abstract

Impact of nuclear structure on the production of superheavy nuclei in complete fusion reactions is discussed. Possible proton shell closure at \(Z=120\) is considered.

abstract

The conventional Skyrme interaction is generalized by adding zero-range charge-symmetry-breaking and charge-independence-breaking terms, and the corresponding energy density functional is derived. It is shown that the extended model accounts for experimental values of mirror and triplet displacement energies (MDEs and TDEs) in \(sd\)-shell isospin triplets with, on average, \(\sim 100\) keV precision using only two additional adjustable coupling constants. Moreover, the model is able to reproduce, for the first time, the \(A=4n\) versus \(A=4n+2\) staggering of the TDEs.

abstract

The recent progresses of the collective Hamiltonian and its applications for chiral and wobbling modes are reviewed. In particular, the phenomenon of the multiple chiral doublet bands that are given by the collective Hamiltonian is introduced. In the investigation of the wobbling mode, the wobbling frequency as a function of the rotational frequency by the collective Hamiltonian in comparison with the harmonic frozen alignment approximation results for the longitudinal and transverse wobbling is discussed.

abstract

Pairing reentrance phenomenon in the warm rotating \(^{104}\)Pd nucleus is studied within the Bardeen–Cooper–Schrieffer (BCS)-based approach (the FTBCS1). The theory takes into account the effect of quasiparticle number fluctuations on the pairing field at finite temperature and angular momentum within the pairing model plus non-collective rotation along the symmetry axis. The numerical calculations for the pairing gaps and nuclear level densities (NLD), of which an anomalous enhancement has been experimentally observed at low excitation energy \(E^*\) and high angular momentum \(J\), show that the pairing reentrance is seen in the behavior of pairing gap obtained within the FTBCS1 at low \(E\) and high \(J\). This leads to the enhancement of the FTBCS1 level densities, in good agreement with the experimental observation. This agreement indicates that the observed enhancement of the NLD might be the first experimental detection of the pairing reentrance in a finite nucleus.

abstract

A possibility to use the first, second, third and fourth unique forbidden \(\beta \) decays for the determination of the absolute mass of neutrinos is addressed. For selected nuclear systems with small \(Q\) value, the energy distribution of emitted electrons is presented. Calculations are based on the exact Dirac wave functions of the electron with finite nuclear size and the electron screening taken into account. It is shown that the Kurie plot near the endpoint is within a good linear accuracy in the limit of massless neutrinos like the Kurie plot of the superallowed \(\beta \) decay of tritium.

abstract

An approximation is proposed in Beyond mean field calculations to reduce the size of the grid subtended by the generator coordinates by one order of magnitude. We show the quality of the approximation calculating the excitation energies of the titanium isotopes and the E2 transition probabilities.

abstract

A comprehensive study of various ground-state properties of neutron-rich and neutron-deficient Mg isotopes with \(A=20\)–36 is performed in the framework of the axially symmetric self-consistent Skyrme–Hartree–Fock plus BCS method. The correlation between the skin thickness and the characteristics related with the density dependence of the nuclear symmetry energy is investigated for the same isotopic chain following the theoretical approach based on the coherent density fluctuation model. The results of the calculations show that the behavior of the nuclear charge radii and the nuclear matter properties in the Mg isotopic chain is closely related with the nuclear deformation. We also study the emergence of an “island of inversion” at the neutron-rich \(^{32}\)Mg nucleus proposed from the analyses of spectroscopic measurements of its low-lying energy spectrum and the charge r.m.s. radii of all magnesium isotopes in the \(sd\) shell.

abstract

The theoretical results of the individual \(xn\), \(\alpha xn\), \(pxn\), \(p\alpha xn\), and \(2\alpha xn\) evaporation residue excitation functions in the \(^{16}\)O+\(^{204}\)Pb, \(^{40}\)Ar+\(^{180}\)Hf, \(^{82}\)Se+\(^{138}\)Ba, and \(^{124}\)Sn+\(^{92}\)Zr reactions leading to the \(^{220}\)Th compound nucleus are presented and analyzed with the aim to study the entrance channel effects on the evaporation residue yields. The comparison of the complete theoretical results with the available experimental determinations shows a large difference connected with the unknown and unidentified nuclei of the total ER production. Such a difference between experimental and theoretical results also appears clearly by comparing the trend of the \(\sigma _{{\mathrm {ER}}xn} / \sigma _{\rm ERtot}\) ratio as a function of the excitation energy of the compound nucleus for the investigated reactions.

abstract

A series of experiments show that the physical time is the same kind of quantum observable as the spatial position. The quantum temporal effects seem to be an important feature of physical processes with the characteristic times shorter than femtoseconds. In this paper, the idea of slow (weak temporal effects) and fast (stronger temporal effects) nuclear processes is considered.

abstract

The electron–positron angular correlation was measured for the isoscalar magnetic dipole 18.15 MeV transition in \(^{8}\)Be. Significant, peak-like deviation was observed from the internal pair creation at \({\mit \Theta }\approx 140^{\circ }\) in the angular correlation. This observation might indicate that in an intermediate step a neutral isoscalar particle with a mass of \(16.70\pm 0.35\) (stat.)\(\pm 0.5\)(sys.) MeV\(/c^2\) and \(J^\pi = 1^+\) was created.

abstract

The time-dependent energy density functional with pairing allows to describe a large variety of phenomena from small to large amplitude collective motion. Here, we briefly summarize the recent progresses made in the field using the TD-BCS approach. A focus is made on the mapping of the microscopic mean-field dynamics to the macroscopic dynamics in collective space. A method is developed to extract the collective mass parameter from TD-EDF. Illustration is made on the fission of \(^{258}\)Fm. The collective mass and collective momentum associated to quadrupole deformation including non-adiabatic effects is estimated along the TD-EDF path. With these information, the onset of dissipation during fission is discussed.

abstract

Fission fragment mass- and charge-distributions are among those experimental observables which could be directly compared to the theoretical predictions related to the Poincaré shape transitions accompanying an increase of the nuclear angular momentum. We apply the macroscopic nuclear liquid drop model to illustrate some characteristic features of the Poincaré transitions focusing on the static and dynamical estimates of the fission fragment mass-asymmetry. As an example, the results for \(^{98}\)Mo are shown.

abstract

A collective nuclear model of two-dimensional (2D) axial quadrupole–octupole (QO) vibrations coupled to rotations, originally restricted to coherent vibration modes allowing exact separation of variables and analytic solution of the eigenvalue problem, is developed beyond this restriction. The complete 2D problem is solved by diagonalizing the unrestricted QO Hamiltonian in the basis of the analytic solution. The test calculation for \(^{152}\)Sm showed that in this way the model description of yrast alternating-parity levels and the attendant \(B\)(E1)–\(B\)(E3) transition probabilities is considerably improved compared to the coherent-mode case. At the same time, the shape of the QO potential is unambiguously determined providing model estimates for the quadrupole and octupole deformations of the nucleus.

abstract

Recent applications of the semi-realistic nucleonic interaction to the nuclear mean fields are presented: (i) prediction of magic numbers in the whole nuclear chart and (ii) isotope shifts of the \(Z={\rm magic}\) nuclei with the density-dependent LS interaction. In (i), it is found that the known magic numbers are well reproduced with only a few exceptions, from light to heavy stable and unstable nuclei, with the M3Y-P6 interaction. A part of this success is attributed to the realistic tensor force included in the interaction. In (ii), the kink of the Pb nuclei and the vanishing isotope shift of \(^{48}\)Ca relative to \(^{40}\)Ca, both of which have supplied long-standing problems, can be described fairly well, if we take into account the density-dependence in the LS channel indicated by the chiral effective field theory. These results illustrate that a proper combination of microscopic theories and phenomenology on effective interactions can advance nuclear structure physics.

abstract

The time-dependent density functional theory (TDDFT) provides a unified description of the structure and reaction. The linear approximation leads to the random-phase approximation (RPA) which is capable of describing a variety of collective motion in a harmonic regime. Beyond the linear regime, we present applications of the TDDFT to nuclear fusion and fission reaction. In particular, the extraction of the internuclear potential and the inertial mass parameter is performed using two different methods. A fusion hindrance mechanism for heavy systems is investigated from the microscopic point of view. The canonical collective variables are determined by the adiabatic self-consistent collective coordinate method. Preliminary results of the spontaneous fission path, the potential, and the collective mass parameter are shown for \(^8\)Be\(\rightarrow \alpha +\alpha \).

abstract

In this short communication, we have interpreted TAMU data for peripheral collisions of \(^{40}\)Ca + \(^{112,124}\)Sn and \(^{48}\)Ca + \(^{112,124}\)Sn at \(E/A =32\) MeV with different isospin degrees of freedom which were studied at the Cyclotron Institute of Texas A&M University (TAMU) using the K500 Superconducting Cyclotron. Isotopic yields of light intermediate mass fragments \(Z\leq 8 \), (here, we only consider carbon isotopes) were studied on the basis of the statistical multifragmentation model. It is seen from the fractional yields that the neutron-rich systems preferentially populate the most neutron-rich isotopes. It is confirmed that symmetry energy is the main parameter governing the isotopic composition of the fraction yields.

abstract

We present the first study of the pairing properties of the Skyrme pseudo-potential including higher order gradient terms in cold symmetric nuclear matter.

abstract

The fission fragments mass-yield is obtained by an approximate solution of the eigenproblem of the two-dimensional collective Hamiltonian corresponding to the fission and mass asymmetry modes. The potential energy surface was calculated by the macroscopic–microscopic method using the liquid drop model for the macroscopic part. The microscopic corrections were obtained using the Woods–Saxon single particle levels. The modified Cassini ovals shape parametrization in four dimensions was used to evaluate the potential energy surface. The mass tensor is taken within the cranking-type approximation.

abstract

A new parametrization of nuclear shapes is proposed as a Fourier series of the square of the distance from the symmetry axis to the surface of the nucleus. It is shown that using the three lowest terms of such an expansion is sufficient to obtain a rather good reproduction of the form of the liquid-drop fission barrier. Taking into account higher order terms of the rapidly converging Fourier series increases the precision of the estimates of both macroscopic and microscopic parts of the total nuclear binding energy.

abstract

Over several decades doubt has been cast on the “\(\beta \) vibration” interpretation of the first excited \(0_2^+\) rotational bands in deformed nuclei. Experimental evidence is presented to show that low-lying \(0_2^+\) bands in deformed nuclei are \(2p\)–\(2h\) seniority zero pairing isomers lowered into the pairing gap by configuration-dependent pairing. Doubts then arise about the interpretation of the lowest \(K^\pi =2^+\) rotational bands observed in all deformed nuclei as “\(\gamma \) vibrations”. Experimental evidence for these \(K^\pi =2^+\) rotational bands existing as a consequence of the lack of axial symmetry is addressed. We are forced to conclude that “phonon excitation” models of even–even deformed nuclei are deeply flawed.

abstract

Nuclei in the Businaro–Gallone region are proposed as a relevant tool to study the dynamics of nuclear fission at high temperature. The influence of the macroscopic contribution to the driving potential energy landscape, and its strong dependence on angular momentum, is addressed in this contribution as a first step. An advanced model based on a four-dimensional Langevin approach is used to calculate fission-fragment mass and charge distributions. A good agreement with experiment is observed. The work is in progress, with the goal to explore the major assets of nuclei in this region for probing the modeling of inertia, friction and fluctuations, and particle evaporation.

abstract

The left–right symmetric models provide different mechanisms of the neutrinoless double beta decay (\(0\nu \beta \beta \)-decay) with left-handed and right-handed currents, which might be of comparable importance. A new generation of the \(0\nu \beta \beta \)-decay experiments with improved sensitivity is currently under design and construction. From them practically only the SuperNEMO experiment, which will employ tracking and calorimetry approach, will be able to distinguish among these mechanisms. In this contribution, the single electron energy distribution associated with light neutrino exchange mechanisms of the \(0\nu \beta \beta \)-decay of \(^{48}\)Ca and \(^{82}\)Se is presented and the sensitivity of the SuperNEMO Demonstrator and SuperNEMO experiment to various lepton number violating parameters is calculated.

abstract

A comprehensive calculation of ground state properties of a large number of even–even nuclei has been carried out using the Gogny D1S force within the extended Thomas–Fermi scheme. It is found that the calculated self consistent potentials and densities can be parametrised as Fermi distributions. As the next step, the parametrised potentials and densities are used to calculate the smooth part of energy and the shell corrections within the Wigner–Kirkwood semi-classical averaging scheme. The shell corrections thus obtained, along with a simple liquid drop prescription, is found to yield a reasonably good description of ground state masses for nuclei spanning the entire periodic table.

abstract

The old problem of whether the coefficients of the leptodermous expansion of the finite nucleus incompressibility (Blaizot’s formula) can be fitted using the available experimental data of giant monopole resonances is revisited. Using a mean field model (NL3) as a benchmark, we compute the finite nucleus incompressibility of a large set of nuclei in the scaling approach. These values are fitted to Blaizot’s formula and a covariance matrix analysis is performed. From this study, it is seen that some of the fitted coefficients of the leptodermous expansion are strongly contaminated by the neglected terms and differ considerably from the original coefficients which can be directly computed for the given mean field model. As a consequence, it does not seem possible to use the coefficients of Blaizot’s formula fitted to experimental information on giant monopole resonances to accurately constrain mean field models available in the literature.

abstract

Based on the Woods–Saxon potential, we have developed a configura-tion-constrained potential energy surface calculation. This method has been successfully applied to the calculations of various multi-quasiparticle high-\(K\) states in different mass regions, well reproducing the experimental excitation energies and other observations. Further, we have developed the configuration-constrained total Routhian surface calculation for the rotations of the multi-quasiparticle high-\(K\) states. The pairing calculation is improved by a particle-number-conserving pairing method which always gives converged solutions for the cranking Hartree–Fock pairing calculations. In this paper, we focus on the predictions of possible octupole deformed high-\(K\) states in the actinide mass region. Using the developed configuration-constrained total Routhian surface method, we have investigated high-\(K\) rotations for nuclei around \(Z=100\) and 102 with \(N\approx 150\).

abstract

The low-lying structures of the even–even Gd isotopes, including the partial dynamical symmetry candidates \(^{156\textrm {--}162}\)Gd, are investigated in the framework of five-dimensional collective Hamiltonian based on the covariant density functional theory with the density functional PC-PK1. The available experimental data are reproduced by the microscopic calculations. A shape evolution from the \(\gamma \)-soft \(^{150}\)Gd to the well-deformed prolate \(^{162}\)Gd is presented. The ground states of the partial dynamical symmetry candidates \(^{156\textrm {--}162}\)Gd are all well-deformed prolate at \(\beta \sim 0.35\).