Collisions of very heavy ions at energies close to the Coulomb barrier are discussed as a unique tool to study the behavior of the electron-positron field in the presence of strong extemal electromagnetic fields. To calculate the excitation processes induced by the collision dynamics, a semiclassical model is employed and adapted to describe the field-theoretical many-particle system. An expansion in the adiabatic molecular basis is chosen. Energies and matrix elements are calculated using the monopole approximation. In a supercritical (2, + Z, 2 173) quasiatomic system the 1s level joins the antiparticle continuum and becomes a resonance, rendering the neutral vacuum state unstable. Several methods of treating the corresponding time-dependent problem are discussed. A projectionOperator technique is introduced for a fully dynamical treatment of the resonance. Positron excitation rates in s„, andp,,] states are obtained by numencal solution of the coupled-channel equations and are compared with results from first- plus second-order perturbation theory. Calculations are performed for subcritical and supercritical collisions of Pb-Pb, Pb-U, U-U, and U-Cf. Strong relativistic deformations of the wave functions and the growing contributions from inner-shell bound states lead to a very steep Z dependence of positron production. The results are compared with available data from experiments done at GSI. Correlations between electrons and positrons are briefly discussed.

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Theory of positron production in heavy-ion collisions

Review of the SCA method for inner shell ionization - results, limitations and possibilities

We calculate the ionization probability of the quasimolecular 1sσ-state in collisions of very heavy ions with (Z
1+Z
2) α≳1. Multistep excitation processes between bound and continuum states are investigated. Due to the multistep processes the number of created 1sσ-vacancies is typically increased by a factor 2–5 over that obtained within time-dependent perturbation theory (i.e. the one-step processes). Some implications of the many-electron problem and the Pauli principle are discussed. The δ-electron distribution is compared with recent experimental data.

Coupled channel analysis of inner-shell vacancy formation in superheavy quasimolecules

An analytical formula for the excitation probability of the quasimolecular 1sσ orbital as a function of the impact parameterb is derived for collision systems withα(Z1+Z2)≳1. This formula describes well all existing experimental data for those collision systems except for the heaviest system Pb+Cm (Z1+Z2=178) at impact parametersb≲40 fm. It is discussed in which way energies of the quasimolecular 1sσ orbital can be extracted from experimental 1sσ vacancy production data.

The quasimolecular 1sσ orbital in collision systemsα(Z1+Z2)≳1, its excitation and spectroscopy

Electron excitations in superheavy quasimolecules

From 90° line width analysis ofKα1 lines excited in very heavy ion-atom collisions (Z1 +Z2>137) mean impact parameters for the ionization probability are derived. The experimental mean impact parameters are shown to obey the Bang-Hansteen scaling rule¯bE(R)=C · ħv correlating the minimum momentum transferE(R)/v and the mean impact parameterb. Theoretical values of the constantC are (0.8±0.1) for 2p1/2σ excitation and (1.0±0.1) for 1sσ excitation in the rangeZ1+Z2=140–160. It is proposed to apply the scaling rule as a spectroscopic tool to study the 1sσ and 2p1/2σ levels in superheavy quasimolecules. The need of a sound theoretical base justifying the application of the scaling rule is emphasized.

A tool for spectroscopy of super-heavy quasimolecules (Z 1+Z 2>137) the Bang-Hansteen scaling rule

Projectile and targetK-shell ionization cross sections induced by 3.6-, 4.7-, and 5.9 MeV/u132Xe ions and 1.4-, 3.6-, 4.7-, and 5.9 MeV/u208Pb ions from the UNILAC in thin solid targets between C and U are measured. The cross sections are discussed in terms of the molecular model of innershell vacancy production in heavy ion-atom collisions. The sharing of 2p
1/2σ vacancies between theK shells of the two collision partners in these very heavy ion-atom collisions is found to deviate from the Meyerhof-Demkov formula forR≦10−2. The measured ionization cross sections are compared with theoretical calculations for 1sσ and 2p
1/2σ excitation cross sections. AZ
UA=Z1+Z
2 dependence is found independent ofZ
1/Z
2. Outer-shell vacancy configurations measured in these close encounters are reported.

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Measurements of K-shell ionization with 132 Xe and 208 Pb projectiles in the energy range of 1.4 5.9 MeV/u

Using particle x-ray coincidence techniques, the probability to produceK-shell vacancies in 4.7 MeV/u Pb+Z2 (42≦Z2≦92) collisions for impact parametersb<100 fm was measured. For these impact parameters, the 1sσ excitation probability is greater than 1 σ 10−2 and the 2p1/2σ excitation probability is greater than 1 σ 10−1. Binding energies of the 1sσ state derived from the measured probabilities agree well with theoretical calculations.

Measurements of the probability for 1 sσ excitation in very heavy ion-atom-collisions and determination of the binding energy of the 1 σ molecular orbital

Using particle x-ray coincidence techniques, the probability forK shell ionization has been measured absolutely at two impact parameters for collisions of 5.8 MeV/amu208Pb on Ag and Au. In the asymmetric collision system Pb-Ag, the 1sσ excitation probability of the PbK shell is 2.2% at 25 fm impact parameter, and an exponential probability distribution falls off too quickly to account for the measured total cross section. For the symmetric system Pb-Au, the latter conclusion is also made for the 2pσ excitation probability although in this case, the probability is much larger being 29% at 42 fm.

An absolute measurement of the probability for 1 s σ and 2 p σ excitation of the lead K shell

Projectile (Z
1) and target (Z
2)K-vacancy production cross sections induced by 3.6-, 4.75-, and 5.9-MeV/amu238U ions in selected targets between C and U are reported. The cross sections are discussed within the context of the molecular model of inner-shell vacancy production in heavy-ion-atom collisions. The measured 1sσ and 2pσ excitation cross sections are compared with semiempirical formulas, and with the perturbed-stationary-states calculations of Betz et al. The dependence of these cross sections onZ

 u
 =Z1+Z
2 agrees well with the Betz calculations. However, the measured cross sections are factors of 2 to 4 (1sσ) and 4 to 5 (2pσ) larger than the theoretical values.

P. H. Mokler

Papers

A tool for spectroscopy of super-heavy quasimolecules (Z 1+Z 2>137) the Bang-Hansteen scaling rule

Measurements of K-shell ionization with 132 Xe and 208 Pb projectiles in the energy range of 1.4 5.9 MeV/u

Measurements of the probability for 1 sσ excitation in very heavy ion-atom-collisions and determination of the binding energy of the 1 σ molecular orbital

An absolute measurement of the probability for 1 s σ and 2 p σ excitation of the lead K shell

K-vacancy production by 3.6-, 4.75-, and 5.9-MeV/amu 238 U Ions