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Fri, 14 Jul 2006 10:41:26 +0200Fri, 14 Jul 2006 10:41:26 +0200Quantum-mechanical treatment of high-energy channeling radiation
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2379
An alternative theoretical description of axial electron channeling in the multi-GeV region has been developed. We solve a kinetic equation to evaluate an electron distribution function in axially oriented single crystals. Based on the single-string model, the required matrix elements for radiation and scattering by lattice vibrations are calculated employing solutions of the Dirac equation in cylindrical coordinates. Results obtained for 150-GeV electrons propagating along the 〈110〉 axis of germanium are in good agreement with experimental observations.Jürgen Augustin; Andreas Schäfer; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2379Fri, 14 Jul 2006 10:41:26 +0200Cold-fission yields at effective excitation energies
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2378
The experimental cold-fission yields for the system 233U(nth, f) are analyzed as function of the effective total excitation energy (TXE). The nuclear level density effect is taken into account at higher TXE, in order to benefit by the lower experimental data uncertainty as well as to avoid the quantitative account of the level densities close to fragment ground states. In this way the odd-even staggering which appears in the yields extrapolated at zero excitation energy by using the level densities, vanishes. We conclude that the cold nuclear fragmentation theory including the dynamical model describes well the experimental data.Vlad-Gabriel Avrigeanu; A. Florescu; Aurel Săndulescu; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2378Fri, 14 Jul 2006 10:37:14 +0200Two-dimensional nuclear inertia : analytical relationships
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2377
The components of the nuclear inertia tensor, functions of the separation distance R and of the radius of the light fragment R2, BRR(R,R2), BRR2(R,R2), and BR2R2(R,R2) are calculated within the Werner-Wheeler approximation, by using the parametrization of two intersected symmetric or asymmetric spheres. Analytical relationships are derived. When projected to a path R2=R2(R), the reduced mass is obtained at the touching point. The two one-dimensional parametrizations with R2=const, and the volume V2=const previously studied, are found to be particular cases of the present more general approach. Illustrations for the cold fission, cluster radioactivity, and α decay of 252Cf are given.Radu A. Gherghescu; Walter Greiner; Dorin N. Poenaruarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2377Fri, 14 Jul 2006 10:32:02 +0200Channeling process in a bent crystal
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2376
We have investigated the channeling process of charged particles in a bent crystal. Invoking simple assumptions we derive a criterion, which determines whether channeling occurs or not. We obtain the same criterion using the Dirac equation. It is shown that the centrifugal force acting on the particle in the bent crystal significantly alters the effective transverse potential. The cases of axial and planar channeling are considered. The channeling probability and the dechanneling probability due to tunneling of the particle under the barrier in the effective transverse potential are estimated. These probabilities depend on the specific scaling parameter characterizing the process. Using the quasiclassical theory of synchrotron radiation we have calculated the contribution to the radiation spectrum, which arises due to the curvature of the channel. This contribution becomes significant to TeV electrons or positrons. Some practical consequences of our results are briefly discussed.Andrey V. Solov'yov; Andreas Schäfer; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2376Fri, 14 Jul 2006 10:28:15 +0200Cluster description of cold (neutronless) alpha ternary fission of 252Cf
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2387
A coplanar three body cluster model (two deformed fragments and an alpha particle) similar to the model used for the description of cold binary fission was employed for the description of cold (neutronless) alpha accompanied fission of 252Cf. No preformation factors were considered. The three body potential was computed with the help of a double folding potential generated by the M3Y-NN effective interaction and realistic fragment ground state deformations. From the minimum action principle, the alpha particle trajectory equations, the corresponding ternary barriers, and an approximate WKB expression for the barrier penetrability are obtained. The relative cold ternary yields were calculated as the ratio of the penetrability of a given ternary fragmentation and the sum of the penetrabilities of all possible cold ternary fragmentations. Different scenarios were considered depending on the trajectories of the fragments. It was shown that two regions of cold fragmentation exist, a deformed one corresponding to large fragment deformations and a spherical one around 132Sn, similarly to the case of the cold binary fission of 252Cf. We have shown that for the scenario corresponding to the Lagrange point, where all forces acting on the alpha particle are in equilibrium, the cold alpha ternary yields of 252Cf are strongly correlated with the cold binary yields of the daughter nucleus 248Cm into the same heavy fragments. For all other scenarios only the spherical splittings are favored. We concluded that due to the present available experimental data on cold alpha ternary yields only the Lagrange scenario could describe the cold alpha ternary fission of 252Cf.Aurel Săndulescu; F. Carstoiu; Ionel Bulboaca; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2387Fri, 14 Jul 2006 10:20:20 +0200Cold fission as cluster decay with dissipation
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2386
For cold (neutronless) fission we consider an analytical model of quantum tunneling with dissipation through a barrier U(q) evaluated with a M3Y nucleon-nucleon force. We calculate the tunneling spectrum, i.e., the fission rate as a function of the total kinetic energy of the fragments. The theoretical results are compared with the experimental data obtained for the fine structure of two cold fission modes of 252Cf: 148Ba+104Mo and 146Ba+106Mo. Taking into account the dissipative coupling of the potential function U(q) and of the momentum p with all the other neglected coordinates, we obtain a remarkable agreement with the experimental data. We conclude that the cold fission process is a spontaneous decay with a spectrum determined by the shape of the barrier and an amplitude depending on the strength of the dissipative coupling.E. Stefanescu; Werner Scheid; Aurel Săndulescu; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2386Fri, 14 Jul 2006 10:18:06 +0200Prospects for parity-nonconservation experiments with highly charged heavy ions
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2385
We discuss the prospects for parity-nonconservation experiments with highly charged heavy ions. Energy levels and parity mixing for heavy ions with 2–5 electrons are calculated. We investigate two-photon transitions and the possibility of observing interference effects between weak-matrix elements and Stark matrix elements for periodic electric field configurations.M. Maul; Andreas Schäfer; Walter Greiner; Paul Indelicatoarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2385Fri, 14 Jul 2006 10:17:31 +0200Self-energy correction to the hyperfine structure splitting of hydrogenlike atoms
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2384
A first testing ground for QED in the combined presence of a strong Coulomb field and a strong magnetic field is provided by the precise measurement of the hyperfine structure splitting of hydrogenlike 209Bi. We present a complete calculation of the one-loop self-energy correction to the first-order hyperfine interaction for various nuclear charges. In the low-Z regime we almost perfectly agree with the Z alpha expansion, but for medium and high Z there is a substantial deviation.Hans Persson; Stefan M. Schneider; Walter Greiner; Gerhard Soff; Ingvar Lindgrenarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2384Fri, 14 Jul 2006 10:16:51 +0200Structure of the vacuum in nuclear matter: a nonperturbative approach
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2383
We compute the vacuum polarization correction to the binding energy of nuclear matter in the Walecka model using a nonperturbative approach. We first study such a contribution as arising from a ground-state structure with baryon-antibaryon condensates. This yields the same results as obtained through the relativistic Hartree approximation of summing tadpole diagrams for the baryon propagator. Such a vacuum is then generalized to include quantum effects from meson fields through scalar-meson condensates which amounts to summing over a class of multiloop diagrams. The method is applied to study properties of nuclear matter and leads to a softer equation of state giving a lower value of the incompressibility than would be reached without quantum effects. The density-dependent effective sigma mass is also calculated including such vacuum polarization effects.Amruta Mishra; P. K. Panda; Stefan Schramm; Joachim Reinhardt; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2383Fri, 14 Jul 2006 10:15:51 +0200Transition to delta matter from hot, dense nuclear matter within a relativistic mean field formulation of the nonlinear sigma and omega model
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2382
An investigation of the transition to delta matter is performed based on a relativistic mean field formulation of the nonlinear sigma and omega model. We demonstrate that in addition to the Delta-meson coupling, the occurrence of the baryon resonance isomer also depends on the nucleon-meson coupling. Our results show that for the favored phenomenological value of m* and K, the Delta isomer exists at baryon density ~ 2–3 p0 if beta=1.31 is adopted. For universal coupling of the nucleon and Delta, the Delta density at baryon density ~ 2–3 p0 and temperature ~ 0.4–0.5 fm-1 is about normal nuclear matter density, which is in accord with a recent experimental finding.Zhuxia Li; Guangjun Mao; Yizhong Zhuo; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2382Fri, 14 Jul 2006 10:15:10 +0200Hot nuclear matter in the quark meson coupling model
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2381
We study here hot nuclear matter in the quark meson coupling model which incorporates explicitly quark degrees of freedom, with quarks coupled to scalar and vector mesons. The equation of state of nuclear matter including the composite nature of the nucleons is calculated at finite temperatures. The calculations are done taking into account the medium-dependent bag constant. Nucleon properties at finite temperatures as calculated here are found to be appreciably different from the value at T=0.P. K. Panda; Amruta Mishra; Judah M. Eisenberg; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2381Fri, 14 Jul 2006 10:14:40 +0200Role of the higher static deformations of fragments in the cold binary fission of 252Cf
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2393
We study the binary cold fission of 252Cf in the frame of a cluster model where the fragments are born to their respective ground states and interact via a double-folded potential with deformation effects taken into account up to multipolarity lambda=4. The preformation factors were neglected. In the case when the fragments are assumed to be spherical or with ground-state quadrupole deformation, the Q-value principle dictates the occurrence of a narrow region around the double magic 132Sn, like in the case of cluster radioactivity. When the hexadecupole deformation is turned on, an entire mass region of cold fission in the range 138–156 for the heavy fragment arise, in agreement with the experimental observations. This fact suggests that in the above-mentioned mass region, contrary to the usual cluster radioactivity where the daughter nucleus is always a neutron/proton (or both) closed shell or nearly closed shell spherical nucleus, the clusterization mechanism seems to be strongly influenced by the hexadecupole deformations rather than the Q value.Aurel Săndulescu; Serban Misicu; Florin Carstoiu; A. Florescu; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2393Fri, 14 Jul 2006 10:14:00 +0200Potential energy surfaces of superheavy nuclei
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2392
We investigate the structure of the potential energy surfaces of the superheavy nuclei 158258Fm100, 156264Hs108, 166278112, 184298114, and 172292120 within the framework of self-consistent nuclear models, i.e., the Skyrme-Hartree-Fock approach and the relativistic mean-field model. We compare results obtained with one representative parametrization of each model which is successful in describing superheavy nuclei. We find systematic changes as compared to the potential energy surfaces of heavy nuclei in the uranium region: there is no sufficiently stable fission isomer any more, the importance of triaxial configurations to lower the first barrier fades away, and asymmetric fission paths compete down to rather small deformation. Comparing the two models, it turns out that the relativistic mean-field model gives generally smaller fission barriers.Michael Bender; Klemens Rutz; Paul-Gerhard Reinhard; Joachim A. Maruhn; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2392Fri, 14 Jul 2006 10:13:20 +0200Coulomb effects on electromagnetic pair production in ultrarelativistic heavy-ion collisions
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2391
We calculate the asymptotic high-energy amplitude for electrons scattering at one ion, as well as at two colliding ions, by means of perturbation theory. We show that the interaction with one ion eikonalizes and that the interaction with two ions causally decouples. We are able to put previous results on perturbative grounds and propose further applications for the obtained rules for interactions on the light cone. We discuss the implications of the eikonal amplitude on the pair production probability in ultrarelativistic peripheral heavy-ion collisions. In this context the Weizsäcker-Williams method is shown to be exact in the ultrarelativistic limit, irrespective of the produced particles’ mass. A new equivalent single-photon distribution is derived, which correctly accounts for Coulomb distortions. The impact on single-photon induced processes is discussed.U. Eichmann; Joachim Reinhardt; Stefan Schramm; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2391Fri, 14 Jul 2006 10:12:20 +0200Shell structure of superheavy nuclei in self-consistent mean-field models
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2390
We study the extrapolation of nuclear shell structure to the region of superheavy nuclei in self-consistent mean-field models—the Skyrme-Hartree-Fock approach and the relativistic mean-field model—using a large number of parametrizations which give similar results for stable nuclei but differ in detail. Results obtained with the folded-Yukawa potential which is widely used in macroscopic-macroscopic models are shown for comparison. We focus on differences in the isospin dependence of the spin-orbit interaction and the effective mass between the models and their influence on single-particle spectra. The predictive power of the mean-field models concerning single-particle spectra is discussed for the examples of 208Pb and the spin-orbit splittings of selected neutron and proton levels in 16O, 132Sn, and 208Pb. While all relativistic models give a reasonable description of spin-orbit splittings, all Skyrme interactions show a wrong trend with mass number. The spin-orbit splitting of heavy nuclei might be overestimated by 40%–80%, which exposes a fundamental deficiency of the current nonrelativistic models. In most cases the occurrence of spherical shell closures is found to be nucleon-number dependent. Spherical doubly magic superheavy nuclei are found at 184298114, 172292120, or 184310126 depending on the parametrization. The Z=114 proton shell closure, which is related to a large spin-orbit splitting of proton 2f states, is predicted only by forces which by far overestimate the proton spin-orbit splitting in 208Pb. The Z=120 and N=172 shell closures predicted by the relativistic models and some Skyrme interactions are found to be related to a central depression of the nuclear density distribution. This effect cannot appear in macroscopic-microscopic models or semiclassical approaches like the extended Thomas-Fermi-Strutinski integral approach which have a limited freedom for the density distribution only. In summary, our findings give a strong argument for 172292120 to be the next spherical doubly magic superheavy nucleus.Michael Bender; Klemens Rutz; Paul-Gerhard Reinhard; Joachim A. Maruhn; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2390Fri, 14 Jul 2006 10:11:29 +0200Vacuum-polarization contribution to the hyperfine-structure splitting of hydrogenlike atoms
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2407
A calculation of the vacuum-polarization contribution to the hyperfine splitting for hydrogenlike atoms is presented. The extended nuclear charge distribution is taken into account. For the experimentally interesting case 209Bi82+ we predict a delta-lambda- -1.6 nm shift for the transition wavelength of the ground-state hyperfine splitting.Stefan M. Schneider; Walter Greiner; Gerhard Soffarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2407Wed, 12 Jul 2006 10:17:26 +0200Induced decay of composite JPC=1++ particles in atomic Coulomb fields
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2406
The electron-positron pairs observed in heavy-ion collisions at Gesellschaft für Schwerionen-forschung Darmstadt mbH have been interpreted as the decay products of yet unknown particles with masses around 1.8 MeV. The negative results of resonant Bhabha scattering experiments, however, do not support such an interpretation. Therefore we focus on a more complex decay scenario, where the e+e- lines result from a two-collision process. We discuss the induced decay of a metastable 1++ state into e+e- pairs. For most realizations of a 1++ state such a decay in leading order can only take place in the Coulomb field of a target atom. This fact has the attractive consequence that for such a state the Bhabha bounds are no longer valid. However, the absolute value of the e+e- production cross section turns out to be unacceptably small.E. Stein; J. Reinhardt; Andreas Schäfer; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2406Wed, 12 Jul 2006 10:14:06 +0200Photon-photon interaction in axial channeling
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2405
We investigate the possibility that high-energy photons are channeled, when passing through an oriented single crystal, due to Delbrück scattering. For this purpose the exact electron propagator for the single-string model is constructed. Starting from a separation of variables, we solve the Dirac equation for a cylindrical electrostatic potential. The propagator for such external fields is constructed from solutions of the radial Dirac equation. This propagator is applied to a calculation of the S matrix for Delbrück scattering. We specify the conditions under which photon channeling takes place. Unfortunately these conditions are only matched for a very small fraction of those photons being produced by channeled electrons.J. Klenner; Jürgen Augustin; Andreas Schäfer; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2405Wed, 12 Jul 2006 10:02:26 +020012C emission from 114Ba and nuclear properties
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2404
We investigate the influence of nuclear masses, radii, and interaction potentials on 12C radioactivity of 114the best representative of a new island of cluster emitters leading to daughter nuclei around the doubly magic 100Sn. Three different models are considered: one derived by Blendowske, Fliessbach, and Walliser (BFW) from the many-body theory of alpha decay, as well as our analytical (ASAF) and numerical (NuSAF) superasymmetric fission models. A Q value larger by 1 MeV or an ASAF potential barrier reduced by 3% are producing a half-life shorter by 2 orders of magnitude. A similar effect can be obtained within BFW and NuSAF by a decrease of the action integral with less than 10% and 5%, respectively. By increasing the radius constant within ASAF or BFW models by 10%, the half-life becomes shorter by 3 orders of magnitude.Dorin N. Poenaru; Walter Greiner; E. Houraniarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2404Wed, 12 Jul 2006 09:54:53 +0200Periodic structure in nuclear matter
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2410
The properties of nuclear matter are studied in the framework of quantum hadrodynamics. Assuming an ω-meson field, periodic in space, a self-consistent set of equations is derived in the mean-field approximation for the description of nucleons interacting via σ-meson and ω-meson fields. Solutions of these self-consistent equations have been found: The baryon density is constant in space, however, the baryon current density is periodic. This high density phase of nuclear matter can be produced by anisotropic external pressure, occurring, e.g., in relativistic heavy ion reactions. The self-consistent fields developing beyond the instability limit have a special screw symmetry. In the presence of such an ω field, the energy spectrum of the relativistic nucleons exhibits allowed and forbidden bands, similar to the energy spectrum of the electrons in solids.István Lovas; Lívia Molnár; Kornél Sailer; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2410Tue, 11 Jul 2006 11:10:51 +0200Formation of heavy quarks in ultrarelativistic heavy-ion collisions
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2412
We investigate the production of heavy quarks in continuum and bound states in nuclear collisions. Creation rates for free bb̅ and tt̅ quark pairs and for bottomonium and toponium in the ground state are computed at energies of the BNL Relativistic Heavy Ion Collider, CERN Large Hadron Collider (LHC), and Superconducting Super Collider. Central and peripheral heavy-ion collisions are discussed. For top-quark creation we assumed a mass range of 90≤mt≤250 GeV. The creation rate for top quarks in peripheral collisions is estimated to be by a factor 40 to 130 smaller compared with corresponding central collisions. For mt=130 GeV we calculated a creation rate of about 4760 top-quark pairs per day at the LHC (3.5 TeV/nucleon) for Pb-Pb collisions.S. M. Schneider; Walter Greiner; G. Soffarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2412Tue, 11 Jul 2006 11:05:24 +0200Multiplicity distribution of electron-positron pairs created by strong external fields
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2414
We discuss the multiplicity distribution of electron-positron pairs created in the strong electromagnetic fields of ultrarelativistic heavy-ion transits. Based on nonperturbative expressions for the N-pair creation amplitudes, the Poisson distribution is derived by neglecting interference terms. The source of unitarity violation is identified in the vacuum-to-vacuum amplitude, and a perturbative expression for the mean number of pairs is given.Christoph Best; Walter Greiner; Gerhard Soffarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2414Tue, 11 Jul 2006 10:52:41 +0200Flavor distributions in the nucleons: SU(2) sea asymmetry or isospin symmetry breaking?
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2413
The Gottfried sum-rule violation reported by the New Muon Collaboration was interpreted as an indication for a flavor asymmetry of the sea quark in the nucleon. We investigate the alternative possibility that isospin symmetry between the proton and the neutron is breaking. We examine systematically the consequences of this possibility for several processes, namely, neutrino deep inelastic scattering, the charged pion Drell-Yan process, the proton Drell-Yan process, and semi-inclusive deep inelastic scattering, and conclude that a decision between the two alternative explanations is possible.Bo-Qiang Ma; Andreas Schäfer; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2413Tue, 11 Jul 2006 10:45:36 +0200New island of cluster emitters
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2424
A new region of proton-rich parent nuclei decaying by spontaneous cluster emission with a measurable branching ratio relative to alpha decay is predicted within the analytical superasymmetric fission model. After a brief presentation of the model and of the seven mass tables used to calculate the released energy, the obtained results are discussed. Measurable half-lives and branching ratios are estimated for 12C, 16O, 28Si, and other cluster radioactivities of some nuclides having proton and neutron numbers in the range Z=56–64 and N=58–72. Such nuclei far from stability could be produced in reactions induced by radioactive beams.Dorin N. Poenaru; Walter Greiner; Radu A. Gherghescuarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2424Tue, 11 Jul 2006 10:33:18 +0200Ionization and pair creation in relativistic heavy-ion collisions
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2423
Ionization, pair creation, and electron excitations in relativistic heavy-ion collisions are investigated in the framework of the coupled-channel formalism. Collisions between heavy projectiles and Pb82+ are considered for various bombarding energies in the region E=500 up to 2000 MeV/u. Useful symmetry relations for the matrix elements are derived and the influence of gauge transformations onto the coupled-channel equations is explored.Klaus Rumrich; Gerhard Soff; Walter Greinerarticlehttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/2423Tue, 11 Jul 2006 10:17:27 +0200