J. A. Maruhn

The asymmetrie two center shell model

The previously developed two center shell model for symmetric fission has been extended to break-ups into unequal fragments. The potentials of the separate fragments have equal depth. The rounded barrier between them can have varying height. The two fragments can also have different deformations. Generalizedl ·s- andl2-terms are included. This allows for the description of a great variety of nuclear shapes. The mathematical details are presented together with the analytically solvable matrix elements. For a few asymmetric fission processes the level spectra have been calculated.

Superheavy nuclei in self-consistent nuclear calculations

ing normal nuclear properties but differences in some detail. For the nonrelativistic SHF calculations we consider the parametrizations SkM* @19#, SkI1 @17#, SkP @20#, SLy6 @16# which all employ the standard form but differ in bias. The force SkP uses effective mass m*/m51 and is designed to allow a self-consistent treatment of pairing. The other forces all have smaller effective masses around m*/m50.720.8. The force SkM* was first to deliver acceptable incompressibility and fission properties and it is still a benchmark in this area. The force SLy6 stems from an attempt to cover properties of pure neutron matter together with normal nuclear ground-state properties; one can expect reliable extrapolations to neutron-rich nuclei from this force. The force SkI1 stems from a recent systematic fit~along the strategy of @21#! already embracing data from exotic nuclei; it is biased to

Shape coexistence and the effective nucleon-nucleon interaction

The phenomenon of shape coexistence is discussed within the self-consistent Hartree-Fock method and the nuclear shell model. The occurrence of the coexisting configurations with different intrinsic shapes is traced back to the properties of the effective Hamiltonian. {copyright} {ital 1999} {ital The American Physical Society}

Pairing gaps from nuclear mean-fieldmo dels

We discuss the pairing gap, a measure for nuclear pairing correlations, in chains of spherical, semi-magic nuclei in the framework of self-consistent nuclear mean-field models. The equations for the conventional BCS model and the approximate projection-before-variation Lipkin-Nogami method are formulated in terms of local density functionals for the effective interaction. We calculate the Lipkin-Nogami corrections of both the mean-field energy and the pairing energy. Various definitions of the pairing gap are discussed as three-point, four-point and five-point mass-difference formulae, averaged matrix elements of the pairing potential, and single-quasiparticle energies. Experimental values for the pairing gap are compared with calculations employing both a delta pairing force and a density-dependent delta interaction in the BCS and Lipkin-Nogami model. Odd-mass nuclei are calculated in the spherical blocking approximation which neglects part of the the core polarization in the odd nucleus. We find that the five-point mass difference formula gives a very robust description of the odd-even staggering, other approximations for the gap may differ from that up to 30% for certain nuclei.

Relativistic hydrodynamics for heavy-ion collisions. I. General aspects and expansion into vacuum☆

Abstract We present algorithms to solve relativistic hydrodynamics in (3+1)-dimensional situations without apparent symmetry to simplify the solution. In simulations of heavy-ion collisions, these numerical schemes have to deal with the physical vacuum and with equations of state with a first order phase transition between hadron matter and a quark-gluon plasma, i.e. rather special conditions fluid-dynamical algorithms are usually not confronted with. Therefore, prior to applying them directly to the simulation of heavy-ion collisions, one should investigate their performance in well-controlled situations. We consider here the one-dimensional expansion of baryon-free nuclear matter into the vacuum, which is an analytically solvable test problem that incorporates both the aspect of the vacuum as well as that of a phase transition in the equation of state. The dependence of the lifetime of the mixed phase on the initial energy density is discussed.

Nuclear Ground State Observables and QCD Scaling in a Refined Relativistic Point Coupling Model

We present results obtained in the calculation of nuclear ground state properties in relativistic Hartree approximation using a Lagrangian whose QCDscaled coupling constants are all natural (dimensionless and of order 1). Our model consists of four-, six-, and eight-fermion point couplings (contact interactions) together with derivative terms representing, respectively, two-, three-, and four-body forces and the finite ranges of the corresponding mesonic interactions. The coupling constants have been determined in a self-consistent procedure that solves the model equations for representative nuclei simultaneously in a generalized nonlinear least-squares adjustment algorithm. The extracted coupling constants allow us to predict ground state properties of a much larger set of even-even nuclei to good accuracy. The fact that the extracted coupling constants are all natural leads to the conclusion that QCD scaling and chiral symmetry apply to finite nuclei.

Comparison of coordinate-space techniques in nuclear mean-field calculations

Abstract We investigate three different numerical representations for nuclear mean-field calculations: finite differences, Fourier representation, and basis-splines. We compare these schemes with respect to precision and speed. It turns out that Fourier techniques and basis-splines are much superior in precision to finite differences. The Fourier representation in connection with the fast Fourier transformation is advantageous for large grids whereas matrix techniques, derived either from basis-splines or from Fourier representation, are preferable for smaller grids.

Relativistic hydrodynamics for heavy-ion collisions. II. Compression of nuclear matter and the phase transition to the quark-gluon plasma

Abstract We investigate the compression of nuclear matter in relativistic hydrodynamics. Nuclear matter is described by a σ-ω-type model for the hadron matter phase and by the MIT bag model for the quark-gluon plasma, with a first order phase transition between both phases. In the presence of phase transitions, hydrodynamical solutions change qualitatively, for instance, one-dimensional stationary compression is no longer accomplished by a single shock but via a sequence of shock and compressional simple waves. We construct the analytical solution to the “slab-on-slab” collision problem over a range of incident velocities. The performance of numerical algorithms to solve relativistic hydrodynamics is then investigated for this particular test case. Consequences for the early compressional stage in heavy-ion collisions are pointed out.

Potential energy surfaces of superheavy nuclei

We investigate the structure of the potential energy surfaces of the superheavy nuclei {sub 158}{sup 258}Fm{sub 100}, {sub 156}{sup 264}Hs{sub 108}, {sub 166}{sup 278}112, {sub 184}{sup 298}114, and {sub 172}{sup 292}120 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. {copyright} {ital 1998} {ital The American Physical Society}

General collective model and its application to 92 238 U

A general collective model is presented that includes all possible cases, like vibrational, rotational andγ-unstable nuclei. Collective properties are illustrated by the Potential-Energy-Surface (PES), describing all deformation effects of the nucleus. The model is applied to the case of92238U, where very high-spin states are known from experiment.