Study of <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis> nuclei in variation-after-projection framework

Variation-after-projection (VAP) calculations in conjunction with the Hartree- Bogoliubov (HB) ansatz have been carried out for A = 68-88, N = Z nuclei. In this framework, the yrast spectra with , B(E2) transition probabilities and deformation parameter ( ) have been obtained. A pairing interaction for like particles as well as protons and neutrons has been included in the model for a two-body interaction.Received: 28 April 2003, Revised: 20 March 2004, Published online: 14 September 2004PACS: 21.10.-k Properties of nuclei; nuclear energy levels - 21.60.-n Nuclear structure models and methods - 27.50. + e      

Forward on the <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis> line with GASP

The experimental study of the proton-rich nuclei close to the N = Z line is a constant challenge for nuclear spectroscopy, mainly due to the difficulty to produce them with the currently available beam/target combinations. Significant advances on this direction were obtained from experiments performed with the GASP array during the last two years: the yrast line of ⁸⁴Mo was extended up to 10 ⁺ , ⁸⁸Ru observed for the first time, and the N = Z + 1 line was mapped from ⁸¹Zr to ⁹⁵Ag. These new results allow us to have a more complete image of the transition from the well-deformed shell closure at N,Z = 40 to the spherical-shell closure at N,Z = 50, and highlights some particular effects that can be observed only in the vicinity of the N = Z line.Received: 10 January 2003, Published online: 23 March 2004PACS: 21.10.-k Properties of nuclei; nuclear energy levels - 21.10.Pc Single-particle levels and strength functions - 21.10.Re Collective levels - 23.20.-g Electromagnetic transitions     

Pairing of Neutrons and Protons in <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis> Nuclei

Values of neutron–proton pairing based on mass relations are estimated. It is shown that substantially different formulas for calculating the np-pairing energy in self-conjugate nuclei yield similar results. Comparison of the obtained values and the structure of ground state multiplet spectra shows that mass relations can be used to describe the isovector (T = 1) component of np-pairing to sufficient accuracy, but provides little or no information on isoscalar component T = 0.     

Effect of Coriolis Interaction on the Decay of Isotones with <Emphasis Type="Italic">N</Emphasis> = 149 and <Emphasis Type="Italic">N</Emphasis> = 153

The quasi-neutron structure of nuclei in two chains of odd isotones with N = 149 and N = 153: ^243,247Pu, ^245,249Cm, ^247,251Cf, ^249,253Fm, ^251,255No, and is considered. Single-particle energy spectra are calculated using the two center shell model (TCSM). Minimizing the potential energy with respect to the collective coordinates gives the ground state of the studied nucleos, which is subsequently used to describe low-lying quasi-neutron states. The K-mixing of the basis TCSM wave functions is considered by including the Coriolis correction in the total Hamiltonian of the system. The effect of level blocking is also considered in the calculations. The probabilities of the E2 transitions to the ground states and the corresponding lifetimes of the quasi-neutron levels are estimated.     

Single-particle properties of <Emphasis Type="Italic">N</Emphasis> = 12 to <Emphasis Type="Italic">N</Emphasis> = 20 silicon isotopes within the dispersive optical model

Experimental neutron and proton single-particle energies in N = 12 to N = 20 silicon isotopes and data on neutron and proton scattering by nuclei of the isotope ²⁸Si are analyzed on the basis of the dispersive optical model. Good agreement with available experimental data was attained. The occupation probabilities calculated for the single-particle states in question suggest a parallel-type filling of the 1d and 2s _1/2 neutron states in the isotopes ^{26,28,30,32,34}Si. The single-particle spectra being considered are indicative of the closure of the Z = 14 proton subshell in the isotopes ^30,32,34Si and the N = 20 neutron shell.     

The <Emphasis Type="Italic">N</Emphasis> = 2 Heavenly Equation

This paper presents report of the joint work with Z. Popowicz, which appeared in J. Phys. A, concerning the construction of a manifestly N = 2 supersymmetric heavenly equation in 2 + 1 dimensions. Its integrability properties have been derived from an N = 2 supersymmetric Lax pair, based on the n limit of the sl(n;n + 1) superalgebra series. The superhydrodynamical type of restrictions to 1+1 dimensions have been analyzed.     

The neutron drip line in the region of <Emphasis Type="Italic">N</Emphasis>=20 and <Emphasis Type="Italic">N</Emphasis>=28 closures

Experimental studies of neutron drip line nuclei are introduced. The neutron drip line in the oxygen-magnesium region has been explored by the projectile fragmentation of a ⁴⁸Ca beam. New neutron-rich isotopes, ³⁴Ne and ³⁷Na, have been observed together with some evidence for the particle instability of ³³Ne and ³⁶Na. Recent data on mass measurements of neutron-rich nuclei at GANIL and some characteristics of binding energies in this region are discussed. Nuclear binding energies are very sensitive to the existence of nuclear shells, and together with the measurements of instability of doubly magic nuclide ²⁸O, they provide information on changes in neutron shell closures of very neutron-rich isotopes from carbon up to calcium. The conclusion about a rearrangement in neutron shell closures is given. The spectroscopic measurements can reveal details of the underlying microscopic structures; in-beam γ-ray spectroscopy is an effective tool to check for shell closures. The results on the γ-ray energies of the first 2⁺ level in even-even nuclei for the range N=12–32 are discussed. The strength of N=20 and N=28 shells is variable in the region from carbon up to magnesium.     

New neutron magic number <Emphasis Type="Italic">N</Emphasis> = 16 for neutron-rich nuclei

A survey of experimental results obtained at GANIL (Caen, France) on the study of the properties of very neutron-rich nuclei (Z=6–20, A=20–60) near the neutron drip line and resulting in an appearance of further evidence for the new magic number N=16 is presented. Very recent data on mass measurements of neutron-rich nuclei at GANIL and some characteristics of binding energies in this region are discussed. Nuclear binding energies are very sensitive to the existence of nuclear shells, and together with the measurements of instability of doubly magic nuclei ¹⁰He and ²⁸O, they provide information on changes in neutron shell closures of very neutron-rich isotopes. The behavior of the two-neutron separation energies S_2n derived from mass measurements gives very clear evidence for the existence of the new shell closure N=16 for Z=9 and 10 appearing between the 2s_1/2 and 1d_3/2 orbitals. This fact, strongly supported by the instability of C, N, and O isotopes with N>16, confirms the magic character of N=16 for the region from carbon up to neon, while the shell closure at N=20 tends to disappear for Z≤13. Decay studies of these hardly accessible short-lived neutron-rich nuclei from oxygen to silicon using in-beam γ-ray spectroscopy are also reported.     

The <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis><Emphasis Type="Italic">f</Emphasis><Subscript>7/2</Subscript>-shell nuclei: Experimental highlights

During the last decade, as the experimental and computing means and techniques have rapidly evolved, the experimental investigation of the f_7/2-shell nuclei has gained renewed interest. TheN = Z nuclei studied with the GASP array range from ⁴⁴Ti to ⁵²Fe. The results extended the knowledge of their structure up to high spins and excitation energies, above band terminations, where the competition with the charged-particles emission was initially thought to obscure the possibility of gamma-ray spectroscopy investigation. The paper highlights some of the most outstanding properties of these nuclei such as the nuclear rotation and backbending effects, band termination states, yrast traps, non-natural parity bands, competition between T = 0 and T = 1 pn pairing modes.Received: 30 October 2002, Published online: 16 March 2004PACS: 21.10.-k Properties of nuclei; nuclear energy levels - 21.60.Cs Shell model - 23.20.Lv transitions and level energies - 27.40. + z C.A. Ur: On leave from NIPNE Bucharest, Romania     

Projected shell model study on nuclei near the <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis> line

Study of the nuclei in the mass-80 region is not only interesting due to the existence of abundant nuclear-structure phenomena, but also important in understanding the nucleosynthesis in the rp-process. It is difficult to apply a conventional shell model due to the necessary involvement of the g_9/2 sub-shell. In this paper, the projected shell model is introduced to this study. Calculations are systematically performed for the collective levels as well as the quasi-particle excitations. It is demonstrated that calculations with this truncation scheme can achieve a comparable quality as the large-scale shell model diagonalizations for ⁴⁸Cr, but the present method can be applied to much heavier mass regions. While the known experimental data of the yrast bands in the nuclei (from Se to Ru) are reasonably described, the present calculations predict the existence of high-K states, some of which lie low in energy under certain structure conditions.Received: 30 October 2002, Revised: 25 January 2003, Published online: 23 March 2004PACS: 21.60.-n Nuclear structure models and methods     

Synthesis of sterically congested 1,3,4-oxadiazole derivatives from aromatic carboxylic acids, <Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>-dicyclohexylcarbodiimide and (<Emphasis Type="Italic">N</Emphasis>-isocyanimino)triphenylphosphorane

Reactions of (N-isocyanimino)triphenylphosphorane with N,N-dicyclohexylcarbodiimide in the presence of aromatic (or heteroaromatic) carboxylic acids proceed smoothly at room temperature and in neutral conditions to afford sterically congested 1,3,4-oxadiazole derivatives in high yields. The reaction proceeds smoothly and cleanly under mild conditions, and no side reactions were observed.     

<Emphasis Type="Italic">N</Emphasis>=2 de Sitter Super-symmetry Algebra

It was shown that N=1 super-symmetry algebra can be constructed in de Sitter space (Pahlavan et al. in Phys Lett. B 627:217–223, 2005), through calculation of charge conjugation in the ambient space notation (Moradi et al. in Phys. Lett. B 613:74, 2005; Phys. Lett. B 658:284, 2008). Calculation of N=2 super-symmetry algebra constitutes the main frame of this paper. N=2 super-symmetry algebra was presented in Pilch et al. (Commun. Math. Phys. 98:105, 1985). In this paper, we obtain an alternative N=2 super-symmetry algebra.     

Ferromagnetism and ferroelectricity in Eu<Emphasis Type="Italic">X</Emphasis> (<Emphasis Type="Italic">X</Emphasis> = <Emphasis Type="Italic">O</Emphasis>, <Emphasis Type="Italic">S</Emphasis>): pressure effects

Ferromagnetism and ferroelectricity in Eu monochalcogenides have been investigated by ab initio density functional theory in the DFT+U approach. Exchange interaction parameters and Curie temperatures under pressure are studied and discussed using Heisenberg Hamiltonian with first and second-nearest-neighbor interactions. The calculations showed that the hydrostatic pressure perfectly improves the Curie temperature (EuO: T _C = 175 K; EuS: T _C = 33.8 K) and in the other hand it cannot induce the spontaneous polarization (P _s ). The effect of uniaxial and biaxial pressure is also studied. Although the uniaxial strains slightly increases the Curie temperature, it ensures the ferrolectricity in these systems by producing a spontaneous polarization of the order of P _s (EuO) = 57.50 μC/cm² and P _s (EuS) = 42.86 μC/cm² with pressures of 5% and 4%, respectively. The search for new model systems is a necessity to better understand the physics related to multiferroïc materials and to consider possible applications.     

<Emphasis Type="Italic">V</Emphasis>-<Emphasis Type="Italic">A</Emphasis> sum rules with <Emphasis Type="Italic">D</Emphasis> = 10 operators

The difference of vector and axial-vector charged current correlators is analyzed by means of QCD sum rules. The contribution of 10-dimensional 4-quark condensates is calculated and its value is estimated within the framework of the factorization hypothesis. It is compared to the result obtained from an operator fit of Borel sum rules in the complex q ²-plane, calculated from experimental data on hadronic -decays. This fit gives accurate values of the light quark condensate and the quark-gluon mixed condensate. The size of the high-order operators and the convergence of the operator series are discussed.Received: 10 May 2004, Revised: 7 September 2004, Published online: 18 November 2004     

Multiple two-variable <Emphasis Type="Italic">p</Emphasis>-adic <Emphasis Type="Italic">q-L</Emphasis>-function and its behavior at <Emphasis Type="Italic">s</Emphasis> = 0

The objective of this paper is to construct a multiple p-adic q-L-function of two variables which interpolates multiple generalized q-Bernoulli polynomials. By using this function, we solve a question of Kim and Cho. We also define a multiple partial q-zeta function which is related to the multiple q-L-function of two variables. Finally, we give a finite-sum representation of the multiple p-adic q-L-function of two variables and prove a multiple q-extension of the generalized formula of Diamond and Ferrero-Greenberg.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) Cosmology from <Emphasis Type="Italic">q</Emphasis>-theory

From a macroscopic theory of the quantum vacuum in terms of conserved relativistic charges (generically denoted by q ^(a) with label a), we have obtained, in the low-energy limit, a particular type of f(R) model relevant to cosmology. The macroscopic quantum-vacuum theory allows us to distinguish between different phenomenological f(R) models on physical grounds. The text was submitted by the authors in English.     

1/<Emphasis Type="Italic">N</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> countings in baryons

The 1/N _c -power countings for baryon decays and configuration mixings are determined by means of a nonrelativistic quark picture. Such countings are expected to be robust under changes in the quark masses and, therefore, valid as these become light. It is shown that excited baryons have natural widths of \(\mathcal{O}(N_c^0 )\). These dominant widths are due to the decays that proceed directly to the ground-state baryons, with cascade decays being suppressed to \(\mathcal{O}(1/N_c )\). Configuration mixings, defined as mixings between states belonging to different O(3) × SU(2N _f ) multiplets, are shown to be subleading in an expansion in \(1/\sqrt {N_c }\) when they involve the ground-state baryons, while the mixings between excited states can be \(\mathcal{O}(N_c^0 )\).     

A reanalysis of finite temperature <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>) gauge theory

We revise the SU(N _c ), N _c =3,4,6, lattice data on pure gauge theories at finite temperature by means of a quasi-particle approach. In particular, we focus on the relation between the effective mass of the quasi-particle and the order of the deconfinement transition, the scaling of the interaction measure with N²_c -1N^{2}_{c} -1, the role of gluon condensate, and the screening mass.     

Non-vacuum Bianchi types <Emphasis Type="Italic">I</Emphasis> and <Emphasis Type="Italic">V</Emphasis> in <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) gravity

In a recent paper (Sharif and Shamir in Class. Quantum Grav. 26:235020, 2009), we have studied the vacuum solutions of Bianchi types I and V spacetimes in the framework of metric f (R) gravity. Here we extend this work to perfect fluid solutions. For this purpose, we take stiff matter to find energy density and pressure of the universe. In particular, we find two exact solutions in each case which correspond to two models of the universe. The first solution gives a singular model while the second solution provides a non-singular model. The physical behavior of these models has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated.