International Journal of Modern Physics E

A further extension of a model of coherent quadrupole–octupole vibrations and rotations and its application to alternating-parity spectra in heavy even–even nuclei is presented. Within the model the yrast alternating-parity sequence includes the ground state band and the lowest negative parity levels with odd angular momenta, while the non-yrast sequences include excited β-bands and higher negative-parity levels. Electric transition operators reflecting the complex shape characteristics associated with the quadrupole–octupole vibration modes are introduced. By using them B(E1), B(E2) and B(E3) reduced transition probabilities within and between the different energy sequences are calculated. It is shown that the model successfully reproduces yrast and non-yrast alternating-parity bands together with the attendant B(E1)–B(E3) transition rates in the nuclei ¹⁵⁴Sm, ¹⁵⁶Gd and ¹⁰⁰Mo.

Calculations of half-lives of superheavy nuclei (SH) show an unexpected result: For some of them heavy particle radioactivity (HPR) dominates over α decay (branching ratios larger than 1). The new mass table AME11 and the theoretical KTUY05 and FRDM95 masses are used to determine Q-values. For Z = 124 we found isotopes with half-lives in the range of ns to ps.

The decay process of hot and rotating compound nuclei is studied. In particular the competition between fission and n, p and α-particle emission is discussed. The nuclear fission process is described by a Langevin equation coupled to Master equations for particle evaporation. Light particle emission rates obtained with the Weisskopf theory and the semiclassical phase-space distribution-function approach are compared. Coulomb barriers for the emission of charged particles are studied.

The nonrelativistic Skyrme energy density functional (EDF) based collective Hamiltonian, that takes into account dynamical correlations related to the restoration of broken symmetries and fluctuations of quadrupole collective variables, is applied to quantitatively study the impurity effect of Λ hyperon on the collectivity of ⁴⁴S. Several Skyrme forces for both the nucleon–nucleon (NN) and Λ-nucleon (ΛN) interactions are used. The influence of pairing strengths on the polarization effect of Λ hyperon is also examined. It is found that although these Skyrme forces with different pairing strengths give somewhat different low-lying spectra for ⁴⁴S, all of them give similar and generally small size of Λ reduction effect (within 5%) on the collective properties.

Recent progress in the study of fission barriers of actinides and superheavy nuclei within covariant density functional theory is overviewed.

In these proceedings, we report first results for particle-number and angular-momentum projection of self-consistently blocked triaxial one-quasiparticle HFB states for the description of odd-A nuclei in the context of regularized multi-reference energy density functionals, using the entire model space of occupied single-particle states. The SIII parametrization of the Skyrme energy functional and a volume-type pairing interaction are used.

We analyze theoretically the neutron skin thickness in nuclei and its correlation with the symmetry energy by using semiclassical and mean field approaches together with nuclear effective interactions. Semiclassical approaches reveal that the neutron skin thickness in nuclei is formed by a combination of bulk and surface contributions. To investigate the neutron skin thickness predicted by mean field models, we fit the corresponding densities by two-parameter Fermi distributions. Using these parametrized densities, we study the neutron skin thickness as well as its bulk and surface contributions in ²⁰⁸Pb and in Zr isotopes, where the influence of shell effects along the isotopic chain is discussed.

A time-dependent approach to the scission process, i.e., to the transition from two fragments connected by a thin neck (deformation α_i) to two separated fragments (deformation α_f) is presented. This transition is supposed to take place in a very short time interval ΔT. Our approach follows the evolution from α_i to α_f of all occupied neutron states by solving numerically the two-dimensional time-dependent Schrödinger equation with time-dependent potential. Calculations are performed for mass divisions from A_L = 70 to A_L = 118(A_L being the light fragment mass) taking into account all neutron states (Ω = 1/2, 3/2, …, 11/2) that are bound in ²³⁶U at α_i. ΔT is taken as parameter having values from 0.25×10^-22 to 6×10^-22 s. The resulting scission neutron multiplicities ν_sc and primary fragments' excitation energies are compared with those obtained in the frame of the sudden approximation (ΔT = 0). As expected, shorter is the transition time more excited are the fragments and more neutrons are emitted, the sudden approximation being an upper limit. For ΔT = 10^-22 which is a realistic value, the time dependent results are 20% below this limit. For transition times longer than 6×10^-22 s the adiabatic limit is reached: No scission neutrons are emitted anymore and the excitation energy at α_f is negligible.

The effect of rotation on the shapes of nuclei is discussed within Strutinsky's optimal-shape approach generalized to nonaxial deformations. The limiting value of the angular momentum at which the nucleus loses its stability with respect to fission, as well as the angular momentum at which the Jacobi transition takes place, are calculated as function of the fissility parameter. The results are compared with those obtained for triaxial spheroidal forms.

The effect of neutron enrichment of the neck formed during reseparation of two colliding nuclei was studied with the aim to infer an information on the density dependence of the asymmetry energy term in the equation of state. By using a version of the QMD model of Łukasik it is shown that the neutrons-to-protons ratio of the intermediate mass fragments (IMF) emitted from the neck, 〈N/Z〉, is not a sufficiently sensitive observable to discriminate between different assumptions regarding the symmetry term of the equation of state. As an alternative, isotopic ratios of selected pairs of isotopes turned out to be useful observables more sensitive to the assumed form of the symmetry term of the equation of state. A comparison with experimental data on isotopic ratios for beryllium and boron IMFs from the ¹²⁴Sn + ⁶⁴Ni reaction at 35 MeV/nucleon tentatively suggests that the ASY-SOFT option of the symmetry energy term in EOS is preferred.

The order-to-chaos transition in the dynamics of the quantum gas of independent particles was studied within the nuclear model based on the time-dependent mean-field approach. The excitation of the quantum gas in the Woods–Saxon potential with a small diffuseness of its surface rippled according to the Legendre polynomials P₂ and P₃ are obtained for a slow and small amplitude collective motion. We found strong correlations between time-derivatives of the excitation energies (one-body friction coefficients) and shell-correction energies as functions of the particle number. Semiclassical estimates of the friction coefficients were obtained within the periodic orbit theory by using the uniform approximation.

The time-dependent pairing equations are developed to include the Landau–Zener effect and a pair breaking mechanism. The new formalism provide information about the configuration mixing and the dissipation for a dynamical evolution of a nuclear system. A formula for a nonadiabatic cranking inertia is also deduced. Results concerning cluster decay and fission processes are presented.

We analyze collective properties of the ^110-116Cd isotopes in the framework of the general Bohr Hamiltonian which is obtained from the ATDHFB theory with the Skyrme interaction. Calculated energies and B(E2) transition probabilities and experimental data are in good agreement.

In this paper we collect a number of technical issues that arise when constructing the matrix representation of the most general nuclear mean field Hamiltonian within which "all terms allowed by general symmetries are considered not only in principle but also in practice". Such a general posing of the problem is necessary when investigating the predictive power of the mean field theories by means of the well-posed inverse problem. [J. Dudek et al., Int. J. Mod. Phys. E21 (2012) 1250053]. To our knowledge quite often ill-posed mean field inverse problems arise in practical realizations what makes reliable extrapolations into the unknown areas of nuclei impossible. The conceptual and technical issues related to the inverse problem have been discussed in the above-mentioned topic whereas here we focus on "how to calculate the matrix elements, fast and with high numerical precision when solving the inverse problem" [For space-limitation reasons we illustrate the principal techniques on the example of the central interactions].

The quality of the description of masses of heavy nuclei by theoretical models is analyzed. Five of widely used macroscopic–microscopic models and one semi-empirical model are considered. All measured masses of nuclei with proton number Z≥82 and neutron number N≥126 are used in the analysis. Besides the accuracy of the description of the masses, the predictive power of the models in this description is also examined. It is obtained that the best accuracy is reached for the semi-empirical model (which is of a local type, specially adjusted to heavy nuclei). This model does not show, however, the best predictive power.

Nuclear effective interactions are often modeled by simple analytical expressions such as the Skyrme zero-range force. This effective interaction depends on a limited number of parameters that are usually fitted using experimental data obtained from doubly magic nuclei. It was recently shown that many Skyrme functionals lead to the appearance of instabilities, in particular when symmetries are broken, for example unphysical polarization of odd–even or rotating nuclei. In this paper, we show how the formalism of the linear response in infinite nuclear matter can be used to predict and avoid the regions of parameters that are responsible for these unphysical instabilities.

The giant dipole resonance (GDR) in N = 28 isotones (⁴⁸Ca, ⁵⁰Ti, ⁵²Cr, ⁵⁴Fe) is analyzed in the framework of the Skyrme random-phase-approximation (RPA). Three Skyrme forces, SkM*, SLy6 and SV-bas, are used. The effects beyond RPA are simulated by the double folding procedure. We show that dipole strength exhibits a large collective shift, which testifies to a strong impact of the residual interaction and signals on considerable anharmonic effects. In ⁵²Cr, a significant pairing impact is found. For exception of ⁵⁰Ti, an acceptable agreement with the experiment data is obtained, which justifies the ability of Skyrme forces to describe GDR in light nuclei.

Symmetry problems of the generator coordinate method (GCM) in intrinsic frame of a many-body system (nuclei) are considered. The appropriate generator functions and the corresponding GCM equations are derived. An important role of the symmetrization group in construction of Griffin–Hill–Wheeler (GHW) equations is emphasized.

The macroscopic–microscopic model with the Lublin–Strasbourg Drop, the Yukawa–folded single-particle potential and a monopole pairing force is used together with the cranking model to describe rotational bands in even–even actinide (Ra–Cn) isotopes. The pairing strength is adjusted for every nucleus to reproduce the experimentally known energy of the rotational 2⁺ state. The average pairing strength obtained in this way is used to predict the rotational states in superheavy No–Cn nuclei. A simple mechanism which takes into account a dynamical coupling of rotation with the pairing field is explained in detail.

Two systematic sources of error in most current microscopic evaluations of fission-barrier heights are studied. They are concerned with an approximate treatment of the Coulomb exchange terms (known as the Slater approximation) in the self-consistent mean-fields and the projection on good parity states (e.g., of positive parity for the spontaneous fission of an even–even nucleus) of left–right reflection asymmetric intrinsic solutions (e.g., around the second barrier). Approximate or unprojected solutions are shown to lead each to an underestimation of the barrier heights by a few hundred keV.

In this paper we formulate and discuss the strategy of constructing theories capable of providing not only the numerical predictions sensu stricto but also the distributions of probability that such predictions apply in the predefined physics context. Examples of applications of the presented ideas are illustrated using as a choice the nuclear mean-field theory with two realistic realizations of the underlying Hamiltonians: Phenomenological Woods–Saxon and self-consistent Skyrme–Hartree–Fock.