The Two Centre Dirac Equation

Abstract

During collisions of heavy ions with heavy targets below the Coulomb barrier, adiabatic molecular orbitals are formed for the inner electrons. Deviations from adiabaticity lead to coupling between various states and can be treated by time-dependent perturbation theory. For high charges (Z1+Z2 60) the molecular electrons are highly relativistic. Therefore, the Dirac equation has to be used to obtain the energies and wave functions. The Dirac Hamiltonian is transformed into the intrinsic rotating coordinate system where prolate spheroidal coordinates are introduced. A set of basis functions is proposed which allows the evaluation of all matrix elements of the Dirac Hamiltonian analytically. The resulting matrix is diagonalized numerically. The finite nuclear charge distribution is also taken into account. Results are presented and discussed for various characteristic systems, e. g. Br-Br, Ni-Ni, I-I, Br-Zr, I-Au, U -U, etc.

Relativistic effects in the variable-screening model

“…In relation to the "unscreened" Br+Br correlation diagram calculated from the two-center Dirac equation by Miiller et al [12,13], the diagram shown in Figure 2 exhibits, of course, much smaller binding energies of the electronic levels. A direct comparison with the results of [12,13] becomes possible by using our numerical procedure and the approximation (6) to calculate energy curves for the unscreened Br + Br system.…”

“…The corresponding curves in the non-relativistic approximation are also shown; these agree well with the results of [34], scaled to Z=35. Our values for the parameters characterizing the 2(1/2)g-3(1/2)g pseudocrossing are tabulated in Table 4 and contrasted to those of [13]. The disagreement is striking and cannot be explained merely as a consequence of the neglect of higher-order terms in (6).…”

“…A direct comparison with the results of [12,13] becomes possible by using our numerical procedure and the approximation (6) to calculate energy curves for the unscreened Br + Br system. We concentrate here on the 2(1/2)g-3(1/2)g pseudocrossing which has been studied in detail in [13].…”

“…The quasimolecular Br+Br system has been studied experimentally by Meyerhof et al [4], and the twocenter Dirac equation for one electron in the field of two Br nuclei has been solved numerically by Mtiller et al [12,13]. Therefore, the application of the relativistic VSM to this system seems to be particularly interesting.…”

“…In the last few years, several fully self-consistent, non-relativistic molecularorbital Hartree-Fock calculations have been performed [11] for lighter quasimolecular systems, showing that the influence of screening causes appreciable deviations of the correlation diagrams from the corresponding "unscreened" diagrams. Relativistic effects, on the other hand, have been studied by Miiller et al [12,13] in a numerical solution of the Dirac equation for one electron in the field of two unscreened nuclei (taking into account for "overcritical" systems, with a combined nuclear charge equal to or greater than 137, the finite extension of the nuclear charge distributions). Furthermore, relativistic corrections have been applied [14] to the results of a non-relativistic Hartree-Fock calculation on a 20-electron system simulating the highly ionized I + Au system.…”