Volume 58, Number 910, 2013
Honoring
Prof. Dr. A.A. Răduţă
on his 70 ^{th} Anniversary
Nuclear Physics
Foreword Aureliu Săndulescu Romanian Journal of Physics 58,
10211022 (2013)
Nuclear Structure
FAIR  the Facility for Antiproton and Ion Research Horst Stoecker, Christian Sturm Romanian Journal of Physics 58,
10231030 (2013)
In 2018 a broad spectrum of unprecedented forefront 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.
Shell Model with Realistic LowMomentum TwoBody Effective Interactions A. Covello Romanian Journal of Physics 58,
10311037 (2013)
In this paper, a brief outline is first given of the theoretical framework for shellmodel calculations employing a twobody effective interaction derived from the free nucleonnucleon potential. Then, some selected results of recent studies of nuclei beyond ^{132}Sn are presented, which have been obtained starting from the CDBonn potential renormalized by use of the V_{low−k} approach. Attention is focused on the twovalenceparticle nuclei ^{134}Te and ^{134}Sn and on the oddneutron nucleus ^{137}Xe.
Covariant Density Functional Theory and the Structure of Exotic Nuclei G.A. Lalazissis, P. Ring Romanian Journal of Physics 58,
10381047 (2013)
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.
A Study of ChargeExchange Excitations with SkyrmeType Interactions Using the Finite Rank Separable Approximation A.P. Severyukhin, V.V. Voronov, I.N. Borzov, Nguyen Van Giai Romanian Journal of Physics 58,
10481058 (2013)
We briefly present the finite rank separable approximation (FRSA) of Skyrmetype residual interactions in the case of chargeexchange modes in nuclei. We show how the FRSA can be used to obtain the equations leading to chargeexchange excitations where the coupling between one and twophonon components, as well as pairing effects are treated. Applications are done in the simpler cases of ^{132}Sn and ^{78}Ni. First, we check that the FRSA reproduces reasonably well the full chargeexchange RPA results for the spindipole resonances in ^{132}Sn. Next, the phononphonon coupling effects on the βdecay halflife of ^{78}Ni are studied.
Interacting BosonFermion Model for Strongly Deformed Nuclei R.V. Jolos, A. Gelberg Romanian Journal of Physics 58,
10591063 (2013)
A method is developed to calculate the interaction constants of the bosonfermion Hamiltonian basing on the Nilsson singleparticle Hamiltonian.
Topics in Nuclear Structure A. Escuderos, L. Zamick Romanian Journal of Physics 58,
10641075 (2013)
We consider work performed over the last decade on singlejshell studies. We will discuss four topics.
Structural Evolution of Heavy Nuclei within a New Shell Model Scheme N. lo Iudice, D. Bianco Romanian Journal of Physics 58,
10761085 (2013)
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 ^{132}Sn. 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.
Generalized Parafermionic Oscillators in Physical Systems Dennis Bonatsos, Adriana Martinou Romanian Journal of Physics 58,
10861095 (2013)
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.
Quasiparticles, Phonons and Beyond (Nuclear Structure Calculations in a Large Domain of Excitation Energies) Ch. Stoyanov Romanian Journal of Physics 58,
10961107 (2013)
The complex structure of lowlying as well as those of highlying states is discussed within multiphonon approach. The approach is based on QuasiparticlePhonon Model. This microscopic model goes beyond the quasiparticle randomphase 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 lowlying part of excitations the model has close correspondence with the protonneutron interacting boson model. Within the model highlyexcited singleparticle states in nuclei are coupled with the excitations of a more complex character, first of all with collective phononlike modes of the core. Although, on the level of one and twophonon 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.
Interacting Fermions in Nuclear Physics; from Bound States to Feshbach Resonances Aram Z. Mekjian Romanian Journal of Physics 58,
11081119 (2013)
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.
IsospinMixing Effects on the Structure and Dynamics of Medium Mass Nuclei A. Petrovici Romanian Journal of Physics 58,
11201129 (2013)
Protonrich nuclei in the A~70 mass region manifest shape coexistence and mixing, isospin mixing, and competition between neutronproton and likenucleon pairing correlations. For a realistic description of specific phenomena dominated by their interplay aiming to testing the fundamental interactions and symmetries beyondmeanfield approches are required. Results concerning a selfconsistent 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.
A Model Approach to QuadrupoleOctupole Deformations in Atomic Nuclei Nikolay Minkov Romanian Journal of Physics 58,
11301140 (2013)
This article gives a compact review of a series of geometric model developments aiming to explain the specific properties of quadrupoleoctupole collectivity in various nuclear regions with different degrees of deformability and reflectionasymmetry in a consistent and complementary way.
ProtonNeutron Pairing and AlphaType Quartet Condensation in Nuclei N. Sandulescu, D. Negrea, C.W. Johnson Romanian Journal of Physics 58,
11411147 (2013)
Protonneutron 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 alphalike 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.
Alpha and Heavy Cluster Decay, Nuclear Fragmentation, Fission and Fusion
Cold Fusion Synthesis of a Z=116 Superheavy Element A. Sandulescu, M. Mirea Romanian Journal of Physics 58,
11481156 (2013)
The synthesis of superheavy elements is analyzed in the frame of the macroscopicmicroscopic approach based on the WoodsSaxon superasymmetric twocenter shell model. The fusion is considered as a cold rearrangement process. A simple estimate for the fusion cross section was made.
Alpha Cluster and Fission Decay of Superheavy Nuclei D.N. Poenaru, R.A. Gherghescu, W. Greiner Romanian Journal of Physics 58,
11571166 (2013)
Our analytical superasymmetric fission (ASAF) model is used to calculate the cluster decay and α decay halflives of superheavy nuclei with released energies obtained from the experimental and calculated atomic mass tables. Lower values of rms standard deviations of calculated halflives compared to experimental ones for α emitters are produced by the semiempirical (semFIS) formula. The nuclear dynamics based on potential barriers computed by the macroscopicmicroscopic method should be improved in the future by replacing the WernerWheeler nuclear inertia by the cranking inertia tensor. Up to now spontaneous fission halflives of the heaviest superheavy nuclei have been estimated only for neutrondeficient nuclei.
Coherent State Description of αTransitions to Excited States in EvenEven Nuclei D.S. Delion, A. Dumitrescu Romanian Journal of Physics 58,
11671177 (2013)
We describe αdecay transitions to excited states in eveneven nuclei within the Coherent State Model (CSM). This formalism is able to simultaneously describe electromagnetic and αdecays to excited states in spherical, transitional and well deformed nuclei. The αdaughter interaction contains the monopole potential, estimated within the double folding procedure with M3Y interaction plus a repulsive core simulating Pauli principle and a quadrupolequadrupole (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.
Shell and Pairing Influence on SubBarrier Nuclear Fusion R.A. Gherghescu, D.N. Poenaru Romanian Journal of Physics 58,
11781187 (2013)
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 twocenter 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 macroscopicmicroscopic 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.
Population of Rotational States in the GroundBand of Fission Fragments Şerban Mişicu Romanian Journal of Physics 58,
11881197 (2013)
The population of rotational states in the groundstate band of neutronrich fragments emitted in the spontaneous fission of ^{252}Cf is described within a timedependent 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 postbarrier (pure Coulomb) motion. As application we consider the high yield MoBa pair for different number of emitted neutrons.
Study of αRadioactivity of Superheavy Nuclei I. Silisteanu, A.I. Budaca Romanian Journal of Physics 58,
11981207 (2013)
In the last years the quantity and quality of experimental data of new superheavy nuclei (SHN) have increased considerably. These nuclei have now become available for experimental studies with inbeam and decay spectroscopic methods, and also for detailed investigations through a variety of phenomenological and theoretical approaches. This work aims to prove that the αdecay rates of doubly closedshell nuclei and neighbouring isotopes/isotones provide a very sensitive and stringent test for the nuclear shell structure of (SHN).
From Neutron Skin to Pygmy Dipole Resonance: the Roles of Symmetry Energy in a Transport Approach V. Baran, B. Frecus, M. Colonna, M. di Toro, A. Croitoru, D. Dumitru Romanian Journal of Physics 58,
12081220 (2013)
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 LandauVlasov kinetic equation. In an energy density functional approach we employ three different parametrizations with density for the isovector part of the meanfield 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.
Neutrinos, Beta and Double Beta Decays and Related Topics
Search for the Cosmic Neutrino Background and KATRIN Amand Faessler, Rastislav Hodak, Sergey Kovalenko, Fedor Šimkovic Romanian Journal of Physics 58,
12211231 (2013)
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 cm^{3}. 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 ^{4}He 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 10^{10} K. Today their temperature is ~1.95 K and the average density is 56 electronneutrinos per cm^{3}. 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} + ^{3}H → ^{3}He + 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.
PositronEmitting and DoubleEC Modes of Double Beta Decay Jouni Suhonen Romanian Journal of Physics 58,
12321241 (2013)
This is a short review of the present status of the latest theoretical advances on the positronemitting and doubleelectroncapture (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 doubleelectron capture. In order to verify the fulfillment of the resonance condition a host of mass measurements have recently been done by using Penningtype atom traps.
GamowTeller Strength Distributions in the DoubleBeta Decay Partners ^{128,130}Te and ^{128,130}Xe P. Sarriguren, O. Moreno, E. Moya de Guerra Romanian Journal of Physics 58,
12421250 (2013)
We investigate the GamowTeller (GT) strength distributions in the doubleβ decaying nuclei ^{128}Te nd ^{130}Te, as well as in their respective partners ^{128}Xe and ^{130}Xe. 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 chargeexchange reactions ^{128}Te(^{3}He,t)^{128}I and ^{130}Te(^{3}He,t)^{130}I. Combining these results with calculated GT^{+} strength distributions in the Xe isotopes, the nuclear matrix elements for the twoneutrino doubleβ decay processes are evaluated and compared to experiment.
Double Fermi Matrix Element within Perturbation Theory Dušan Štefánik, Fedor Šimkovic Romanian Journal of Physics 58,
12511257 (2013)
The amplitude for doublebeta decay with twoneutrino emission is related to β^{−} and β^{+} transitions of Fermi and GamowTeller type connecting ground state of initial and final nuclei with virtual intermediate nuclear states. The suppression of double Fermi and GamowTeller matrix elements has origin in violation of the isospin SU(2) and spinisospin 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 twoneutrino double beta decay matrix element on the likenucleon pairing, particleparticle and particlehole protonneutron 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.
Weak Responses of Neutral Current NeutrinoNucleus Reactions V. Tsakstara, T.S. Kosmas, J.D. Vergados Romanian Journal of Physics 58,
12581269 (2013)
In this article we study the neutral current induced neutrinonucleus 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 ^{40}Ar$(\nu,\nu')$^{40}Ar^{*} and ^{56}Fe$(\nu,\nu')$^{56}Fe^{*}. We find that the coherent g_{s} and the GT_{0} 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 FermiDirac 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. ^{56}Fe can be used in other standard detectors.
Frontier Topics
Nuclear Structure Aspects of Atomic Parity Violation in Barium O. Moreno, E. Navarro de Martino, E. Moya de Guerra, P. Sarriguren Romanian Journal of Physics 58,
12701279 (2013)
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 pureparity 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.
Saturation of Optimal Entopic Resonance Limits in PionNucleus Scattering in Δ(1236)  Elementary Resonance Region D.B. Ion, M.L.D. Ion Romanian Journal of Physics 58,
12801297 (2013)
In this paper, it is shown that, the experimental values of the nonextensive scattering entropies S_{L}(p) and S_{θ}(q) for the pionnucleus (π^{0}He, π^{0}C, π^{0}O, π^{0}Ca) scatterings, in the energy region corresponding to ∆(1236) resonance in the elementary pionnucleon interaction, are well described by the entropic optimal resonance predictions S_{L}^{01} (p) and S_{θ}^{01} (q) when the nonextensivities indices are correlated by a RieszThorinlike relation: 1/2p+1/2q=1.
Propagation of Electromagnetic Pulses through the Surface of Dispersive Bodies M. Apostol Romanian Journal of Physics 58,
12981318 (2013)
The motion of an electromagnetic pulse (signal) through the surface of a semiinfinite (halfspace) 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 semiinfinite polarizable body (a halfspace) and penetrates into the body. The body reacts through its polarization degrees of freedom, which obey the wellknown DrudeLorentz (plasma) equation of motion. It is shown that the beam obeys the wellknown 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/r^{2}. 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.
On the QuantumClassical Analogies D. Dragoman Romanian Journal of Physics 58,
13191326 (2013)
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 Radiopharmaceuticals Research Center (CCR) of IFINHH at Start I. Ursu, L. Craciun, D. Niculae, N.V. Zamfir Romanian Journal of Physics 58,
13271336 (2013)
The present status of IFINHH CCR (Radiopharmaceuticals Research Centre) project is reviewed and its development perspectives are addressed.
Heavy Metal Accumulation and Translocation in Different Parts of Brassica Oleracea L C. Radulescu, C. Stihi, I.V. Popescu, I.D. Dulama, E.D. Chelarescu, A. Chilian Romanian Journal of Physics 58,
13371354 (2013)
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.
Entanglement of Formation for Gaussian States of Two Bosonic Modes in a Thermal Environment Aurelian Isar Romanian Journal of Physics 58,
13551362 (2013)
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 noninteracting 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.
Physics Education Research
Consequences the Extensive Use of MultipleChoice Questions Might Have on Student's Reasoning Structure C.M. Răduţă Romanian Journal of Physics 58,
13631380 (2013)
Learning physics is a contextdependent process. I consider a broader interdisciplinary problem of where differences in understanding and reasoning arise. I suggest the longrun effects a multiplechoice based learning system as well as society’s cultural habits and rules might have on student’s reasoning structure.
Mathematical Physics, Numerical Analysis and Phenomena Modeling
Some Remarks on Limits in Quantization Valentin Ceausescu Romanian Journal of Physics 58,
13811395 (2013)
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.
TwoProton Emission: A Numerical Approach L.Gr. Ixaru, D.S. Delion Romanian Journal of Physics 58,
13961407 (2013)
The twoproton 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 biproton 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.
Recurrence Relations for the Number of Solutions of a Class of Diophantine Equations M.I. Krivoruchenko Romanian Journal of Physics 58,
14081417 (2013)
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 nonlinear 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.
Multiscale Modeling of Heat Transfer in Composite Materials C. Timofte Romanian Journal of Physics 58,
14181427 (2013)
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.
On Bounds for Real Roots of Polynomials Doru Ştefănescu Romanian Journal of Physics 58,
14281435 (2013)
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.
Quantum and Classical Lie Systems for Extended Symplectic Groups A. Gheorghe Romanian Journal of Physics 58,
14361445 (2013)
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 WeiNorman equations. Moreover, we obtain the solutions of the timedependent 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 $\mathfrak{M}$.
