abstract

The research in the field of superheavy elements started in the sixties of the last century triggered by the prediction of a region of enhanced nuclear stability at the next closed proton and neutron shells beyond \(^{208}\)Pb. Adam Sobiczewski was one of the first predicting proton and neutron numbers for these shell closures at \(Z=114\) and \(N=184\), respectively. In the following decades, extensive efforts led to the synthesis of isotopes of elements up to \(Z=118\) in a fruitful competition of the leading laboratories in the field with FLNR/JINR in Dubna, Russia, LBNL in Berkeley, USA, GSI in Darmstadt, Germany and most recently RIKEN in Wako (Tokyo), Japan. Beyond the synthesis of new elements and isotopes, substantial activities were dedicated to nuclear structure studies, laying the basis for the understanding of this exotic nuclear matter. In-beam spectroscopy as well as decay spectroscopy after separation (DSAS) together with the support by theory have the potential to lay the basis for a successful approach of the so-called island of stability, the firm grounds, the creation of which had been started by pioneers like Adam Sobiczewski in the beginning of the second half of last century. In this paper, some of the achievements mainly of DSAS will be presented, with an emphasis on the guidance by theory and the work of Adam Sobiczewski, to whom this paper is dedicated.

abstract

A consistent framework for treating the energy dependence of fission-fragment neutron multiplicities is presented. The shape evolution of the compound nucleus towards scission is treated in the strong damping limit using the Metropolis walk method. The available excitation energy at scission is then divided statistically between the two fragments using microscopic level densities. Deformation energies, which contribute to the excitation energy when the fragments relax to their ground-state shapes, are also computed. From the total fragment excitation energies, the number of emitted neutrons is obtained and illustrated for neutron-induced fission of \(^{235}\textrm {U}\).

abstract

Different Skyrme functional parametrizations were tested for Ce and Nd isotopes for \(N \gt 82\). The method employed in the study is the axial Skyrme–Hartree–Fock model+BCS. For selected parametrizations, ground-state deformations \(\beta _{2}, \beta _{3}\) and \(\beta _{4}\) have been found and the evolution of single-neutron and single-proton states around the Fermi level along the chain of Ce and Nd isotopes has been investigated. These results were then compared to the existing experimental data.

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The energies of low-lying non-rotational states are calculated taking into account the residual pairing and phonon–quasiparticle interactions. Two mean-field potentials, Woods–Saxon- and Skyrme-based potentials, are used. The hot fusion reactions \(^{50}\)Ti+\(^{247-249}\)Bk and \(^{51}\)V+\(^{246-248}\)Cm are compared for the synthesis of element 119.

abstract

We discuss and illustrate a computer-designed algorithm allowing to construct the nuclear potential energy surfaces generated by a mean field Hamiltonian \(H(\alpha )\) as functions of the ensemble of nuclear deformation variables \(\alpha \) for multi-particle multi-hole excited configurations. The algorithm in question serves to eliminating the undesired effect of the so-called avoided crossing mechanism, a consequence of the well-known property referred to as Landau–Zener non-crossing rule.

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Transport coefficients, such as the collective potential, inertia, friction and diffusion tensors, that are required in any dynamical description of the fission process are reviewed. These are mandatory when solving e.g. the Langevin equation that allows to follow the time evolution of a deformed, hot rotating nucleus from its formation in a heavy-ion collision up to the scission instability. The present study is carried out using a new shape parametrization which we have developed and which is based on a Fourier expansion of the nuclear shape function.

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We present the formalism of the linear response theory in symmetric nuclear matter for a finite-range central interaction including zero-range spin–orbit and tensor components.

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Following a recent discovery of the simultaneous signs of the octahedral and tetrahedral symmetries in \(^{152}\)Sm, we discuss the issue of a competition between the two symmetries in atomic nuclei together with the identification criteria. Illustrations using selected rare-earth and zirconium nuclei as examples are presented.

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We discuss criteria for experimental identification of the nuclear tetrahedral and octahedral so-called high-rank symmetries based on the mean-field and group representation theories. We examine the possibly largest search zones on the \((Z,N)\)-plane: in addition to traditionally discussed areas of even–even nuclei with proton and neutron numbers surrounding the tetrahedral magic ones (\(Z_0^{\mathrm {t}},N_0^{\mathrm {t}} = 32\), 40, 56, 64, 70, 90, 112, 136), we discuss also the odd–even and even–odd nuclei for which the identification criteria non-trivially differ from those for the even–even ones. We also propose the appropriately chosen particle–hole excited states to profit from the deformation driving mechanism contributed by combinations of certain orbitals. The discussion is summarised in the form of a series of ‘user’ instructions.

abstract

We discuss the problem of time in quantum systems. We present experimental observations which are hard or impossible to explain on the grounds of conventional quantum mechanics. The need of introducing time as an observable and not just a numerical parameter is stressed. We show that this is possible in the projection evolution approach.

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We apply a new calculation scheme of a finite element method (FEM) for solving an elliptic boundary-value problem describing a quadrupole vibration collective nuclear model with tetrahedral symmetry. We use shape functions constructed with interpolation Lagrange polynomials on a triangle finite element grid and compare the FEM results with those obtained earlier by a finite difference method.

abstract

Experimental data related to the discovery of elements 107 to 112 measured at the velocity filter SHIP at GSI, Darmstadt, confirmed the predictions of a region of relatively high nuclear stability of deformed super-heavy nuclei. This region is located at proton and neutron numbers 108 and 162, respectively. The isotopes were successfully produced using cold fusion reactions. Experimental exploration of the predicted island of spherical super-heavy nuclei was only possible using hot fusion reactions. At the GSI SHIP, one of these reactions was studied using a \(^{248}\)Cm target. In reactions with a \(^{48}\)Ca beam, the previously known data on isotopes of element 116 were confirmed. Results from an attempt to search for element 120 using a \(^{54}\)Cr beam are presented. In a complementary study, relative masses, model-dependent shell-correction energies, and related heights of fission barriers were deduced from measured \(Q_\alpha \) values. The results are compared with predictions of macroscopic–microscopic models. The consequences for calculations of cross sections are discussed.

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Study of shell evolution and the appearance of new magic numbers make an important tool to improve and study the monopole effect. In the framework of studying and understanding the role of the latter, shell model calculations have been realized for interpreting and developing the two-body matrix elements of \(N\)–\(N\) interaction. In this context and in order to reproduce the nuclear spectra of even–even \(Z=38\) isotopes, we have performed these calculations using recent experimental single-particle energies (SPEs), by means of NuShellX@MSU nuclear structure code. The two-body matrix elements (TBMEs) of the using effective interaction were deduced from the \(jj44bpn\) realistic interaction for \(^{56}\)Ni mass region. The received results show an acceptable agreement with the available experimental data, which prove the influence of the monopole effect.

abstract

Thermal Shape Fluctuation (TSF) Model describes the properties of the Giant Dipole Resonance (GDR) radiation emitted by hot rotating nuclei. This approach turned out to be a very efficient method of extracting the information about the shapes of nuclei and their evolution with increasing angular momentum. The GDR can be built also on the ground-state band but this process needs advanced microscopic methods to be described adequately. We propose to investigate the GDR strength function with the developed for this purpose TSF model. The potential energy surface, which allows to calculate the shape probability using the so-called Boltzmann factor, is obtained within macroscopic–microscopic method, where the Folded-Yukawa model is used for macroscopic part and Folded-Yukawa plus exponential mean-field potential to generate the single-particle energies. The Strutinsky shell-, and the particle number projected BCS pairing-correction energies give the microscopic contribution to the energy of a nucleus at each given deformation. The method has been tested for selenium and neodymium isotopes for which the photo-absorption spectra were measured and preliminary results will be presented.

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We summarize a description of heavy-ion fragmentation reactions at low and intermediate energies in terms of a Boltzmann–Vlasov transport approach for the production of the hot, excited primary fragments, followed by a statistical decay of these to arrive at the measured cold fragments. We compare isotope distributions and velocity spectra to experimental data. While the isotopic distributions are reasonably well-described by this microscopic approach, there are larger differences in the velocity distributions. These seem to be due to too small fluctuations in the transport calculation and to the presence of more direct reaction processes in the data.

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Recently, the magnetic and electric radiative decay rates of the 7.8 eV \(^{229m}\)Th isomer have been predicted within a model of nuclear collective quadrupole–octupole (QO) and single particle (s.p.) motions with the Coriolis interaction. As a next step, in the study we examine the magnetic dipole moment (MDM) in the \(K=5/2^{+}\) ground and \(K=3/2^{+}\) isomeric states based on the parity-projected s.p. wave functions obtained for the odd neutron in both states without consideration of the Coriolis mixing effects. The comparison with experimental data shows that the description of MDMs may impose additional constraint on the model parameters providing further tuning of the predicted isomer-decay rates in favour of the efforts for establishing of a “nuclear clock” frequency standard.

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The fine structure of the scissors mode is investigated within the Wigner Function Moments (WFM) method. The solution of time-dependent Hartree–Fock–Bogoliubov equations by WFM method with the isovector–isoscalar coupling taken into account predicts splitting of the scissors mode into three branches. Together with the conventional scissors mode generated by the counter-rotation of protons against neutrons, two new modes arise when the spin degrees of freedom are taken into account. First, we turn to \(^{160,162,164}\)Dy isotopes. Accounting for spin scissors allows to explain the nature of two groups of M1 excitations with an anomalously large summed magnetic strength experimentally detected in \(^{164}\)Dy. A comparison with the recently reanalyzed data of Oslo-type experiments is presented.

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We discuss advanced statistical methods to improve parameter estimation of nuclear models. In particular, using the Liquid Drop Model for nuclear binding energies, we show that the area around the global \(\chi ^2\) minimum can be efficiently identified using the Gaussian Process Emulation. We also demonstrate how the Markov-chain Monte Carlo sampling is a valuable tool for visualising and analysing the associated multidimensional likelihood surface.

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We adopt the Hartree–Fock (HF) method and the nucleon–\({\mit \Lambda }\) Tamm–Dancoff Approximation (N\(\Lambda \) TDA) to study the energy spectra of selected medium mass hypernuclei composed of a \({\mit \Lambda }\) hyperon bound to an even–even and odd–even nuclear cores. Our calculations are carried out using the \(YN\) LO potential plus the chiral potential NNLO\(_{\mathrm {sat}}\), which includes explicitly the 3-body \(NNN\) force. This component, while improving the r.m.s. radii of the nuclear cores and the relative distances between levels or group of levels of the hypernuclear spectra, strongly reduces the binding energies indicating that the inclusion of more complex configurations is badly needed.

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Rotational energies of heavy and super-heavy nuclei are evaluated in the cranking model which couples the pairing field with the rotational motion. The nuclear ground-state deformation is determined within the macroscopic–microscopic model.

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The history of the discovery of super-heavy nuclei is strongly related to the name of Professor Adam Sobiczewski who passed away two years ago. Already in 1966, he and his co-workers had predicted new proton and neutron magic numbers in very heavy nuclei that had not yet been observed at that time. During the last 50 years his and his group’s theoretical estimates of properties of super-heavy nuclei such as spontaneous fission probabilities or alpha-decay half-lives have served to experimentalists all over the world as a guideline in exploring this terra incognita in the chart of atomic nuclei.

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Electron scattering is a tool that can provide relatively clean view of the nuclear structure in both ground and excited states, as it depends on the well-known electromagnetic interaction. But since the common expressions for its cross section were derived with certain assumptions, in this paper, we describe several nontrivial steps necessary for a proper theoretical calculation within the current density-functional framework, namely with Skyrme QRPA for axial nuclei, with the aim to enable comparison of the theoretically predicted low-lying \(1^-\) toroidal modes with future \((e,e')\) experiments.

abstract

A new Skyrme functional including tensor terms is presented. The tensor terms have been determined by fitting the results of relativistic Brueckner–Hartree–Fock (RBHF) studies on neutron–proton drops. Unlike all previous studies, where the tensor terms were usually determined by fitting to experimental data of single-particle levels, the pseudodata calculated by RBHF does not contain beyond mean-field effect such as the particle-vibration coupling and, therefore, can provide information on the tensor term without ambiguities. The obtained new functional, named SAMi-T, can describe well ground-state properties such as binding energies, radii, spin–orbit splittings and, at the same time, the excited state properties such as those of the Giant Monopole Resonance (GMR), Giant Dipole Resonance (GDR), Gamow–Teller Resonance (GTR), and Spin-Dipole Resonance (SDR).

abstract

The symmetry energy of the D1 family of Gogny interactions, which describe finite nuclei properties in good agreement with experimental data, shows too soft a behaviour above saturation density. As a consequence, the D1 family of Gogny forces often cannot describe the properties of neutron stars when extrapolated to the high-density region. To overcome this limitation, we have proposed reparametrizations of the D1M interaction with very minimal changes. The modified interactions retain the quality of the original force for dealing with finite nuclei and, at the same time, are able to describe the neutron star physics with a quality similar to the one provided by the Skyrme SLy4 force, which was specially designed for this purpose.

abstract

We use the Weizsäcker–Skyrme (WS) mass models to systematically investigate nuclear deformation energies. With an accuracy of 298 keV for the known masses, the WS4 mass model is quite helpful for exploring new magic numbers in neutron-rich region and nuclear deformation energies. We note that the predicted deformation energies of nuclei with the Hartree–Fock–Bogoliubov (HFB25) model are systematically larger than those with the WS models, especially for nuclei with sub-shell closures. The comparison of the deformation energies from the two models and the corresponding charge radii for nuclei with \(N=14\) are also presented.