppose that the two colliding ions, when they come close to each other, stick together for a certain time Δt before separating again. The longer the sticking, the better is the static approximation. For Δt very long, a very sharp line should be observed in the positron spectrum with a width corresponding to the natural lifetime of the resonant positron-emitting state. The observation of such a sharp line will indicate not only the spontaneous decay of the vacuum but also the formation of giant nuclear systems (Z > 180). See Linewidth, Nuclear molecule

Search for spontaneous positron emission

The search for spontaneous positron emission in heavy-ion collisions began in 1976. Of special interest are peak structures in the positron energy distribution. However, the issue of spontaneous positron production in strong fields remains open. If line structures have been observed at all, they are most likely due to nuclear conversion processes. The observation of vacuum decay very much depends on the existence of sufficiently long-lived (at least 10-20 s) giant nuclear molecular systems. Therefore, the investigation of nuclear properties of heavy nuclei encountering heavy nuclei at the Coulomb barrier is a primary task.

Other field theories

The idea of overcriticality also has applications in other field theories, such as those of pion fields, gluon fields (quantum chromodynamics), and gravitational fields (general relativity).

A heavy meson may be modeled as an ellipsoidal bag, with a heavy quark Q and antiquark located at the foci of the ellipsoid. The color-electric or glue-electric field lines do not penetrate the bag surface. The Dirac equation may be solved for light quarks q and antiquarks in this field of force. In the spherical case the potential is zero, and the solutions with different charges degenerate. As the source charges Q and are pulled apart, the wave functions start to localize. At a critical deformation of the bag, positive and negative energy states cross; that is, overrcriticality is reached and the color field is strong enough that the so-called perturbative vacuum inside the bag rearranges so that the wave functions are pulled to opposite sides and the color charges of the heavy quarks are completely shielded. Hence two new mesons of types q and Qappear; the original meson fissions. See Gluons, Quantum chromodynamics, Quarks

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.