abstract

The study of nuclear limits has been performed and new physical mechanisms and exotic shapes allowing the extension of nuclear landscape beyond the commonly accepted boundaries have been established. The transition from ellipsoidal-to-toroidal shapes plays a critical role in potential extension of nuclear landscape to hyperheavy nuclei. Rotational excitations leading to the birth of particle (proton or neutron) bound rotational bands provide a mechanism for an extension of nuclear landscape beyond spin-zero proton and neutron drip lines.

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In a macroscopic–microscopic approach, the Fourier parametrization of deformed shapes is used to describe the deformation-energy landscapes of nuclei in a 6-dimensional deformation space. A special attention is hereby paid to the convergence of this expansion, in particular for nuclear shapes in the vicinity of the scission configuration. It is shown that the Fourier expansion converges very rapidly and that contributions of multipolarity higher that 4 can be safely neglected, even for extreme deformations as they occur close to the scission configuration.

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We show that semiclassical methods that are traditionally used to describe many-body sytems in physics can also be used to describe partitions that are studied in the number theory within pure mathematics. For the partitions \(P(n)\) of a number \(n\) into sums of distinct squares, we show that the smooth asymptotic part \(P_{\mathrm {as}}(n)\) can be well-reproduced by quantum statistical methods, and that its oscillating part \(\delta P(n)=P(n)-P_{\mathrm {as}}(n)\) is well-reproduced by the periodic orbit theory in terms of a few “orbits” that can be related to Pythagorean triples \((m,p,q)\) of integers with \(m^2+p^2=q^2\).

abstract

The study of the emitted particles, comparing pre-equilibrium and thermal components, is a useful tool to examine the nuclear structure. Possible clustering effects, which may change the expected decay chain probability, could be highlighted on the competition between different reaction mechanisms. The NUCL-EX Collaboration (INFN, Italy) has carried out an extensive research campaign on pre-equilibrium emission of light charged particles from hot nuclei. In this framework, the reactions \(^{16}\)O+\(^{30}\)Si, \(^{18}\)O+\(^{28}\)Si, \(^{19}\)F+\(^{27}\)Al at 7 MeV/\(u\) and \(^{16}\)O+\(^{30}\)Si at 8 MeV/\(u\) have been performed using the GARFIELD+RCo array at Legnaro National Laboratories.

abstract

“Stretched” states are examples of the simplest nuclear excitations in the continuum, thus offering an excellent testing ground for various theoretical approaches. The decay of the stretched single-particle state in \(^{13}\)C, located at 21.47 MeV, was investigated in an experiment performed recently at the Cyclotron Centre Bronowice (CCB) at IFJ PAN in Kraków. First experimental information on the proton and neutron decay channels of this resonance was obtained by employing coincidence measurement of protons inelastically scattered on the \(^{13}\)C target and \(\gamma \) rays from daughter nuclei. The new experimental findings will be used for testing predictions obtained by the Gamow Shell Model calculations.

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In this article, we discuss the effects of the shape instability against the first order tetrahedral-symmetry nuclear shape deformation \(t_1 \equiv \alpha _{32}\) for the \(Z=N\) nuclei in the vicinity of \(Z=40\) using a deformed Woods–Saxon realistic mean-field Hamiltonian. We specifically focus on the effects of the tetrahedral deformation in its formally leading order, \(t_1\), since the recent discovery of the experimental evidence of the corresponding symmetry in the \(^{152}\)Sm nucleus opens the new perspectives in experimental identification of the corresponding exotic nuclear configurations by proposing explicit unprecedented techniques for such applications.

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We present a single-particle basis made of plane-wave states confined in a cubic box designed for Hartree–Fock calculations using a general nuclear two-body interaction with triaxial self-consistent symmetry. We show that this basis allows to calculate two-body nuclear potential matrix elements without recourse to center-of-mass transformations and to calculate exactly Coulomb interaction matrix elements in an economical way. Using various two-body nuclear interactions, we study the Hartree–Fock convergence with the two basis parameters: the cubic edge length and a spherical momentum truncation. We show that the former can be determined by the nuclear radius and the latter is essentially related to the momentum cutoff of the nuclear interaction.

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A recent publication announcing the first identification of the tetrahedral and octahedral symmetries in subatomic physics — the symmetries often referred to as “high-rank” — is taken as an opportunity for a presentation of the series of turning points, which have lead to this discovery. It is known that the nuclear collective E2 (and E1) transitions vanish at the exact high-rank symmetry limit. Consequently, the first experimental tests aimed at studying the collective tetrahedral rotational bands with the de-exciting transitions assumed very weak. At the same time, it has been assumed that the two symmetries will be broken, at least to an extent, and at least via the Coriolis angular momentum alignment and via the zero-point quadrupole motion around high-rank symmetric minima. Accordingly, the spin-parity sequences of the tetrahedral rotational bands were sought under the supposition that they resemble well-known octupole band properties. This strategy led to a few encouraging results but turned out to be inexact; the new strategy, based on the group and group-representation theories led finally to the evidence of signals from both tetrahedral and octahedral symmetries in one single nucleus: \(^{152}\)Sm. Evolution covering nearly 25 years of this research is presented and the perspectives are discussed.

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We discuss the problem of time in quantum systems and stress the need of introducing it as an observable and not just a numerical parameter. This approach allows to redefine the quantum evolution in the form of a series of projections onto the spaces of new states. Within this framework, we describe the temporal version of the double-slit experiment in which a particle interferes with itself from a different instance of time.

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The elastic scattering of neutron on nuclei of actinide group has been investigated. The real part of global optical potential has been used. An algorithm based on direct discretization of a two-dimensional equation is proposed for numerically solving the problem of scattering of axially-symmetrical potential. It has been shown that including of non-spherical form of nuclei gives a significant correction in the description of scattering.

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The yrast positive- and negative-parity level sequences in the spectra of \(^{130-136}\)Nd isotopes are examined, showing that in all of them alternating-parity band (APB) structures can be identified as an indication for the possible manifestation of octupole collectivity. The selected band-structures are tested for the presence of quadrupole–octupole (QO) (or pear-shape) deformations within the “rigid” and “soft” limits of a collective QO model. It is found that at moderate angular momenta, the APBs in \(^{130-134}\)Nd exhibit a structure which can be associated with soft QO vibrations and rotation, whereas the APB in \(^{136}\)Nd shows signs of a stabilization of the QO shape. Besides, the higher APB levels in \(^{134}\)Nd give an indication for possible QO shape stabilization and suggest a transition behaviour of this nucleus between the two limits of QO collectivity. The study opens a way for further detailed investigation of the shape dynamics in this nuclear region.

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Using the Fourier shape parametrisation of deformed nuclei developed by us recently, potential-energy landscapes for isotopes of nuclei between platinium (\(Z=78\)) and lead (\(Z=82\)) are analysed in a 4-dimensional deformation space, searching for local extrema, ridges and valleys. A certain number of yet unknown super- and hyper-deformed shape isomers in even–even Pt, Hg and Pb isotopes are predicted. Quadrupole moments in the relevant minima are evaluated. A nice agreement of the theoretical predictions with the experimental ground-state data for these quantities gives strong confidence on the quality of our results for the corresponding isomeric states.

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We develop a novel theoretical method for calculating spectroscopic properties of those nuclei with odd number of nucleons that is based on the nuclear density functional theory and the particle–boson coupling scheme. A self-consistent mean-field calculation based on the DFT is performed to provide microscopic inputs to build the Hamiltonian of the interacting boson–fermion systems, which gives excitation spectra and transition rates of odd-mass nuclei. The method is successfully applied to identify the quantum shape phase transitions and the role of octupole correlations in odd-mass nuclei, and is further extended to odd–odd nuclear systems.

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The paper contains the description of a new method for decomposition of arbitrary Hamiltonians and other operators into the tensor form. The method is based on a special kind of projection operators acting in the space of appropriate operators. The properties of these projection operators and the decomposition method are presented.

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Numerous highlights from the rich scientific attainments of the late Professor Władysław Świątecki are presented. The influence of his main achievements on the development of nuclear theory is shown on a few examples.

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The concept of an intrinsic system can be extended to the case of collective octupole degrees of freedom by exploiting the symmetry properties with respect to transformations of the octahedral group \(O_h\). Explicit formulas for scalar invariants as polynomials of intrinsic variables are presented. A method of constructing a basis in the space of functions on the octupole intrinsic space is proposed.

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The nuclear level densities of superheavy nuclei at the ground state and at the saddle point are calculated using the single-particle energies obtained with the Woods–Saxon potential. The level density parameters are calculated by fitting the obtained results with the Fermi gas expression. The energy and shell correction dependencies of the level density parameter at the ground state and at the saddle point are studied and compared with phenomenological expressions. The ratios of the level density parameters at the saddle point to those of the ground state are calculated.

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Innovative experiments are conducted to widen our approach to fission, aiming notably at a complete identification and characterization of the fragments and the study of unstable fissioning systems. In the GANIL facility, full fission-fragment distributions and fragment kinetic energies are measured, thanks to the inverse kinematics technique and the magnetic spectrometer VAMOS. The access to the scission-point information is possible thanks to the low-energy regime. The initial excitation energy of the systems is also determined due to the well-defined transfer reactions. In this work, fission yields and fission-fragment kinetic energies of \(^{239}\)U, as well as the evolution of the yields with the initial excitation energy of \(^{240}\)Pu, are presented.

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Attempts are discussed to derive covariant density functionals ab initio, i.e. from the bare nucleon–nucleon forces. They are based on the Relativistic Brueckner–Hartree–Fock (RBHF) theory which, in most cases, has been applied for nuclear matter. For semi-microscopic functionals, such calculations are used to derive the density dependence of the parameters. In this way, only very few phenomenological parameters are left for the fine tuning. The RBHF calculations in finite nuclear systems are used to obtain additional formation as, for instance, the strength of effective tensor forces, which are difficult to obtain in a phenomenological way from the data.

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The Generating Coordinate Method applied to the description of the collective quadrupole states of both the even- and the odd-particle nuclei is resumed. The five laboratory components of the spherical quadrupole tensor are taken as the generator coordinates. Use of the method for the even and the odd systems is confronted with regard to the conservation of the time-reversal symmetry. The adiabatic approximation for the overlaps of the generating functions in the case of systems with the conserved and the broken time-reversal symmetry is formulated. In that approximation, the Hill–Wheeler equations can be substituted by the one second-order differential equation in the case of the time-even nuclei, and by the system of the two coupled second-order differential equations in the case of those with the broken time-reversal symmetry. In the former case, the new formulae for the weight, the inertial functions and moments of inertia, and the potential of the Bohr Hamiltonian were obtained. In the latter one, the new approach to the description of the collective quadrupole states of the odd nuclei was formulated.

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We present the calculation of the symmetry energy \(E_\mathrm {sym}\), its first \(L_\mathrm {sym}\) and second derivative \(K_\mathrm {sym}\). To achieve it, we will further extend the Relativistic Mean Field (RMF) model already developed with finite nucleon volumes inside Nuclear Matter (NM). The correction to the nucleon energy \(\varepsilon _A\) is proportional to the product of nucleon volume \(V_N\) and pressure. It gives the first order differential equation for energy \(\varepsilon _A\) and we derive here a similar differential equation for \(E_\mathrm {sym}\). The resulting Equations of State (EoS) are softer.

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We present recent shell-model calculations of the \(\gamma \)-decay in \(sd\)–\(pf\)- and \(pf\)-shell nuclei. We focus on the M1 part of the dipole strength which was shown to exhibit interesting low-energy effects, in particular a low-energy enhancement which can have a considerable impact on the radiative neutron capture. We discuss the persistence of the shell effects in the nuclear quasi-continuum and the relation between the shape of the strength function at low-energy and nuclear deformation.

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Recent work on the symmetry energies of nuclear matter at supra-saturation densities by the ab initio Relativistic Brueckner–Hartree–Fock calculations as well as the nonrelativistic and relativistic state-of-the-art density functional theories is reviewed, which was motivated by the historical detection of gravitational waves from GW170817. By investigating the neutron star and the neutron drop, i.e. , a certain number of neutrons confined in an external field, strong correlations are found between the neutron star tidal deformability and the symmetry energies of nuclear matter at supra-saturation densities. From the correlations and the upper limit on the tidal deformability extracted from GW170817, the symmetry energy at twice saturation density is constrained by the ab initio Relativistic Brueckner–Hartree–Fock theory and the state-of-the-art density functional theories.

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We apply a new calculation scheme of a finite element method and upgraded program KANTBP in the coupled-channels calculations for heavy-ion fusion reactions. We diagonalize the matrix of close coupled effective potentials to formulate ingoing wave boundary conditions in point within a pocket of the potential well with a true set of thresholds. Efficiency of the proposed approach is shown by successfully described experimental data for the sub-barrier and above-barrier fusion cross section of some reaction systems.

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The chirality in atomic nucleus has attracted a lot of attention in the last few decades. Based on the covariant density functional theory, the multiple chiral doublets (M\(\chi \)D), i.e. , more than one pair of chiral doublet bands in one single nucleus, has further been predicted in 2006, and attracted extensive attention. In this contribution, the M\(\chi \)D with octupole correlations observed in \(^{78}\)Br are discussed within the framework of recently developed reflection-asymmetric triaxial particle rotor model (RAT-PRM). In particular, the effects of the triaxial and octupole deformation degrees of freedom are discussed.

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Nuclear chirality is one of the hot topics in nuclear physics and has attracted great interests in the past decades. Studies on nuclear chirality in both experimental and theoretical sides have been carried out extensively. Among various theoretical investigations, the microscopic covariant density functional theory (CDFT) plays important roles. In this contribution, recent applications of the three-dimensional tilted axis cranking covariant density functional theory (3DTAC-CDFT) on nuclear chirality are reviewed. In particular, the multiple chirality in \(^{106}\)Rh and the chiral conundrum in \(^{106}\)Ag are discussed.