Proceedings Series

Vol. 10 (2017), No. 1, pp. 1 - 290

XXIII Nuclear Physics Workshop “Marie and Pierre Curie” Essential Problems in Nuclear Physics

Recent Progress in the Studies of Neutron-rich and High-\(Z\) Systems Within the Covariant Density Functional Theory

Acta Phys. Pol. B Proc. Suppl. 10, 7 (2017)

page 7 •


The analysis of statistical and systematic uncertainties and their propagation to nuclear extremes has been performed. Two extremes of nuclear landscape (neutron-rich nuclei and superheavy nuclei) have been investigated. For the first extreme, we focus on the ground state properties. For the second extreme, we pay a particular attention to theoretical uncertainties in the description of fission barriers of superheavy nuclei and their evolution on going to neutron-rich nuclei.

Energy Landscapes at Finite Angular Momentum Within the Fourier Shape Parametrization

Acta Phys. Pol. B Proc. Suppl. 10, 17 (2017)

page 17 •


Deformation-energy landscapes for nuclei at finite angular momentum are presented and analysed with respect to possible shape transitions known as Maclaurin, Jacobi and Poincaré instabilities. To be able to perform such a study, it turns out that a vast variety of nuclear shapes needs to be considered. For such an analysis, we rely on the recently developed Fourier shape parametrization, together with the macroscopic–microscopic model, an approach which proves to yield excellent results.

Collective Hamiltonian for Chiral and Wobbling Modes: From One- to Two-dimensional

Acta Phys. Pol. B Proc. Suppl. 10, 27 (2017)

page 27 •


The recent progresses of the two-dimensional collective Hamiltonian and its applications for chiral and wobbling modes are reviewed. In particular, the comparisons between the results by one- and two-dimensional collective Hamiltonian are introduced.

full authors' list

M. Ciemała, M. Kmiecik, A. Maj, B. Wasilewska, M. Ziębliński, A. Bracco, F. Camera, F.C.L. Crespi, F. Gramegna, S. Valdré, G. Casini

Fission of Highly Excited \(^{88}\)Mo Compound Nucleus

Acta Phys. Pol. B Proc. Suppl. 10, 35 (2017)

page 35 •


Here, a detailed view of the fusion-fission channel analysis is presented. Experimental data were analysed, and compared to calculations done with statistical model code GEMIINI++. Presented is a good agreement between calculations and experimental data. Results prove that GEMINI++ calculations can be used to reproduce experimental fusion-fission cross sections as well as fission fragments velocities.

The Hybrid Configuration Mixing Model and the Spectroscopy of Odd Nuclei

Acta Phys. Pol. B Proc. Suppl. 10, 43 (2017)

page 43 •


We introduce a new approach which is meant to be a step towards complete low-lying spectroscopy of odd nuclei. In the first applications, we limit ourselves to a magic core plus an extra neutron or proton. The model does not contain any free adjustable parameter, but is based on a Hartree–Fock (HF) description of particle states and Random Phase Approximation (RPA) calculations for core excitations. With respect to traditional particle-vibration coupling calculations, in which one can only address single-nucleon states and particle-vibration multiplets, we can also describe states of shell-model type like 2 particle–1 hole. The underlying spirit is, of course, related to filling the gap between shell-model-like approaches for low-lying spectroscopy, and the traditional HF+RPA approach to high-lying states like giant resonances.

Narrowing the Confidence Intervals in Nuclear Structure Predictions Through Elimination of Parametric Correlations

Acta Phys. Pol. B Proc. Suppl. 10, 51 (2017)

page 51 •


As it is well-known, the existence of correlations among the parameters of mathematical models such as typical physics theories implies that any attempt of optimisation of the parameters becomes impossible or highly unstable. When this happens, one says that the parameter determination (usually referred to as inverse problem) becomes an ill-posed mathematical problem. In this article, we suggest a regularisation method of ill-posed or nearly ill-posed inverse problems in the context of the nuclear mean-field applications with the help of the Monte Carlo methods. We present the approach and illustrate its numerical results on the example of the parameter adjustments of the phenomenological Woods–Saxon Hamiltonian in the \(^{208}\)Pb nucleus treated as a test case.

Alpha Decay of Deformed Even–Even Nuclei

Acta Phys. Pol. B Proc. Suppl. 10, 69 (2017)

page 69 •


Using the decay theory of Goldberger and Watson, we analyzed the \(\alpha \) decay of even–even axially symmetric nuclei. The decay is regarded as a transition, caused by any residual interaction, between the bound state of the parent nucleus and the continuous spectrum. In addition, the corrections to nuclear and Coulomb interactions due to deformation are also treated as a perturbation. Basis wave functions of the continuous spectrum, calculated in quasi-classical approximation, are shown to have inside the nucleus the amplitude of the order of square root from the transmission coefficient through the Coulomb barrier. General formula is derived for the \(\alpha \)-decay rate, which correlates with standard result in the case of transitions between the ground states of even–even nuclei.

Wilczyński Plots Forever?

Acta Phys. Pol. B Proc. Suppl. 10, 81 (2017)

page 81 •


Correlations between the energy and the deflection angle of the projectile-like fragments were studied for the \(^{136}\)Xe + \(^{209}\)Bi reaction at \(E/A = 28\) and 62 MeV. Experimental correlations were compared with model calculations performed by QMD code, including only one-body and both one- and two-body dissipations — only in the latter case an agreement with experimental data was obtained. It is shown that at a bombarding energy of 62 MeV/nucleon, the reaction cross section is still dominated by dissipative binary reactions involving the survival of well-defined projectile- and target-like fragments.

The External Clock and the Decay of a Two-particle System Inside a Spatial Box

Acta Phys. Pol. B Proc. Suppl. 10, 85 (2017)

page 85 •


A series of experiments show that the physical time is the same kind of quantum observable as the spatial position. Using the projection evolution as the extension of the standard Schrödinger type evolution, the decay of a two-particle system in the case of limited allowed space (box) is considered. A very schematic model is used to show the size effects in the decay probability distribution.

Parametric Basis Functions for Collective Nuclear Models

Acta Phys. Pol. B Proc. Suppl. 10, 99 (2017)

page 99 •


We consider calculation schemes in the framework of the Kantorovich method — reduction of a elliptic boundary-value problem to a system of second order ordinary differential equations (ODEs) using the surface functions depending on the ODEs-independent variable as a parameter. We propose construction of the new parametric surface basis functions in an analytical form for solving the boundary-value problem of a quadrupole vibration collective nuclear model.

Nuclear Monopole Effect on Odd–Odd Particle-hole Nuclei in \(^{132}\)Sn Mass Region

Acta Phys. Pol. B Proc. Suppl. 10, 107 (2017)

page 107 •


Study of nuclear monopole interaction effects around closed shell cores provides important information on the shell evolution and the effective single-particle energies. In the aim of studying and understanding the role of these effects, and in order to resolve spectroscopic problems originated from the ignored three-body interactions, 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 odd–odd \(N=81\) isotones, we have performed some calculations using recent experimental single particle and single hole energies, by means of the Oxbash nuclear structure code. The two-body matrix elements (TBMEs) of the used effective interaction were deduced from the sn100pn realistic interaction for \(^{100}\)Sn mass region, and the single particle or single hole energies were taken from \(^{132}\)Sn mass region. The getting results for the one particle–one hole nucleus are in agreement with the experimental data. However, the new interaction cannot reproduce the experimental spectra of three particles–one hole and five particles–one hole isotones.

First Estimation of the Fission Dynamics of the Spectator Created in Heavy-ion Collisions

Acta Phys. Pol. B Proc. Suppl. 10, 113 (2017)

page 113 •


In peripheral high-energy heavy-ion collisions only parts of colliding nuclei interact leading to the production of a fireball. The remnants of such nuclei are called spectators. We estimated the excitation energy of nuclear remnants as a function of impact parameter. Their excitation energy is of the order of 100 MeV. The dynamical evolution of hot nuclei is described by solving a set of Langevin equations in four-dimensional collective coordinate space. The range of nuclear masses and excitation energies suits very well the ability of our model. Thus, for the first time, we investigate dynamically the fission and evaporation channels in deexcitation of the spectators produced in heavy-ions collision.

Projectile Fragmentation and Isotopic Scaling in a Transport Approach

Acta Phys. Pol. B Proc. Suppl. 10, 121 (2017)

page 121 •


We investigate projectile fragmentation using transport theory coupled with statistical decay codes for the excited primary fragments. We concentrate on isotope distributions and on an isoscaling analysis of isotope ratios to obtain information about the symmetry energy. The analysis is performed depending on the impact parameter since the thermodynamic properties of the primary fragments depend on it strongly. We compare reaction systems with different neutron and proton excess, \(^{38}\)Ar, \(^{40}\)Ca+\(^9\)Be and \(^{48}\)Ca, \(^{40}\)Ca+\(^9\)Be both at 140 \(A\)MeV, to investigate the range of validity of the isoscaling assumption. We find it is well-justified for isotopes which are mainly produced by the secondary decay. However, for isotopes with \(N\) or \(Z\) near the incident projectile for grazing impact parameters, the process is more direct and the distributions are not well-represented by statistical ensembles. In the range of validity, the extracted symmetry energies are generally reasonable.

Proton–Neutron Random Phase Approximation Studied by the Lipkin–Meshkov–Glick Model in the SU(2)\(\times \)SU(2) Group

Acta Phys. Pol. B Proc. Suppl. 10, 131 (2017)

page 131 •


We study the proton–neutron RPA with an extended Lipkin–Meshkov–Glick model. We pay attention to the effect of correlated ground state and the case when neutron and proton numbers are different. The effect of the correlated ground state is tested on the basis of quasi-boson approximation. We obtain the result that the RPA excitation energies and transition strengths are in a good agreement with the exact solution up to a certain strength of the particle–particle interaction. However, the transition strength shows deviations from the exact solution if we consider the case in which neutron and proton numbers are different even at a weak particle–particle interaction.

The Time Scale of Nuclear Reactions from Deep Inelastic to Projectile–Target Fragmentation

Acta Phys. Pol. B Proc. Suppl. 10, 139 (2017)

page 139 •


During the last fifteen years, professor Janusz Wilczyński devoted a large part of his scientific activity to Heavy-Ion (HI) experiments performed with the CHIMERA detector in the Fermi energy domain. He was an outstanding member of the international CHIMERA Collaboration. The reaction mechanism for semi-peripheral collisions at Fermi energy was carefully examined by him and his research group in close collaboration with both experimentalists and theorists in Catania. Since the earlier pioneering works in deep-inelastic collisions, the unifying concept of Wilczyński’s analysis of the experimental data has been driven by the powerful notion of one-body semi-classical deflection function. Wilczyński extended in the early 1970s the application of this concept to describe in a coherent way both the energy dissipation and the time scale evolutions of dissipative collisions. In this paper, we focus mainly on the time scale of the reaction mechanism in gentle three-body reactions between two interacting heavy ions at Fermi energy.

full authors' list

W. Parol, B. Włoch, A. Kozela, I. Ciepał, P. Kulessa, B. Kłos, A. Rusnok, A. Wilczek, I. Skwira-Chalot

Configuration Efficiency for Deuteron Breakup Reaction Investigation

Acta Phys. Pol. B Proc. Suppl. 10, 149 (2017)

page 149 •


The elastic scattering and deuteron breakup data were collected in the experiment performed at KVI with the use of unpolarized deuteron beam of 80 MeV per nucleon, impinging on hydrogen target. The aim of the analysis is to obtain absolute values of the differential cross section for deuteron breakup reaction. Precise determination of the detection efficiency is indispensable for that purpose. This report explains the efficiency correction introduced to account for the detector granulation and geometry.

The Density Dependence of the Nuclear Symmetry Energy in Heavy-ion Collisions

Acta Phys. Pol. B Proc. Suppl. 10, 153 (2017)

page 153 •


The density dependence of the nuclear symmetry energy is of great interest over a broad range of densities from very dilute matter in supernovae up to very dense neutron stars. However, more information and stronger constraints on the symmetry energy below and above saturation density are needed. An important way to investigate the symmetry energy is to perform heavy-ion collisions. In this contribution, we give an overview of the methods to extract the symmetry energy with transport theories. We discuss the role of fluctuations in transport approaches to describe the production of light clusters and intermediate mass fragments. We discuss, in more detail, three representative examples: the equilibration of the isospin in peripheral collisions between nuclei of different asymmetry, the pre-equilibrium emission of light clusters in the compression stage of a collision, and the isospin flow at high density. We summarize with the discussion of presently known constraints and open questions about the symmetry energy with emphasizing the need of more data from heavy-ion collisions and from astrophysical observations.

Nucleon–Nucleon Correlations and the Isospin and Spin Symmetry Energy

Acta Phys. Pol. B Proc. Suppl. 10, 165 (2017)

page 165 •


Using the Hellmann–Feynman theorem, we calculate the potential and kinetic energy contributions to the binding energy of symmetric nuclear matter, neutron matter and polarized neutron matter. These energies are used to analyze the symmetry energy of nuclear matter and the spin symmetry energy of neutron matter. The analysis is performed within the Brueckner–Hartree–Fock approach using the Argonne V18 realistic potential plus the Urbana IX three-body force. The kinetic energy difference between the correlated system and the underlying Fermi sea is used to estimate the importance of nucleon–nucleon correlations in the different systems concluding that at a given density, symmetric nuclear matter is more correlated than neutron matter, and that this is more correlated than polarized neutron matter. Our microscopic results show no indication of a ferromagnetic transition in neutron matter.

Potential Energy Surfaces of Mercury up to Uranium Isotopes in the 4D Fourier Shape Parametrisation

Acta Phys. Pol. B Proc. Suppl. 10, 173 (2017)

page 173 •


The potential energy landscapes of Hg–U nuclei were calculated within the macroscopic–microscopic method with a Fourier nuclear shape parametrisation and the Lublin–Strasbourg Drop for the macroscopic energy. Microscopic corrections based on the Yukawa folded single-particle potential were obtained with the Strutinsky shell-correction method and the BCS approximation. The energy landscapes of even–even isotopes of Hg, Po, Ra and U were analysed in a 4-dimensional deformation space and projected onto the quadrupole–octupole plane. Extrema, ridges and valleys were localized and the electric quadrupole moments in these minima were evaluated. A comparison with the experimental data for the ground state is shown for the Hg isotopes.

Fragment Mass Distributions in Low-energy Fission of \(^{236}\)Pu

Acta Phys. Pol. B Proc. Suppl. 10, 183 (2017)

page 183 •


The fission-fragment mass distribution is evaluated in a quantum mechanical framework using mass asymmetry, neck and elongation as the relevant collective degrees of freedom. The potential energy surfaces (PES) are calculated within the macroscopic–microscopic model based on the Lublin–Strasbourg Drop (LSD), the Yukawa-folded (YF) single-particle potential and a monopole pairing force. The PES is presented and analysed in detail for the isotope \(^{236}\)Pu, which reveals a deep asymmetric valley. The fission-fragment mass distribution is obtained from the eigenstates of a collective Hamiltonian computed within the Born–Oppenheimer approximation (BOA), applying the WKB approximation and introducing a neck-dependent fission probability. For spontaneous fission of \(^{236}\)Pu, the calculated mass distribution is found in a good agreement with the data.

On the Collective Octupole Degrees of Freedom

Acta Phys. Pol. B Proc. Suppl. 10, 191 (2017)

page 191 •


The collective octupole degrees of freedom are considered. The spherical components of a real, electric octupole tensor are treated as collective octupole laboratory coordinates. Decomposition of the octupole irreducible representation of orthogonal group O(3) onto three irreducible representations of the cubic O\(_{\rm h}\) group is presented. Intrinsic cubic coordinates are introduced. The two O\(_{\rm h}\)-symmetric intrinsic coordinate frames are defined. Relations between the laboratory coordinates and the intrinsic cubic ones are discussed in the two cases of intrinsic frame. Operator of the angular momentum and Hamiltonian for the octupole motion are given and expressed in terms of both sets of the intrinsic coordinates. Differences between description of the octupole and the quadrupole degrees of freedom are concluded.

full authors' list

D. Ward, B.G. Carlsson, Th. Døssing, P. Möller, J. Randrup, S. Åberg

Fission Dynamics with Microscopic Level Densities

Acta Phys. Pol. B Proc. Suppl. 10, 201 (2017)

page 201 •


We present a consistent framework for treating the energy and angular-momentum dependence of the shape evolution in the nuclear fission. It combines microscopically calculated level densities with the Metropolis-walk method, has no new parameters, and can elucidate the energy-dependent influence of pairing and shell effects on the dynamics of warm nuclei.

Three-body Model for Nuclei Near and Beyond Drip Line

Acta Phys. Pol. B Proc. Suppl. 10, 211 (2017)

page 211 •


We discuss firstly possible experimental probes for the strong di-neutron correlations in halo nuclei \(^6\)He and \(^{11}\)Li. We then secondly study a nucleus beyond the drip line \(^{26}\)O through the direct two-neutron decay. The excites 2\(^+\) state of \(^{26}\)O is also discussed. We use consistently a three-body model to this end, taking into account the coupling to the continuum. Calculated results are compared with the recent experimental data from RIBF (Radioactive Ion Beam Factory) in RIKEN.

Quasifission Dynamics and Stability of Superheavy Systems

Acta Phys. Pol. B Proc. Suppl. 10, 225 (2017)

page 225 •


Recent experiments revealed intriguing similarities in the \(^{64}\)Ni\(+^{207}\)Pb, \(^{132}\)Xe\(+^{208}\)Pb, and \(^{238}\)U\(+^{238}\)U reactions at energies around the Coulomb barrier. The experimental data indicate that for all systems, a substantial energy dissipation takes place in the first stage of the reaction, although the number of transferred nucleons is small. On the other hand, in the second stage, a large number of nucleons are transferred with small friction and small consumption of time. To understand the observed behavior, various reactions were analyzed based on the microscopic time- dependent Hartree–Fock (TDHF) theory. From a systematic analysis for \(^{40,48}\)Ca\(+^{124}\)Sn, \(^{40}\)Ca\(+^{208}\)Pb, \(^{40}\)Ar\(+^{208}\)Pb, \(^{58}\)Ni\(+^{208}\)Pb, \(^{64}\)Ni\(+^{238}\)U, \(^{136}\)Xe\(+^{198}\)Pt, and \(^{238}\)U\(+^{238}\)U reactions, we find that the TDHF reproduces well the measured trends. In addition, the Balian–Vénéroni variational principle is applied to head-on collisions of \(^{238}\)U\(+^{238}\)U, and the variance of the fragment masses is compared with the experimental data, showing a significant improvement. The underlying reaction mechanisms and possible future studies are discussed.

Dynamical Effects in Invariant Coordinates for \(dp\) Breakup

Acta Phys. Pol. B Proc. Suppl. 10, 241 (2017)

page 241 •


Regular studies of few-nucleon systems reveal various dynamical components, such as three-nucleon force, Coulomb force and relativistic effects, which play an important role in correct description of nuclear interaction. A large set of existing experimental data for \(^1\)H\((d, p p)n\) reaction allows for systematic investigations of these dynamical effects, which vary with energy and appear with different strength in certain observables and phase space regions. In order to perform systematic comparisons with precise theoretical calculations, the experimental data are transformed to the variables based on the Lorentz invariants.

Toroidal Nuclear Matter Distributions of Superheavy Nuclei from Constrained Skyrme–HFB Calculations

Acta Phys. Pol. B Proc. Suppl. 10, 249 (2017)

page 249 •


Using the Hartree–Fock–Bogoliubov (HFB) self-consistent mean-field theory with the SkM* Skyrme energy-density functional, we study nuclear structure properties of even–even superheavy nuclei (SHN) of \(Z=120\) isotopes and \(N=184\) isotones. The shape of the nucleus along the lowest energy curve as a function of the quadrupole moment \(Q_{20}\) makes a sudden transition from the oblate spheroids (biconcave discs) to the toroidal shapes, in the region of large oblate quadrupole moments.

Pasta-phase Transitions in the Inner Crust of Neutron Stars

Acta Phys. Pol. B Proc. Suppl. 10, 259 (2017)

page 259 •


We perform calculations of nuclear pasta phases in the inner crust of neutron stars with the Thomas–Fermi method and the Compressible Liquid Drop Model using the Barcelona–Catania–Paris–Madrid (BCPM) energy density functional and several Skyrme forces. We compare the crust–core transition density estimated from the crust side with the predictions obtained from the core by using the thermodynamical and dynamical methods. Finally, the correlation between the crust–core transition density and the slope of the symmetry energy at saturation is briefly analyzed.

full authors' list

A.A. Gusev, S.I. Vinitsky, O. Chuluunbaatar, V.L. Derbov, A. Góźdź, P.M. Krassovitskiy

Transmission of Clusters Consisting of a Few Identical Particles Through Barriers and Wells

Acta Phys. Pol. B Proc. Suppl. 10, 269 (2017)

page 269 •


The problem of quantum transmission through potential barriers and wells is studied for a composite system consisting of a few identical particles coupled by pair oscillator potentials in the new symmetrised-coordinate representation. A closed-channel method for solving the relevant boundary value problem is applied. We confirm the efficiency of the proposed approach by calculating the complex energy values of metastable states and analysing the shape and Feshbach resonances in systems of identical particles on a line, which give rise to quantum transparency of the repulsive barriers and the resonance reflection from the wells.

Reflections on Wilczyński’s Scientific Work in Groningen

Acta Phys. Pol. B Proc. Suppl. 10, 275 (2017)

page 275 •


Remembering Janusz Wilczyński, means for the authors looking back at the most successful work of the KVI in the field of heavy-ion reaction studies. We will review some of the high-lights, focusing on the most important concepts Wilczyński introduced.

Shell-model Calculation of Isospin-symmetry Breaking Correction to Superallowed Fermi beta Decay

Acta Phys. Pol. B Proc. Suppl. 10, 285 (2017)

page 285 •


We investigate the radial-overlap part of the isospin-symmetry breaking correction to superallowed \(0^+ \to 0^+\) \(\beta \) decay. The 8 \(sd\)-shell emitters with masses between \(A=22\) and \(A=38\) have been re-examined. The Fermi matrix element is evaluated with realistic spherical single-particle wave functions, obtained from spherical Woods–Saxon (WS) or Hartree–Fock (HF) potentials, fine-tuned to reproduce the experimental data on charge radii and separation energies for nuclei of interest. The elaborated adjustment procedure removes any sensitivity of the correction to a specific parametrisation of the WS potential or to various versions of the Skyrme interaction. The present results are generally in a good agreement with those already reported. At the same time, we find that the calculations with HF wave functions result in systematically lower values of the correction.


ver. 2021.05.07 • we use cookies and MathJax