International Journal of Modern Physics E

I point out a conceptual misunderstanding in the exposition of relativity, namely the mistaken belief that light has something to do with the essence of relativity. This misunderstanding can be clarified by stressing that the content of Special Relativity is simply that "we live in a Minkowski spacetime", together with a thought experiment that illustrates how one could discover this fact without ever mentioning even the existence of light. I also note a recently uncovered implication of living in Minkowski spacetime, namely the Copenhagen reinterpretation of Quantum Mechanics, developed in the past decade.

The method of 'cold' fusion reactions has been applied successfully to synthesize isotopes of elements up to Z=113. However, the cross sections were found to decrease nearly exponential with increasing atomic number.

The production of isotopes up to Z=118 using ⁴⁸Ca - projectiles and actinide targets was claimed from experiments performed at the Dubna Gasfilled Separator (DGFRS). Attempts to confirm the results from one of the used reactions (⁴⁸Ca + ²³⁸U) have been performed at other laboratories. The results of the different experiments are compared.

In order to increase our knowledge on the structure of heaviest nuclei an experimental program on α - γ - decay spectroscopy of transfermium isotopes was started at SHIP, GSI. Results on trends in single particle levels in odd mass einsteinium isotopes as well as on the identification of a (possible) K-isomer in ²⁵²No will be presented.

A time-dependent microscopic approach of the fission process based on the constrained HFB approach with the Gogny force and the Hill and Wheeler configuration mixing method is described. Recent results concerning fragment distributions (mass, kinetic and deformation energies) and other fragment observables in ²³⁸U obtained with such an approach are presented and discussed.

Constrained Skyrme-Hartree-Fock calculations of static fission barriers are performed for even-even elements with Z = 100÷110 as well as for superheavy N=184 isotones. In our study we use the Skyrme parametrization SLy4 and a seniority pairing force treated in the BCS approximation. The computations are carried out applying a code that makes it possible to break all self-consistent symmetries of the nuclear mean field, including axial symmetry and reflection symmetry. The influence of reflection-asymmetric and triaxial degrees of freedom on fission barriers are discussed.

The dependence of the capture and fusion excitation functions on the nuclear shell structure and initial orientation angles of the symmetry axis of the deformed projectile- and target-nucleus are explored by the dynamical model based on the dinuclear system concept and Langevin calculations. The fusion cross sections for ¹⁶O+²³⁸U and ⁶⁰Ni+¹⁵⁴Sm reactions obtained by averaging of the results for the all orientation angles are in good agreement with the experimental data. The capture and fusion cross sections for the ¹⁶O+²³⁸U reaction are nearly the same while those are different for the ⁶⁰Ni+¹⁵⁴Sm reaction due to presence of the hindrance to fusion as quasifission. The largest of the fusion cross section for the orientation angles of the reactants in the range 60° < α_i < 90° (A) in comparison with that for angles 0° < α_i < 30° (B) was explained by the increase of the quasifission contribution in the last case (B). The physical reason of this phenomenon is connected by the largest of the intrinsic fusion barrier B*_fus in case (B) than that for the case (A). The observed difference between the excitation functions of evaporation residues for the ⁸⁶Kr+¹³⁰Xe and ¹²⁴Sn+⁹²Zr reactions is explained by the difference between the B*_fus values which depend on the nuclear shell corrections.

It is shown that the measured cross section for the Σ production reactions, the observed properties of Σ atoms, and the two-body hyperon-nucleon data indicate that the ΣN interaction is well represented by the Nijmegen model F of the hyperon-nucleon interaction. It is demonstrated how the strong-interaction shifts and widths measured in Σ^-Pb atoms may be used to obtain information on the nucleon density distributions in Pb.

The exact Richardson solution of the reduced BCS Hamiltonian is reviewed with special emphasis on the structure of the many-body wavefunction. A clear definition of the Cooper pairs in the superconducting or Fermi superfluid medium emerges. The structure of the Cooper pair wavefunction is general enough to describe large overlapping pair resonances in the weak coupling limit (BCS) as well as a Bose-Einstein condensate (BEC) of quasi-bound molecules in the strong coupling limit.

Hartree-Fock-Bogolyubov solutions corresponding to the tetrahedral deformation are found in six tetrahedrally doubly-magic nuclei. Values of the β₃₂ deformation, depths of the tetrahedral minima, and their energies relative to the co-existing quadrupole minima are determined for several versions of the Skyrme force. Reduction of the tetrahedral deformation energies by pairing correlations is quantitatively analysed. In light nuclei, shallow tetrahedral minima are found to be the lowest in energy, while in heavy nuclei, the minima are deeper but appear at a few MeV of excitation.

A new parameterization of the effective Gogny interaction is investigated. It has the property of fitting the neutron matter Equation Of State (EOS) as predicted by a variational calculation. Its properties in nuclear matter (saturation point, compressibility, …) and in nuclei (binding energies) are presented.

The fully self-consistent Random Phase Approximation (RPA) is constructed within the Unitary Correlation Operator Method (UCOM), which describes the dominant interaction-induced short-range central and tensor correlations by a unitary transformation. Based on the correlated Argonne V18 interaction, the RPA is employed in studies of multipole response in closed-shell nuclei across the nuclide chart. The UCOM-RPA results in a collective character of giant resonances, and it describes rather well the properties of isoscalar giant monopole resonances. However, the excitation energies of isovector giant dipole resonances and isoscalar giant quadrupole resonances are overestimated due to the missing long-range correlations and three-body contributions.

It is shown how a priori information can be introduced in an optimal way to extract optical-model parameters in a model-independent way from incomplete elastic scattering data.

The paper describes an extension of the model treating dissipative collective motion of hot and dilute nuclear droplets on two-fluid case. The previous results obtained for adiabatic isoscalar modes¹ and those for dissipative isoscalar modes² are generalized. The present formulation includes isovector modes on the same footing as isoscalar ones and allows to estimate the effect of isovector modes on the spinodal decomposition of infinite nuclear matter and finite nuclear droplets at their expansion phase.

The properties observed for the one-proton and two-proton radioactivity of the (21⁺) isomer in ⁹⁴Ag are briefly summarized. The occurrence of both types of radioactivity from one and the same nuclear state is a unique phenomenon on the entire chart of nuclides. In particular, the first observation of energy correlations for two-proton radioactivity is discussed in comparison with predictions obtained from of a three-body breakup model. On the basis of this comparison it is tentatively suggested that the two protons are emitted simultaneously either from one of the poles or from opposite poles of a strongly deformed nucleus. Future experimental and theoretical studies are sketched which may help to explain this puzzling result.

Coulomb excitation experiments were performed with ⁹⁶Mo, ⁹⁸Mo and ¹⁰⁰Mo isotopes using both beam and target excitation. As a result, quadrupole deformation parameters were deduced for two lowest-lying (ground and excited) 0⁺ states. Surprising shape changes of these states were observed.

Low energy quadrupole collective excitations are investigated using a model based on the Adiabatic Time Dependent HFB theory. Distinctive feature of proposed method is an extension of the collective space by adding variables referring to pairing degrees of freedom. In the microscopic part of the model effective Skyrme interaction and constant G pairing force are employed. Calculated energy levels and B(E2) transition probabilities in the ¹²⁸Xe nucleus are compared with the experimental data.

Extensive comparisons of E1 strength calculations within framework of the various methods are performed in atomic nuclei near beta-stability line. Photoabsorption cross-sections are calculated and compared with experimental data to test radiative strength function models.

We investigate the effect of the parity-violating weak interaction in the process of n-induced low-energy fission within a time-dependent microscopic description. We display two different mechanisms of enhancement: a) the well-known enhancement due to the chaotic complexity of compound nuclear states and the concomitant high density of levels, b) an additional dynamical enhancement which arises whenever the substates of a parity doublet cross as a function of the intrinsic octupole moment Q₃₀ on the way to fission. In the last section we discuss other examples of this additional enhancement mechanism which is due to a spontaneous symmetry breaking.

By using a unique set of experimental data on (1n, 2n, 3n and 4n) fusion-evaporation cross sections for ⁴⁸Ca + ²⁰⁶Pb and ⁴⁸Ca + ²⁰⁸Pb reactions, measured by Oganessian et al., we have tested the conventional Bohr-Wheeler description of the competition between evaporation and fission in these reactions. Level densities in both, the equilibrium and saddle-point configurations were calculated using the Reisdorf-Ignatyuk prescription. Strutinsky shell corrections of Möller et al. were used for the equilibrium, and zero shell corrections were assumed for the saddle-point configuration. The model does not contain adjustable parameters.

Using the 4π CHIMERA detector system we have observed a dynamical, non-equilibrated fission of projectile-like fragments as well as an equilibrated fission component in collisions ¹²⁴Sn + ⁶⁴Ni and ¹¹²Sn + ⁵⁸Ni at 35A MeV. The velocity and angular distributions of projectile-like fission fragments were analyzed. The contribution of the "dynamical fission" component is larger in the neutron rich ¹²⁴Sn + ⁶⁴Ni system than in the neutron poor ¹¹²Sn + ⁵⁸Ni one.

A four-dimensional deformation space adapted to describe the fission dynamics of hot, rotating nuclei is proposed. The deformation coordinates consisting of the elongation, neck formation, left-right asymmetry and nonaxiality result in fission barriers much lower and thiner than those obtained in the spherical-harmonics expansion using the same number of deformation parameters.

The dynamical hindrance of fusion after the system of two colliding nuclei overcomes the Coulomb barrier is calculated. Langevin equations, in which the stochastic white noise is added to the conservative and dissipative forces, are solved in the multidimensional space. It is shown that in case of very heavy systems the dynamical trajectories lead from the Coulomb barrier towards the fission valley at locations rather outside the saddle point and then turn downward to scission. Only due to fluctuations a small fraction of trajectories can overcome the saddle point and lead to fusion. Fusion probabilities determined by the ratio of fusion-to-scission fluxes are calculated. In cold fusion reactions induced by different projectiles on ²⁰⁸Pb and ²⁰⁹Bi targets, the fusion probability drops down by almost ten orders of magnitude for a range of projectiles from ⁴⁸Ca (Z_cn = 102) to ⁸⁶Kr (Z_cn = 118).

In the framework of the macroscopic-microscopic model fission barriers in the region of actinide nuclei are investigated. Taking left-right mass asymmetric and non-axial shapes into account is demonstrated to have a substantial effect on fission barrier heights.

In this paper we consider the time as a dynamical variable. In particular we apply the time operator to an example of the particle arrival problem within two-dimensional space–time.

The presence of trilinear R-parity violating interactions in the MSSM lagrangian leads to existence of quark–squark and lepton–slepton loops which generate mass of the neutrino. By introducing interaction with an external photon the magnetic moment is obtained. We derive bounds on that quantity being around one order of magnitude stronger than those present in the literature.

Pairing plays an important role in both mean-field and macroscopic-microscopic description of the fission process. We discuss two kinds of pairing models: monopole (g = const) and state dependent (δ-type force). As is known the BCS theory leads to the particle number symmetry braking. To restore the symmetry one uses a projection methods (projection before- or after variation) or one solves the Lipkin-Nogami equations. We apply all these methods in the case of monopole pairing. Fission barriers, inertia parameters and spontaneous fission half-lives are studied in the case of Z = 112 isotopes.

Alpha-decay chain of ²⁷¹Ds (²⁷¹110) is described theoretically. Transition energies and half-lives T_α are analyzed. The energies are described within a macroscopic-microscopic approach. Single-particle excitations of the nuclei are treated in the one-quasiparticle approximation. The half-lives T_α are described by a simple 3-parameter phenomenological formula expressing them as functions of . A good agreement with measured values is obtained. Average of the absolute values of the discrepancies for is 0.17 MeV. The half-lives T_α are reproduced within a factor of 3.8, on the average. No free parameters are used in the description.

Applying a variational multiparticle-multihole mixing method whose purpose is to include correlations beyond mean field in an unified way without particle number and Pauli violations, we investigate ground state properties of ²²O nucleus, in the case of pairing-type correlations. The same interaction is used for the mean field and the residual part of the hamiltonian, namely, the density-dependent D1S Gogny force.

A new method for determining the average nuclear pairing energy is proposed. By applying a recently proposed Strutinky-type folding procedure in particle-number space, a simple and stable method to calculate the total microscopic corrections consisting of shell and pairing energies is obtained.

Selfconsistent mean-field calculations have been performed with the SkM* Skyrme force for 140 spherical even-even nuclei at temperatures 0≤T≤4 MeV. Single-particle level densities for this sample of nuclei are determined for various temperatures. The average dependence of the single-particle level density on mass number A and isospin is given and compared with previous estimates obtained using the relativistic mean-field and different semiclassical approaches.

The global mass dependence of the nuclear symmetry energy a_sym(A) and its two basic ingredients due to the mean-level spacing ε(A) and effective strength of the isovector mean-potential κ(A) is studied within the Skyrme-Hartree-Fock model. In particular, our study determines the ratio of the surface-to-volume contributions to a_sym(A) to be r_S/V~1.6 and reveals that after removing momentum-dependent effects by rescaling ε and κ with isoscalar and isovector effective masses, respectively, one obtains ε^⋆ ≈ κ^⋆.

The three-dimensional cranking model is used to investigate the microscopic aspects of the rotation of nuclei with the tetrahedral symmetry. Two classes of rotation axes are studied corresponding to two different discrete symmetries of the rotating hamiltonian. Self-consistent Hartree-Fock-Bogoliubov calculations show that the tetrahedral minimum remains remarkably stable until the first single-particle crossing.

Collisions of a very heavy ¹⁹⁷Au + ¹⁹⁷Au system have been studied at an energy of 15 MeV/nucleon with the aim to investigate a possible change of the energy dissipation mechanism from one-body dissipation (presumably dominating at low excitation energies) to two-body dissipation. The experiment was carried out in 4π geometry using the CHIMERA multidetector array. A class of ternary events satisfying nearly complete balance of mass numbers was selected. Preliminary results suggest that the selected ternary events represent mostly prompt ternary partitions of the colliding system, in which the lightest fragment is quite massive. In the light of theoretical predictions of Cârjan, Sierk and Nix this result may imply that the observed ternary reactions are driven by the two-body dissipation mechanism already at 15 MeV/nucleon.

The toy model of "fission" shows the way how to get the temporal characteristics of the fission process within the projection evolution approach.

A systematic study of the intrinsic deformation parameters of 150 super-heavy nuclei in the region 150 ≤ N ≤ 190, 100 ≤ Z ≤ 126 has been done within the framework of the Hartree-Fock-Bogoliubov theory with the Gogny force. We find a stronger dependence of the β_n parameters and the pairing energies with the neutron number than with the proton number. The proton pairing energies are on the average much larger than the neutron ones. Large octupole deformations are predicted for N = 188, 190 nuclei.

The neutrino propagation in asymmetric nuclear matter is studied in the framework of the linear response method. The medium effects are treated in the Hartree-Fock approach with an effective Skyrme interaction. The neutrino opacity for the nuclear matter has been calculated in a wide range of densities and temperatures.

The Gamov–Teller transitions were investigated within the boson model based on the idea of proton–neutron interaction and describing the 0⁺ and 1⁺ levels of A = 96 - 100 nuclei.

Modern methods for the description of the nuclear many-body system use the concepts of density functional theory (DFT) and of effective field theory (EFT). Relativistic Hartree Bogoliubov (RHB) theory is a covariant version of this method, which takes into account Lorentz symmetry and pairing correlations in a fully self-consistent way. This theory has been used in the past for a very successful phenomenological description of ground state properties of nuclei all over the periodic table. Recently is also has been extended for the investigation of excited states. We discuss the calculation of rotational bands within cranked RHB-theory and recent investigations of vibrational excitations within the framework of relativistic Quasiparticle Random Phase Approximation (QRPA).

We study the continuum coupling correction to the eigenvalues of closed quantum systems in the rigorously solvable limit of the shell model embedded in the continuum.

Minimisation of the total nuclear energies in the 5-dimensional deformation space {α₂₀,α₂₂,α₃₀,α₃₂,α₄₀} gives us a possibility to examine more realistically the total energy surfaces in the (β,γ) space but also in the exotic (α₃₀,α₃₂) projections. Basing on those results we have performed also a multi-dimensional calculations in the space of tetrahedral symmetry preserving deformations.

Results of the DSAM lifetime measurements in supposed chiral partner bands of ¹²⁸Cs and ¹³²La are presented. Experimental reduced transition probabilities in ¹²⁸Cs are compared with theoretical calculations done in the frame of the Core-QuasiParticle Coupling model. The electromagnetic properties and energy pattern of partner bands show that ¹²⁸Cs is the best candidate revealing the chiral symmetry breaking phenomenon.

The structure of spin densities and the associated spin-current densities, induced by the coupling of external vector fields to the orbital and spin degrees of freedom, is studied within the framework of the Extended Thomas-Fermi method, a semiclassical version of the density-functional theory. A special emphasis is put on the rotational case where our approach amounts to perform a semiclassical approximation of the so-called generalized Routhian approach.