International Journal of Modern Physics E

We determine the wavefunctions and eigen-values of electrons bound to a positively charged mesoscopic metallic cluster covered by an insulating surface layer. The radius of the metal core and the thickness of the insulating surface layer are of the order of a couple of Ångström. We study in particular the electromagnetic decay of externally located electrons into unoccupied internally located states which exhibits a resonance behaviour. This resonance structure has the consequence that the lifetime of the "mesoscopic atoms" may vary by up to 6 orders of magnitude depending on the values of the parameters (from sec to years).

Nuclear alpha-clustering has been the subject of intense study since the advent of heavy-ion accelerators. Looking back for more than 40 years we are able today to see the connection between quasimolecular resonances in heavy-ion collisions and extremely deformed states in light nuclei. For example superdeformed bands have been recently discovered in light N=Z nuclei such as ³⁶Ar, ⁴⁰Ca, ⁴⁸Cr, and ⁵⁶Ni by γ-ray spectroscopy. The search for strongly deformed shapes in N=Z nuclei is also the domain of charged-particle spectroscopy, and a number of these nuclei have been studied with the charged particle multidetector array ICARE at the VIVITRON. Recently the search for γ-decays in ²⁴Mg has been undertaken in a range of excitation energies where previously nuclear molecular resonances were found in ¹²C+¹²C collisions. The breakup reaction ²⁴Mg+¹²C has been investigated at an energy which corresponds to a ¹²C+¹²C resonance. Very exclusive data were collected with the Binary Reaction Spectrometer in coincidence with EUROBALL IV installed at the VIVITRON. Results on the population of specific structures of large deformation will be presented.

We summarize recent developments of the semiclassical description of shell effects in finite fermion systems with explicit inclusion of spin degrees of freedom, in particluar in the presence of spin-orbit interactions. We present a new approach that makes use of spin coherent states and a correspondingly enlarged classical phase space. Taking suitable limits, we can recover some of the earlier approaches. Applications to some model systems are presented.

Using the Euroball array, we have recently performed several experiments devoted to the study of high-spin states of nuclei with A~80–130, produced from fission following various fusion reactions. High-spin level schemes of many neutron-rich nuclei have been extended or newly established. We present here the new experimental results obtained in some neutron-rich odd-Z nuclei from ₄₃Tc to ₄₉In. All the band-head configurations have been identified from the behaviour of the collective bands built on them. Therefore the single-proton states, located around the Fermi levels for Z=43 to 49, can be discussed as a function of the neutron number (and the deformation). In all these isotopic series, three-quasiparticle states have been measured above 2 MeV excitation energy. The case of ₄₉In nuclei is discussed in the framework of shell-model calculations. Futhermore the individual identification of each fragment by means of its emitted γ transitions allows us to have a new insight into the mechanism of fission induced by heavy ions. Preliminary results of the total number of emitted neutrons are discussed as a function of the N/Z ratios of the fragments.

We propose methods of analysis of the symmetries of the rotor space. A few examples of the point symmetries and their consequences for the state space of the quantum rotors are shortly considered.

An experiment has been performed to investigate the structure at high spin of the neutron-deficient polonium isotopes using the Recoil Filter Detector coupled to the EUROBALL IV gamma array. High spin states of ^200,201Po have been populated by the ³⁰Si+¹⁷⁶Yb reaction at a beam energy of 160 MeV. We report here the performances of the RFD + EUROBALL IV coupling.

The mechanism of shell formation will be explored, incorporating three-body forces, now known to be an indispensable part of the nuclear Hamiltonian.

We present pre-equilibrium models of cluster (deuterons to alphas) emission from reactions induced by light projectiles at energies below the pion threshold. The main attention is given to the hard components of the emission spectra. The pre-equilibrium mechanisms of cluster emission show a kind of competition between pickup and knockout reactions in some cases, in addition to the classical coalescence. We discuss the processes in force and the interplays of competing mechanisms.

The nucleus ¹⁵⁰Nd was Coulomb excited using ¹⁴N, ⁵⁸Ni and ⁹²Mo beams. The overall result of the experiments performed consists of 780 measured gamma yields, which combined with available spectroscopic data gave about 800 data points to overdetermine the set of matrix elements needed to describe the observed processes. A number of E1, E2 and E3 matrix elements coupling the low-lying states has been determined in a model-independent way. In addition, an influence of E4 moments, competing with double E2 excitations, was tested with the low energy ¹⁴N beam. Possible interpretations of the unusual electromagnetic structure found experimentally may pose the challenge to the theorists.

Subtracting the Strutinsky shell corrections from the selfconsistent energies obtained within the Relativistic Mean Field Theory (RMFT) we have got estimates for the macroscopic part of the binding energies of 142 spherical even-even nuclei. By minimizing their root-mean-square deviations from the values obtained with the Lublin-Srasbourg Drop (LSD) model with respect to the nine RMFT parameters we have found the optimal set (NL4). The new parameters reproduce also the radii of these nuclei with an accuracy comparable to that obtained with the NL1 and NL3 sets.

This contribution summarizes the predictions obtained in the domain of superheavy nuclei from self-consistent microscopic calculations employing the Gogny force. Results concerning shell gaps, fission barriers and stability against alpha-decay are recalled. Recent work involving α-decay chains in odd nuclides is also presented and discussed.

The definition of experimental shell energies for nuclear ground states is generalized to finite angular momenta corresponding to a systematic expansion of the (N,Z)-plane to an (N,Z,I) space. Special emphasis is put on high-spin states where it is expected that odd and even nuclei should have similar properties. Different coupling schemes are compared and energetically favoured conditions to build high-spin states are discussed.

Peripheral heavy-ion collisions at relativistic energy are proposed as a new experimental approach dedicated to nuclear dissipation studies and, in particular, to investigate transient effects which are responsible for the inhibition of fission at the beginning of the process. To extract reliable information from the data, an analytical approximation of the time-dependent fission decay width is used in connection with new experimental signatures of relaxation effects.

The influence of the proton–neutron pairing force on low–lying collective excitations of even nuclei is investigated within the interacting boson model containing isocsalar and isovector bosons. The application of the boson scheme shows that the deuteron–like pairs can be formed in the valence g–shell of a nucleus (both for protons and neutrons).

The recently revised liquid drop model (PRC 67(2003) 044316) containing the curvature term reproduces the masses of 2766 experimentally known isotopes having Z≥8 and N≥8 with the r.m.s. deviation equal to 0.698 MeV when the microscopic corrections of Moeller et al. is used. The influence of the congruence energy as well as the compression term on the barrier heights is discussed within this new macroscopic model. The r.m.s. deviation of the fission barrier heights of 40 isotopes with Z≥34 is 1.73 MeV only when deformation-dependent congruence energy is included. The effect of the compression term in the liquid drop energy has rather weak influence on the barrier heights.

The δ-pairing strengths for rare-earth nuclei are estimated from nuclear masses of odd and even systems. The masses are calculated for a variety of macroscopic and microscopic models. We use the BCS and Lipkin-Nogami methods, with a blocking effect in case of odd nuclei. The rms mass deviations obtained in different models are from 0.66 to 1.46.

The macroscopic-microscopic method is applied to calculate the energies of heavy nuclei (A>220) in a multidimensional deformation space {α_λ,μ} including axial and non-axial quadrupole (λ=2,μ=0,2), axial and non-axial octupole (λ=3,μ=0,2) and axial hexadecapole (λ=4,μ=0) degrees of freedom. Shell and pairing corrections are calculated from the single-particle energies of the Woods-Saxon potential with the universal parameters and added to the macroscopic energy of the newest Lublin-Strasbourg Drop (LSD) model to obtain the total deformation energy.

Neutron rich nuclei have been populated using the ⁸²Se+¹⁹²Os deep-inelastic reaction. New experimental results on ¹⁸⁸W, ^188,190Os target-like nuclei, as well as ^74,76,78Ge beam-like nuclei are presented.

We consider the generalized rotor Hamiltonians capable of describing quantum systems invariant with respect to symmetry point-groups that go beyond the usual D₂-symmetry of a tri-axial rotor. We discuss the canonical de-quantisation procedure to obtain the classical analogs of the original quantum Hamiltonians. Classical and quantum solutions to the Hamiltonians relevant in the nuclear physics applications are illustrated and compared using the 'usual' (D₂) and an 'exotic' (T_d) symmetries.

In this talk, we present a method which allows the introduction of correlations beyond a Skyrme Hartree-Fock calculation by symmetry restoration and configuration mixing on the axial quadrupole moment. A first application to ²⁴⁰Pu is discussed, to show the potential of the method. As an example of the shape coexistence phenomenon in Pb isotopes, results for collective spectra and transition probabilities are then presented for ¹⁸⁸Pb.

The superdeformed band of ³⁶Ar is studied with the Gogny force D1S and the angular momentum projected generator coordinate method for the quadrupole moment. The band head excitation energy, moments of inertia, B(E2) transition probabilities and stability against quadrupole fluctuations at low spin are studied. The Self Consistent Cranking method is also used to describe the superdeformed rotational band. In addition, properties of some normal deformed states are discussed.

We present a concise account of our development of the first genuine Local Density Approximation (LDA) to the Energy Density Functional (EDF) for fermionic systems with superfluid correlations, with a particular emphasis to nuclear systems.

On the basis of the symmetry-unrestricted, cranked Skyrme-Hartree-Fock (SHF) calculations, we discuss superdeformed (SD) rotational bands in (1) the ⁴⁰Ca region along the N=Z line, and (2) neutron-rich Sulfur isotopes up to the neutron-drip line. The calculation was carried out with the use of the three-dimensional (3D) coordinate-mesh representation without imposing any symmetry restriction. Stability of the SD bands against exotic deformations breaking both reflection and axial symmetries were carefully examined. The analysis indicates possible appearance of negative-parity rotational bands associated with octupole shape vibrational excitations built on the SD yrast band. We then present results of selfconsistent RPA calculation for such a new type of collective vibrational modes. The selfconsistent RPA calculations based on the SD local minima obtained by the SHF calculation were carried out by means of the mixed representation on the 3D Cartesian mesh in a box.

We have performed angular momentum projection with double-constrained Hartree-Fock-Bogoliubov wave functions with the Gogny interaction for the ³²Mg. We show that the more relevant degree of freedom is the quadrupole deformation. Minima of the ground state obtained in single-constrained calculations with this operator are hardly modified in double-constrained calculations insuring thereby the stability of the solution.

Constrained HFB calculations with the Gogny force are performed in order to investigate the bimodal fission of ²⁵⁸Fm. The single-particle orbitals are analyzed in both fission modes. Density distributions of single nucleons show that the cores of the fragments are well separated far before the scission point.

The energies and characteristics of giant resonances obtained from HF+RPA calculations with the Gogny force are derived in three doubly magic exotic nuclei. The results show a lowering of the monopole resonance energy compared to systematic values in stable nuclei, in particular in ⁷⁸Ni. The Isovector Giant Dipole Resonance (IVGDR) in the two tin isotopes appears splitted into two major peaks.

A method of calculating giant resonance strength functions using Time-Dependent Hartree-Fock techniques is described. An application to isoscalar giant monopole resonances in spherical nuclei is made, thus allowing a comparison between independent 1-, 2- and 3-Dimensional computer codes.

A generalized parameterization of the Skyrme effective force is discussed. Preliminary results are presented for infinite symmetric and asymmetric nuclear matter. In particular, it is shown that an enlarged density dependence based on two terms allows to choose independently the incompressibility and the isoscalar effective mass.

Shell structures in nuclear mean field potentials are analyzed using semiclassical periodic-orbit theory. r^α-type potential model is taken as an approximation of Woods-Saxon model, and spin-orbit coupling is also taken into account. Using this model, we examine shell structure as functions of deformation, nuclear size (diffuseness), and spin-orbit coupling strength. Significant roles of periodic orbit bifurcations for strong deformed shell effects are clarified. Special attentions will be paid to bifurcations of the 'bridge orbits', which emerge from symmetric orbits and then submerge in other symmetric orbits by varying a potential parameter.

We develop a stochastic approach to obtain the energies and wave functions of the full spectrum of the nuclear pairing Hamiltonian (i.e. not only the ground-state but also the excited states of the nuclear many-body systems). We assume that nuclear Cooper pairs may spontaneously jump from one energy configuration to another, the mechanism resembling that of the random walk on a mesh of non-equidistant points. A probability distribution associated with such a random walk is modelled and the resulting solutions tested using an exact quantum algorithm. We use the Hamiltonian parameters characteristic for the nuclear scale: at present an agreement between the quantum and stochastic treatment is of the order of a few permille in terms of eigen-energies.

We recall the main features of the (tetrahedral) symmetry in atomic nuclei and present realistic mean-field calculations supporting the existence such a symmetry all over the nuclear chart. A few potential candidate-nuclei are investigated and the possible experimental signatures of the tetrahedral symmetry are also briefly discussed.

We present an attempt to describe low lying quadrupole collective excitations within the frame of the RMF theory. Single particle wavefunctions obtained from the RMF are used to calculate mass parameters in the cranking approximation of the ATDHFB. The general Bohr hamiltonian with the calculated mass parameters yields collective energies and wavefunctions. Theoretical results are compared with the experimental data in the case of the γ soft ¹¹⁰Ru and ¹²⁶Ba nuclei.

We present self-consistent semi-classical local densities characterising the structure of rotating nuclei. A particular emphasis is put on those densities which are generated by the breaking of time-reversal symmetry through the cranking piece of the Routhian, namely the current density and the spin vector density. Our approach which is based on the Extended-Thomas-Fermi method goes beyond the Inglis cranking approach and contains naturally the Thouless-Valatin self-consistency terms expressing the response of the mean field to the time-odd part of the density matrix.

A general BCS Ansatz based on the Generator Coordinate Method is proposed to study pairing properties in superconducting grains. The formalism is applied to the pairing Hamiltonian where we reproduce the exact solution in the weak, crossover and strong pairing regimes.

In this article we present a method to parametrise the exact solutions to the nuclear pairing problem, for realistic large-scale many-body spaces. This new approach allows for rapid and quite accurate estimates of the pairing influence on the excitation energies of the nucleus, treated in the standard mean-field approximation.

Lifetimes of the h_11/2 decoupled band in ¹³¹La and supposed chiral bands in odd-odd ¹³²La have been measured using the Doppler Shift Atenuation method. The properties of all bands have been calculated in terms of the Core Quasi Particle Coupling and Core Particle Hole Coupling models by using in both cases the same phenomenological core of ¹³⁰Ba. A new band in ¹³²La has been found.

We investigate "shell structure" from Babylonian times: periodicities and beats in computer-simulated lunar data corresponding to those observed by Babylonian scribes some 2500 years ago. We discuss the mathematical similarity between the Babylonians' recently reconstructed method of determining one of the periods of the moon with modern Fourier analysis and the interpretation of shell structure in finite fermion systems (nuclei, metal clusters, quantum dots) in terms of classical closed or periodic orbits.

The fusion cross sections are considered to be given by the product of three factors: the cross section to overcome the Coulomb barrier, the probability for the resulting system to reach the compound nucleus configuration by diffusion, and the probability for the compound nucleus to survive fission. The first and third factors are treated by more or less conventional equations, and the second by Brownian diffusion in one dimension. Adjusting one free parameter in the theory one can reproduce the twelve measured cross sections to within a factor of two.

Recent results on limiting temperatures and caloric curves are discussed with respect to the question of identifying critical behavior in the disassembly of nuclei. We suggest that the best candidates for exploring such behavior are light nuclei in which the Coulomb Energies are less disruptive.

Use of the free energy in dynamical fission calculations and of the level density in simultaneous particle-evaporation yields raises the question of compatibility of these two pieces of input of quite different origin in calculations of the decay of hot compound nuclei. Seeming discrepancies between the Bethe formula for the level density and the popular assumption of a quadratic temperature dependence of the free energy are discussed in the framework of the picket-fence model, where the theory of partitions allows to calculate all thermodynamic functions analytically together with their limits for large systems and high temperature.

Nuclear dissipation in capture reactions is investigated using backtracing. Combining the analysis procedure with dynamical models, the difficult and long-standing problem of competition and mixing of quasi-fission and fusion-fission is solved for the first time. At low excitation energy a new protocol able to handle low statistics data gives access to the prescission neutron multiplicity in two different systems ⁴⁸Ca+²⁰⁸Pb, Pu. The results are in agreement with a domination of fusion-fission in the case of ²⁵⁶No and an equal mixing of quasi-fission and fusion-fission in the case of Z=114. The nature of the relevant dissipation is determined as one-body dissipation.

The creation of the nucleus of a superheavy element follows an extremely complex reaction path starting with the crossing of an external potential barrier (or distribution of barriers). This is followed by the evolution towards an equilibrated compound nucleus, which takes place in competition with pre-compound-nucleus fission (quasi-fission). Once formed the equilibrated compound nucleus must still survive against true fusion to yield a relatively long-lived evaporation residue. Much of this path is poorly understood, though recently, progress has been made on the role of the entrance-channel in quasi-fission. This will be briefly reported and a method proposed to measure the total capture cross section for such systems directly.

The fusion-fission process for the synthesis of superheavy elements is discussed on the basis of fluctuation-dissipation model. We employ three-dimensional Langevin equation. We investigate the fusion-fission process by analyzing not only the mass distribution of fission fragments but also neutron multiplicity on fusion-fission process.

Fusion potentials are calculated for a number of reactions within the static Hartree-Fock method with the Skyrme force SkM*. Fusion barriers agree with the data considerably better than reaction Q values. This suggests some error cancellation, possibly with the relative kinetic energy term. Our results are consistent with the idea of fusion hindrance in tip collisions. Some comparison to results of the frozen density method is made.

Using the collective potential between colliding ions based on the effective nucleon-nucleon interactions of the Skyrme type and the semi-classical Extended Thomas-Fermi approach we describe heavy-ion fusion cross sections applying a Monte-Carlo sampling method of trajectories with the Langevin formalism using friction as described in the so-called Surface-Friction Model.

Fusion barrier distributions for the ²⁰Ne + ^112,116,118Sn systems have been extracted from quasi-elastic scattering cross sections measured at the Warsaw HIL Cyclotron. Results are compared to coupled-channels calculations performed with the CCFULL code. The overall widths of the distributions are reproduced on taking account of the low-lying collective states of the target and projectile but some puzzling discrepancies in their shapes remain to be explained.

We present a model which allows for the calculation of fragment excitation energy, fragment kinetic energies and neutron evaporation in nuclear fission. The model is based on the assumption that, at the end of the fission process, fragments are excited to a temperature which is proportional to the reaction Q-value. Starting from this assumption the distribution functions of fragment excitation can be formulated and the distribution functions for the kinetic energies can be derived by a Monte Carlo method. From the distribution functions for the excitation energy neutron evaporation characteristics are calculated.

The behavior of several nuclear properties with temperature is analyzed within the framework of the Finite Temperature Hartree-Fock-Bogolyubov (FTHFB) theory with the Gogny force and large configuration spaces. As representative examples the nuclei ¹⁶⁴Er, ¹⁵²Dy, ¹⁹²Hg and ²⁴⁰Pu are studied. Numerical results for the deformed to spherical shape phase transitions are presented. Thermal shape fluctuations in the quadrupole degree of freedom, around the mean field solution, are taken into account with the Landau prescription. We found a substantial effect of these fluctuations in the average value of several observables.

New data from GSI on the production-cross-section for fragmentation of the systems ⁵⁶Fe+p and ¹³⁶Xe+p at 1 A GeV revealed the appearance of even-odd staggering in the cross-section distribution for chains of isotopes with given N-Z. The staggering is strongly enhanced for the chain N=Z, it reduces as the production moves away from the N=Z chain, and it reverses for the most neutron-rich odd-A residues. These phenomena, observed in the residues of rather violent reactions, are related to structural effects in the level-densities below the particle-emission threshold.

The halo factor is one of the experimental data which describes a distribution of neutrons in the nuclear periphery. In the presented paper we use Skyrme-Hartree (SH) and the Relativistic Mean Field (RMF) models to calculate the neutron excess factor Δ_B which differs slightly from the halo factor f_exp. The results of the calculations are compared to the measured data.

The nuclear periphery was studied by using antiprotons. Two experimental methods were applied: analysis of the antiproton annihilation residues one mass unit lighter than the target mass by nuclear spectroscopy and the measurement of strong interaction effects on antiprotonic level widths and shifts. 26 isotopes from a wide range of mass numbers (40<A<238) were investigated. The gathered antiprotonic-atom data were compared with the results obtained using hadron scattering methods and with some expectations from theoretical approaches.

We examine the fission barriers, mass parameters and spontaneous fission half lives of Fermium isotopes within the framework of the macroscopic-microscopic model with a δ-pairing interaction. Four different macroscopic models are applied and studied. The results are compared to experimental data and to the ones of the corresponding monopole pairing approach. The half lives obtained in the δ-pairing model are comparable with experimental data.

It is known, that i.r. of double point groups can be expressed in terms of Wigner functions. Using the projection method proposed by O. Barut and R. Raczka the appropriate basis of i.r. of double point groups within the harmonic oscillator space have been derived. The appropriate numeric and symbolic algebra programs have been constructed.

We are studying the potential energy describing the entrance channel of a heavy-ion collisions for the axially symmetric deformed and arbitrarily oriented nuclear shapes. The paper presents an analysis of the influence of different orientations of the deformed ions on the height and shape of the fusion barrier. The net effect of the deformation degree of freedom on the transmission at sub-barrier energies is to enhance the fusion cross section. This problem is very important especially in the perspective of the synthesis of super-heavy elements.

We present the possible influence on the half-life of neutrinoless double beta decay coming from the existence of n extra spatial dimensions. The half-life in question depends on the mass of the electron neutrino. We base our analysis on the Majorana neutrino mass mechanism in Arkani-Hamed–Dimopoulos–Dvali model.

The inner crust of a neutron star consists of nuclei immersed in a superfluid neutron liquid. As these nuclei move through the fermionic medium they bring it into motion as well. As a result their mass is strongly renormalized and the spectrum of the ion lattice vibrations is significantly affected. Consequently we predict that the specific heat and the lattice thermal energy of the Coulomb crystal at these densities are noticeably modified.