In 2018 a broad spectrum of unprecedented fore-front research becomes available at the Facility for Antiproton and Ion Research, FAIR. The new facility is being constructed within the next five years adjacent to the existing accelerator complex of the GSI Helmholtz Centre for Heavy Ion Research at Darmstadt/Germany, expanding the research goals and technical possibilities substantially. At worldwide unique accelerator and experimental facilities, FAIR will open the way for a large variety of experiments in hadron, nuclear, atomic and plasma physics as well as applied sciences which will be briefly described in this article.

In this paper, a brief outline is first given of the theoretical framework for shellmodel calculations employing a two-body effective interaction derived from the free nucleon-nucleon potential. Then, some selected results of recent studies of nuclei beyond ¹³²Sn are presented, which have been obtained starting from the CD-Bonn potential renormalized by use of the V_low−k approach. Attention is focused on the twovalence-particle nuclei ¹³⁴Te and ¹³⁴Sn and on the odd-neutron nucleus ¹³⁷Xe.

In recent years covariant density functional theory has developed as a very successful tool to describe nuclear structure phenomena. We discuss in this article, why Lorentz invariance should be taken seriously in this context and show several very successful nuclear applications of relativistic density functional theory.

We briefly present the finite rank separable approximation (FRSA) of Skyrmetype residual interactions in the case of charge-exchange modes in nuclei. We show how the FRSA can be used to obtain the equations leading to charge-exchange excitations where the coupling between one- and two-phonon components, as well as pairing effects are treated. Applications are done in the simpler cases of ¹³²Sn and ⁷⁸Ni. First, we check that the FRSA reproduces reasonably well the full charge-exchange RPA results for the spin-dipole resonances in ¹³²Sn. Next, the phonon-phonon coupling effects on the β-decay half-life of ⁷⁸Ni are studied.

A method is developed to calculate the interaction constants of the boson-fermion Hamiltonian basing on the Nilsson single-particle Hamiltonian.

We consider work performed over the last decade on single-j-shell studies. We will discuss four topics.

A new matrix diagonalization iterative algorithm endowed with an importance sampling is reviewed and implemented numerically for large scale shell model calculations. The good convergence of the iterative process allows to treat heavy nuclei not easily accessible to other shell model approaches. The method is adopted to generate complete spectra and to evaluate electric and magnetic transitions for chains of isotones and isotopes in a wide region around the doubly magic ¹³²Sn. In virtue of the attained good agreement between theory and experiments, the calculations offer a detailed, exhaustive and reliable description of the spectroscopic properties of each nucleus and show how nuclear structure evolves as nuclei depart from shell closures.

Manifestations of generalized parafermionic oscillators in quantum superintegrable systems, as well as in selected cases in the structure of molecules, atomic nuclei, and bright solitons in Bose–Einstein condensates are discussed.

The complex structure of low-lying as well as those of high-lying states is discussed within multiphonon approach. The approach is based on Quasiparticle-Phonon Model. This microscopic model goes beyond the quasiparticle random-phase approximation by treating a Hamiltonian of separable form in a microscopic multiphonon basis. It is therefore able to describe the anharmonic features of collective modes. In the case of low-lying part of excitations the model has close correspondence with the proton-neutron interacting boson model. Within the model highly-excited singleparticle states in nuclei are coupled with the excitations of a more complex character, first of all with collective phonon-like modes of the core. Although, on the level of one and two-phonon admixtures, the fully chaotic GOE regime is not reached, the eigenstates of the model carry significant degree of complexity that can be quantified with the aid of correlational invariant entropy.

A study of Feshbach resonances and the role of bound states in nuclear physics is presented. This work is an extension of parallel studies in cold atoms. The tuning in atomic physics is via a magnetic field while the nuclear case can be tuned by varying the proton fraction. The unitary limit of infinite scattering length is studied. Applications to the interaction energy, equation of state, compressibility, entropy, viscosity to entropy density are given.

Proton-rich nuclei in the A~70 mass region manifest shape coexistence and mixing, isospin mixing, and competition between neutron-proton and like-nucleon pairing correlations. For a realistic description of specific phenomena dominated by their interplay aiming to testing the fundamental interactions and symmetries beyond-meanfield approches are required. Results concerning a self-consistent description of isospinmixing effects on the structure and dynamics of these nuclei within the complex Excited Vampir model using a realistic effective interaction in a rather large model space will be presented.

This article gives a compact review of a series of geometric model developments aiming to explain the specific properties of quadrupole-octupole collectivity in various nuclear regions with different degrees of deformability and reflection-asymmetry in a consistent and complementary way.

Proton-neutron pairing in nuclei is commonly described by generalized BCS/HFB models. By construction, these models do not conserve the particle number and the isospin. Here we shall review an alternative approach, based on quartets instead of Cooper pairs, in which both the particle number and the isospin are exactly conserved. In this approach the ground state of N=Z nuclei is approximated by a condensate of alpha-like quartets built by two neutrons and two protons coupled to the isospin T=0. For nuclei with N > Z the ground state is taken as a superposition of a quartet condensate and a pair condensate formed by the neutrons in excess relative to the isotope with N=Z. The comparison with exact shell model calculations shows that the quartet condensation model gives accurate results for the isovector pairing correlations in nuclei with protons and neutrons moving in the same major shell.

The synthesis of superheavy elements is analyzed in the frame of the macroscopic-microscopic approach based on the Woods-Saxon superasymmetric two-center shell model. The fusion is considered as a cold rearrangement process. A simple estimate for the fusion cross section was made.

Our analytical superasymmetric fission (ASAF) model is used to calculate the cluster decay and α decay half-lives of superheavy nuclei with released energies obtained from the experimental and calculated atomic mass tables. Lower values of rms standard deviations of calculated half-lives compared to experimental ones for α emitters are produced by the semiempirical (semFIS) formula. The nuclear dynamics based on potential barriers computed by the macroscopic-microscopic method should be improved in the future by replacing the Werner-Wheeler nuclear inertia by the cranking inertia tensor. Up to now spontaneous fission half-lives of the heaviest superheavy nuclei have been estimated only for neutrondeficient nuclei.

We describe α-decay transitions to excited states in even-even nuclei within the Coherent State Model (CSM). This formalism is able to simultaneously describe electromagnetic and α-decays to excited states in spherical, transitional and well deformed nuclei. The α-daughter interaction contains the monopole potential, estimated within the double folding procedure with M3Y interaction plus a repulsive core simulating Pauli principle and a quadrupole-quadrupole (QQ) interaction. The decaying states are identified with the lowest narrow outgoing resonances in this potential. The αbranching ratios to 2⁺ states were reproduced by using the QQ strength depending linearly on the deformation parameter, as predicted by CSM. The predicted intensities to 4⁺ and 6⁺ states are in a reasonable agreement with available experimental data.

The shell and pairing corrections have been calculated whithin the Strutinsky and BCS methods for the typical fusion configuration of two partially overlapped ellipsoids. The binary character of the approach is induced by the use of the deformed two-center shell model, which provides the crossing level schemes of the two interacting nuclei within the transition geometry from two separated nuclei up to one compound nucleus. The macroscopic-microscopic method is employed to obtain the total deformation energy, and the cranking tensor of inertia completes the dynamics of the system. Applications are presented for the synthesis of some superheavy nuclei.

The population of rotational states in the ground-state band of neutron-rich fragments emitted in the spontaneous fission of ²⁵²Cf is described within a time-dependent quantum model similar to the one used for Coulomb excitation. The initial population probability of the states included in the selected basis is calculated according to the bending model at scission. Subsequently these initial amplitudes are feeding the coupled dynamical equations describing the population of rotational states in both fragments during the tunnelling and post-barrier (pure Coulomb) motion. As application we consider the high yield Mo-Ba pair for different number of emitted neutrons.

In the last years the quantity and quality of experimental data of new super-heavy nuclei (SHN) have increased considerably. These nuclei have now become available for experimental studies with in-beam and decay spectroscopic methods, and also for detailed investigations through a variety of phenomenological and theoretical approaches. This work aims to prove that the α-decay rates of doubly closed-shell nuclei and neighbouring isotopes/isotones provide a very sensitive and stringent test for the nuclear shell structure of (SHN).

We investigate the effects of the symmetry energy on several properties of neutron rich nuclei, including the neutron skin thickness, polarizability and low energy dipole response, within a microscopic transport model based on Landau-Vlasov kinetic equation. In an energy density functional approach we employ three different parametrizations with density for the isovector part of the mean-field and study the evolution with mass of these properties. While the neutron skin and the polarizability are directly correlated with the slope parameter L of the symmetry energy, for the pygmy resonance a more careful discussion is required to characterize the role of the symmetry energy on its properties.

The Cosmic Microwave Background (CMB) has been detected in 1964 by Penzias and Wilson. It shows today a remarkable constant temperature of T_0γ≈2.7 K independent of the direction. Present density is about 370 photons per cm³. The size of the hot spots, which deviates only in the fifth decimal of the temperature from the average value, tells us, that the universe is flat. About 300 000 years after the Big Bang at a temperature of T_0γ=3000 K already in the matter dominated era the electrons combine with the protons and the ⁴He and the photons move freely in the neutral universe. So the temperature and distribution of the photons give us information of the universe 300 000 years after the Big Bang. Information about earlier times can, in principle, be derived from the Cosmic Neutrino Background (CνB). The neutrinos decouple already 1 second after the Big Bang at a temperature of about 10¹⁰ K. Today their temperature is ~1.95 K and the average density is 56 electron-neutrinos per cm³. Registration of these neutrinos is an extremely challenging experimental problem which can hardly be solved with the present technologies. On the other hand it represents a tempting opportunity to check one of the key element of the Big Bang cosmology and to probe the early stages of the universe evolution. The search for the CνB with the induced beta decay ν_e + ³H → ³He + e⁻ is the topic of this contribution. The signal would show up by a peak in the electron spectrum with an energy of the neutrino mass above the Q value. We discuss the prospects of this approach and argue that it is able to set limits on the CνB density in our vicinity.

This is a short review of the present status of the latest theoretical advances on the positron-emitting and double-electron-capture (β⁺/EC) modes of double beta decay. The double β⁻ mode has been studied intensively for decades, both experimentally and theoretically, but the β⁺/EC modes have attracted little attention thus far. Recently a boost to the β⁺/EC studies was given by the predicted enhancement of the decay rates of the resonant neutrinoless double-electron capture. In order to verify the fulfillment of the resonance condition a host of mass measurements have recently been done by using Penning-type atom traps.

We investigate the Gamow-Teller (GT) strength distributions in the double-β decaying nuclei ¹²⁸Te nd ¹³⁰Te, as well as in their respective partners ¹²⁸Xe and ¹³⁰Xe. Theoretical calculations based on a deformed quasiparticle random phase approximation built on Skyrme selfconsistent mean fields are compared with measured GT⁻ strength distributions extracted from high energy resolution charge-exchange reactions ¹²⁸Te(³He,t)¹²⁸I and ¹³⁰Te(³He,t)¹³⁰I. Combining these results with calculated GT⁺ strength distributions in the Xe isotopes, the nuclear matrix elements for the two-neutrino double-β decay processes are evaluated and compared to experiment.

The amplitude for double-beta decay with two-neutrino emission is related to β⁻ and β⁺ transitions of Fermi and Gamow-Teller type connecting ground state of initial and final nuclei with virtual intermediate nuclear states. The suppression of double Fermi and Gamow-Teller matrix elements has origin in violation of the isospin SU(2) and spin-isospin SU(4) symmetries, respectively. We study double Fermi matrix elements within an exactly solvable model. By using perturbation theory up to the first order a dependence of the two-neutrino double beta decay matrix element on the like-nucleon pairing, particle-particle and particle-hole proton-neutron interactions by assuming a weak violation of isospin symmetry of Hamiltonian expressed with generators of the SO(5) group. It is found that there is a dominance of transition through a single state of the intermediate nucleus.

In this article we study the neutral current induced neutrino-nucleus cross sections as a function of neutrino energy for targets of experimental interest both for the neutron coherent elastic as well as inelastic scattering. In particular we study the re00 actions ⁴⁰Ar$(\nu,\nu')$⁴⁰Ar^* and ⁵⁶Fe$(\nu,\nu')$⁵⁶Fe^*. We find that the coherent g_s and the GT₀ resonance are the most important for low energy neutrino sources. We then apply our results considering the supernova neutrino spectrum, which for each neutrino type, namely i) $\nu_e$ , ii) $\bar{\nu}_e$ and iii) $(\nu_x, \bar{\nu}_x)$ for all other flavours together, is represented by a Fermi-Dirac distribution with definite temperature and chemical potential (degeneracy parameter). The low threshold high resolution spherical gaseous time projection counter filled, e.g., with Ar is considered as an excellent detector. ⁵⁶Fe can be used in other standard detectors.

The weak interaction between an atomic nucleus and the orbiting electrons is responsible for small parity mixings in the electron wave functions that give rise to atomic transitions forbidden between pure-parity states. The degree of the parity mixing, and thus the strength of the nominally forbidden atomic transitions, depends on the weak charge of the nucleus, driven mainly by the neutron distribution. We focus in this work on polarized electron elastic scattering by nuclei as a tool to extract information on the nuclear weak charge and radius needed to analyze atomic parity violation measurements. A set of Barium isotopes of interest for atomic parity violation experiments have been chosen in this work.

In this paper, it is shown that, the experimental values of the nonextensive scattering entropies S_L(p) and S_θ(q) for the pion-nucleus (π⁰He, π⁰C, π⁰O, π⁰Ca) scatterings, in the energy region corresponding to ∆(1236) resonance in the elementary pion-nucleon interaction, are well described by the entropic optimal resonance predictions S_L⁰¹ (p) and S_θ⁰¹ (q) when the nonextensivities indices are correlated by a Riesz-Thorin-like relation: 1/2p+1/2q=1.

The motion of an electromagnetic pulse (signal) through the surface of a semiinfinite (half-space) polarizable body is investigated. The incident pulse of electromagnetic radiation propagating in vacuum is assumed to be of finite duration and finite spatial extension. As regards its extension along the transverse directions, two cases are considered. First, we assume a large (infinite) extension (in comparison with the wavelength), as for a plane wave (beam, ray); second, a very narrow pulse is assumed (zero thickness, close to the diffraction limit). In its motion the pulse encounters the plane surface of a semi-infinite polarizable body (a half-space) and penetrates into the body. The body reacts through its polarization degrees of freedom, which obey the wellknown Drude-Lorentz (plasma) equation of motion. It is shown that the beam obeys the well-known refraction law (Fresnel equations), with a specific discussion, which is provided. For the narrow pulse, both the normal and oblique incidence are analysed. It is shown that far away from the incidence direction (large transverse distance r) the motion is governed by the polaritonic eigenmodes, which yields a pulse, approximately of the same shape as the original one, propagating with the group velocity and with an amplitude which decreases as 1/r². The group velocity is always smaller than the speed of light in vacuum c. In the vicinity of the propagation direction (small distance r), the original pulse is almost entirely preserved, including its propagation velocity c, with a distorted amplitude, which depends on the transverse direction. This picture is in fact the diffraction limit of the narrow pulse. The transmitted coefficient is computed for normal incidence. The reflected pulse is also computed, as well as the refracted pulse for oblique incidence. While the reflection law is preserved (reflection angle is equal to the incidence angle), the refraction law is different from Snell’s law of refraction of a plane wave, in the sense that the highly localized (narrow) pulse along the transverse direction preserves its propagation direction on entering into the body.

The issue of analogies between classical optics and quantum mechanics is analyzed in details. The appropriateness and limitations of these analogies are discussed for both Schrödinger and Dirac type quantum states.

The present status of IFIN-HH CCR (Radiopharmaceuticals Research Centre) project is reviewed and its development perspectives are addressed.

The aim of this study was to quantify the concentration of seven heavy metals including (Cd, Fe, Mn, Cu, Zn, Pb, and Ni) in soil and to investigate the bioavailability of heavy metals from soil to different parts of Brassica oleracea L. var. capitata. The mobility of heavy metals from soil into the food chain and their bioaccumulation in cabbage has increased from safety point of view. The metal concentrations were determined by Flame Atomic Absorption Spectrometry technique. In this study the highest concentration of copper and iron in soil were obtained. This can be a consequence to the using excessively the fertilizers, pesticides and copper sulphate as treatment for cabbage protection. The manganese, nickel, zinc and cadmium concentrations in soil not exceed the normal values according with the Romanian Regulation. The bioaccumulation factor (BF) of seven heavy metals in cabbage revealed that this vegetable was a poor accumulators of Fe, Ni, Cu, Cd, and Pb (BF<1), and good accumulator of Mn (BF>1). Obviously, only with BF is no possible to establish if the cabbage may be considerate as accumulator species for a certain metals and from this reason the translocation factor (TF) was calculated.

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous variable entanglement for a system consisting of two non-interacting bosonic modes embedded in a thermal environment. By using the entanglement of formation, it is described the evolution of entanglement in terms of the covariance matrix for symmetric Gaussian input states. In the case of an entangled initial squeezed vacuum state, entanglement suppression (entanglement sudden death) takes place, for all temperatures of the thermal bath. For definite values of temperature and dissipation constant, one can observe temporary revivals of the entanglement, but for long times the system evolves to an equilibrium state which is always separable.

Learning physics is a context-dependent process. I consider a broader interdisciplinary problem of where differences in understanding and reasoning arise. I suggest the long-run effects a multiple-choice based learning system as well as society’s cultural habits and rules might have on student’s reasoning structure.

We have selected some topics developed in Symplectic Topology to analyze the impact on the quantization problem.The results presented have stemmed from the works of Gromov, Witten, Floer, Hofer and others; our intention is simply to relate the emerging picture - the deformation of classical cohomologies to quantum cohomologies to other approaches (geometric quantization) to the problem and point the ”limits” in having a coherent view.

The two-proton decay process is studied within the framework of stationary scattering theory. A new procedure to numerically integrate the 2D Schrödinger equation is proposed. We consider the external (barrier) problem in the bi-proton emission by solving the 2D Schrödinger equation with outgoing asymptotic solution. A two stage numerical procedure based on the log derivative matrix is formulated and we show that this procedure produces accurate and stable results for the decoupled case. We then feel very encouraged to extend this procedure on systems of coupled 2D equations, to finally build up a code with multiple applications in different fields.

Recursive formulas are derived for the number of solutions of linear and quadratic Diophantine equations with positive coefficients. This result is further extended to general non-linear additive Diophantine equations. It is shown that all three types of the recursion admit an explicit solution in the form of complete Bell polynomial, depending on the coefficients of the power series expansion of the generating functions for the sequences of individual terms in the Diophantine equations.

The goal of this paper is to analyze, using homogenization techniques, the effective thermal transfer in a periodic composite material formed by two constituents, separated by an imperfect interface. The imperfect contact between the constituents generates a contact resistance and, depending on the magnitude of this resistance, a threshold phenomenon arises.

We give a device for computing bounds for positive roots of polynomials. Our results allow the computation of absolute values for real and complex roots.

In the framework of Lie systems, we study the affine symplectic group G^AS and the Jacobi group G^J. We construct canonical bases for the irreducible unitary representations of G^J consisting of K^J-vectors, where K^J is the maximal compact subgroup of G^J. We study the quantum Lie systems based on the extended Poincaré disk $\mathfrak{M}$ diffeomorphic to the maximal elliptic coadjoint orbit of G^J. We establish the quasienergy operator reduced to $\mathfrak{M}$ and the corresponding Wei-Norman equations. Moreover, we obtain the solutions of the time-dependent Schrödinger equation with the initial states represented by K^J-vectors. Finally, we obtain a Poisson algebra isomorphism between the quantum and classical Lie systems based on the Poisson manifold $\mathfrak{M}$.