Nuclear matter properties in relativistic mean-field model with σ- ω coupling

The σ-ω coupling is introduced phenomenologically in the linear σ-ω model to study the nuclear matter properties. It is shown that not only the effective nucleon mass M^* but also the effective σ meson mass m _σ ^* and the effective ω meson mass m _ω ^* are nucleon-density-dependent. When the model parameters are fitted to the nuclear saturation point, with the nuclear radius constant r ₀ = 1.14 fm and volume energy a ₁ = 16.0 MeV, as well as to the effective nucleon mass M ^* = 0.85M, the model yields m _σ ^* = 1.09m _σ and m _ω ^* = 0.90m _ω at the saturation point, and the nuclear incompressibility K ₀ = 501 MeV. The lowest value of K₀ given by this model by adjusting the model parameters is around 227 MeV. Received: 23 March 2001 / Accepted: 8 June 2001     

Cosmology with cluster surveys

Surveys of clusters of galaxies provide us with a powerful probe of the density and nature of the dark energy. The red-shift distribution of detected clusters is highly sensitive to the dark energy equation of state parameterw. Upcoming Sunyaev-Zel’dovich (SZ) surveys would provide us large yields of clusters to very high red-shifts. Self-calibration of cluster scaling relations, possible for such a huge sample, would be able to constrain systematic biases on mass estimators. Combining cluster red-shift abundance with limited mass follow-up and cluster mass power spectrum can then give constraints onw, as well as onσ ₈ and Ω_M to a few per cents.     

Determination of nonlinear σ-ω-ρ model parameters in the relativistic mean-field theory by nuclear-matter properties

The parameters of the σ-ω-ρ model in the relativistic mean-field theory with nonlinear σ-meson self-interaction are determined by nuclear-matter properties, which are taken as those extracted by fits to data based on nonrelativistic nuclear models. The values of the relevant parameters are C _σ ²∼ 94, C _ω ²∼ 32, C _ρ ²∼ 26, b∼ - 0.09, c∼ 1, and the σ-meson mass m _σ∼ 370 MeV, while the value of the calculated nuclear- surface thickness is t∼ 1.4 fm. The field system is shown to be stable, since the σ-meson self-interaction energy is a lower bound in this whole parameter region with positive c. On the other hand, the effective nucleon mass M^* is larger than 0.73M, if the symmetry incompressibility K_s is assumed to be negative and the nuclear-matter incompressibility K₀ is kept less than 300 MeV. Received: 27 June 2001 / Accepted: 5 October 2001     

The σK coupling in the chiral unitary approach and the isoscalar ¯N , ¯A interaction

We evaluate the “σ " exchange contribution to the ˉN → ˉN scattering within a chiral unitary approach. We show that the chiral transition potentials for ππ → Kˉ in the t -channel lead to a “σ " contribution that vanishes in the ˉ forward direction and, hence, would produce a null “σ " exchange contribution to the K^- optical potential in nuclear matter in a simple impulse approximation. This is a consequence of the fact that the leading-order chiral Lagrangian gives an I = 0 ππ → Kˉ amplitude proportional to the squared momentum transfer, q². This finding poses questions on the meaning or the origin of “σ " exchange potentials used in relativistic mean-field approaches to the K^- nuclear self-energy. This elementary “σ ” exchange potential in ˉN → ˉN is compared to the Weinberg-Tomozawa term and is found to be smaller than the present theoretical uncertainties but will be relevant in the future when aiming at fitting increasingly more accurate data.     

Self-consistent treatment of the quark condensate and hadrons in nuclear matter

We calculate the contribution of pions to the $\bar qq$-expectation value κ(ρ) =<M|ˉq q|M> in symmetric nuclear matter. We employ exact pion propagator renormalized by nucleon-hole and isobar-hole excitations. Conventional straightforward calculation leads to the “pion condensation” at unrealistically small values of densities, causing even earlier restoration of chiral symmetry. This requires a self-consistent approach, consisting in using the models, which include direct dependence of in-medium mass values on κ(ρ), e.g. the Nambu–Jona-Lasinio–model. We show, that in the self-consistent approach the ρ-dependence of the condensate is described by a smooth curve. The “pion condensate” point is removed to much higher values of density. The chiral restoration does not take place at least while ρ < 2.8ρ₀ with ρ₀ being the saturation value. Validity of our approach is limited by possible accumulation of heavier baryons (delta isobars) in the ground state of nuclear matter. For the value of effective nucleon mass at the saturation density we found m ^*(ρ₀) = 0.6m, consistent with nowadays results of other authors. Received: 8 October 1998     

Nuclear compressibility and its effect on nuclear binding energies from the study of muonic atoms

The variation of nuclear parameter with mass number elicits information about nuclear compressibility. Analysis of muonic x-ray transitions provides an elegant method to investigate the behaviour of the nuclear parameterr ₀. It is observed from the behaviour ofr ₀ that nuclei in the regionA⩽70 are highly compressible while those in the regionA∼210 are almost incompressible. The behaviour ofr ₀ is incorporated into the semi-empirical mass formula through the Coulomb energy term. From the modified mass formula thus obtained binding energies of about 440 spherical nuclei have been calculated. The results suggest that nuclear compressibility imposes certain relationship between excess binding energies (E _exp−E _cal) and neutron. proton number. The present study also points out that shell effects exhibited by nuclear binding energies cannot be accounted for by simply varying the coefficients of the mass formula: on the other hand extra terms are necessary to explain them.     

General SU(2)L × SU(2)R × U(1)EM Sigma Model with External Sources, Dynamical Breaking and Spontaneous Vacuum Symmetry Breaking

We give a general SU(2) _L × SU(2) _R × U(1) _EM sigma model with external sources, dynamical breaking and spontaneous vacuum symmetry breaking, and present the general formulation of the model. It is found that σ and π⁰ without electric charges have electromagnetic interaction effects coming from their internal structures. A general Lorentz transformation relative to external sources is derived, using the general Lorentz transformation and the four-dimensional current of nuclear matter of the ground state with J _gauge = 0, we give the four-dimensional general relations between the different currents of nuclear matter systems with J _gauge≠ 0 and those with J _gauge = 0. The relation of the density’s coupling with external magnetic field is derived, which conforms well to dense nuclear matter in a strong magnetic field. We show different condensed effects in strong interaction about fermions and antifermions, and give the concrete scalar and pseudoscalar condensed expressions of σ₀ and π₀ bosons. About different dynamical breaking and spontaneous vacuum symmetry breaking, the concrete expressions of different mass spectra are obtained in field theory. This paper acquires the running spontaneous vacuum breaking value σ′₀, and obtains the spontaneous vacuum breaking in terms of the running σ′₀, which make nucleon, σ and π particles gain effective masses. We achieve both the effect of external sources and nonvanishing value of the condensed scalar and pseudoscalar paticles. It is deduced that the masses of nucleons, σ and π generally depend on different external sources. PACA numbers: 24.10.-i, 11.30.Qc     

Superconductivity and magnetic ordering in YBa2(Cu1−x Fe x )3O7

Transverse-and zero-field μSR measurements have been made for YBa₂(Cu_1−x Fe _x )₃O₇ withx=0.04, 0.08 and 0.12. The temperature range studied was from approximately 7.5 K to 100 K. The onset of magnetic ordering commences at about 7.5 K forx=0.04, 10 K forx=0.08 and 20 K forx=0.12. The Gaussian depolarization parameter, σ ofG _x (t) = exp(−σ² t ²/2), is depressed by a factor of about 0.6 forx=0.04, but for thex=0.08 sample σ is depressed by a factor of 10 and increasing suppression is seen as the temperature is lowered below 45 K. This decrease in σ is interpreted in terms of decreasing electronic mean free paths.     

Nuclear matter test for a separable non-localN-N interaction

A nuclear matter test has been conducted on a separable non-localN-N interaction proposed by Sirohi and Srivastava. The potential had been constructed by fitting the phase-shifts. The results obtained compare with those obtained by Tabakin in each partial wave. The binding energy per particle and the symmetry energy coefficient obtained are 19.4 MeV and 66.5 MeV respectively atk _F=1.65 fm⁻¹, while the best estimated values for these quantities are 16 MeV and 30–35 MeV atk _F=1.5 fm⁻¹. Single particle potential generated out of this NLSI has in general the same shape as the one obtained through Tabakin potential. Finally as a test of non-locality the integrated photoabsorption cross-section parameterh has been calculated and the value of 1.03 agrees with other reported values.     

Dielectric properties of BiMg1/2Ti1/2O3 and BiMg1/2Zr1/2O3 perovskite ceramics with elimination of the contribution for direct current conductivity

A technique for analysis of the electric modulus spectrum of dielectric ceramics based on the elimination of the direct current conductivity (σ _dc ) contribution has been developed. Expressions are given for the real (M′ _ac ) and imaginary (M′′ _ac ) parts of the complex electrical modulus related only to the dielectric polarization and not containing the contribution of σ _dc . The frequency dependence of M′′ _ac and the M′′ _ac – M′ _ac diagram for BiMg_1/2Ti_1/2O₃ and BiMg_1/2Zr_1/2O₃ perovskite ceramics are analyzed.     

Inclusive electroproduction of pseudo-scalar mesons on a proton: Selection of the strange-quark contribution to the proton spin

In this work, the problem of separating the contribution of a strange quark to the proton spin in the process is studied. Measurements of the quantities Δσ _K and Δσ_±, where Δσ _M =dσ _M (+ +) -dσ _M (+ -) at small z, and the use of definite combinations of them allow important information on the proton-spin structure to be obtained. M. A. Rasulzade Baku State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 21–25, January, 2000.     

The potts glass in uniform and random fields: a monte carlo investigation

As a simple model of an anisotropic orientational glass with short range forces, the 3-state Potts model on the simple cubic lattice with nearest neighbor interactions drawn from a Gaussian distribution is considered. With Monte Carlo methods we study the response of the system to a uniform “field” which favors one of the states. This is motivated by experiments which apply stress that favors one molecular orientation of the quadrupolar glass. The responsem to that fieldh=H/k _BT is analyzed in terms of an expansionm= χ₁ h+χ₁ h ²+χ₁ h ³+..., where χ₁ is the linear susceptibility, and χ₂,χ₁₃ are nonlinear susceptibilities. Unlike the case of spin glasses, where the spin inversion symmetry of the system in the absence of fields implies χ₂≡0,χ₂ is nonzero here and diverges to −∞ at the zero temperature transition of the model, while χ₃ diverges to +∞ as in spin glasses. At inifinite temperature, however, χ₁=1/3, χ₂=1/18 and χ₃=-1/54, i.e. the nonlinear susceptibilities have a different sign as at low temperature. In contrast, a random field does not induce a uniform order parameterm but only a glass order parameterq. The temperature dependence of this glass order parameterq(T) shows for intermediate field strength order parameterq(T) shows for intermediate field strength a maximum of the slopedq(T)/dT very similar to corresponding experiments.     

Observational constraints on decaying vacuum dark energy model

The decaying vacuum model (DV), treating dark energy as a varying vacuum, has been studied well recently. The vacuum energy decays linearly with the Hubble parameter in the late-times, ρ _Λ (t)∝H(t), and produces the additional matter component. We constrain the parameters of the DV model using the recent data-sets from supernovae, gamma-ray bursts, baryon acoustic oscillations, CMB, the Hubble rate and X-rays in galaxy clusters. It is found that the best fit of the matter density contrast Ω _m in the DV model is much lager than that in ΛCDM model. We give the confidence contours in the Ω _m –h plane up to 3σ confidence level. Besides, the normalized likelihoods of Ω _m and h are presented, respectively.     

Angular spread of Gaussian Schell-model array beams propagating through atmospheric turbulence

The closed-form expression for the angular spread of Gaussian Schell-model (GSM) array beams propagating through atmospheric turbulence is derived. It is shown that the angular spread θ _sp of GSM array beams for the superposition of the cross-spectral density function is smaller than of those for the superposition of the intensity. However, the θ _sp of GSM array beams for the superposition of the intensity is less sensitive to turbulence than that for the superposition of the cross-spectral density function. For the superposition of the cross-spectral density function, θ _sp of GSM array beams with smaller coherence length σ ₀, smaller waist width w ₀, smaller beam number N, and larger separation distance x _d are less affected by turbulence than of those with larger σ ₀,w ₀,N, and smaller x _d ; while, for the superposition of the intensity, the effect of turbulence on θ _sp is independent of N and x _d . In addition, the angular spread is nearly the same for the two types of superposition when σ ₀ or w ₀ is small enough, or x _d is large enough. On the other hand, it is found that there exist equivalent GSM array beams for the two types of superposition which may have the same directionality as the corresponding fully coherent Gaussian beam in free space and also in turbulence.     

Universality in the length spectrum of integrable systems

The length spectrum of periodic orbits in integrable hamiltonian systems can be expressed in terms of the set of winding numbers {M ₁,…,M _f} on thef-tori. Using the Poisson summation formula, one can thus express the density, Σδ(T−T _M), as a sum of a smooth average part and fluctuations about it. Working with homogeneous separable potentials, we explicitly show that the fluctuations are due to quantal energies. Further, their statistical properties are universal and typical of a Poisson process as in the corresponding quantal energy eigenvalues. It is interesting to note however that even though long periodic orbits in chaotic billiards have similar statistical properties, the form of the fluctuations are indeed very different.     

μ+SR study of heavy-fermion magnetism in Ce(Cu1-xNix)2Ge2

We report muon spin relaxation (μ⁺SR) studies on the magnetic phase diagram of Ce(Cu_1-xNi_x)₂Ge₂ polycrystals for 0.5≤ x ≤ 0.8. A sharp magnetic transition, evidenced by the appearance of a fast Gaussian relaxation component σ, has been observed in the x = 0.5 alloy at 4.0 K in zero applied field. The average local field < B_μ> at the stopping sites of the muons, extracted from σ, exhibits a linear temperature dependence. We associate these features with an incommensurate spin density wave (SDW) ordering. Magnetic ordering, either long range or short range, and signatures of non-Fermi liquid behaviour have not been observed down to 2.0 K at x = 0.8. This revised version was published online in August 2006 with corrections to the Cover Date.     

The SMBH mass versus <Emphasis Type="Italic">M</Emphasis><Subscript>G</Subscript><Emphasis Type="Italic">σ</Emphasis><Superscript>2</Superscript> relation: a comparison between real data and numerical models

The relation between the mass of supermassive black holes located in the center of the host galaxies and the kinetic energy of random motions of the corresponding bulges can be reinterpreted as an age–temperature diagram for galaxies. This relation fits the experimental data better than the M _•−M _G, M _•−L _G, and M _•−σ laws. The validity of this statement has been confirmed by using three samples extracted from different catalogues of galaxies. In the framework of the ΛCDM cosmology our relation has been compared with the predictions of two galaxy formation models based on the Millennium Simulation.     

Influences on the pseudospin symmetry from the different fields of mesons in deformed nuclei

Influences from different fields of mesons on the pseudospin symmetry are investigated for deformed nuclei. The energy splitting between pseudospin partners are extracted from the relativistic mean field calculations. The results show that the σ-field contribution to the pseudospin energy splitting has nearly the same magnitude as the one obtained by the ω-field, but with opposite signs. The pseudospin energy splittings either for neutron or for protons are almost the same if the σ-field (V _σ ) and the ω-field (V _ω ) change at the same scale. The pseudospin energy splitting depends in the same way as the nucleus binding energy of the cancellation of these two potentials, and is controlled by the same nuclear physics scale as the potential sum V _ω + V _σ In comparison with the σ- and ω-fields, it is seen that the ρ meson field produces a minor influence on the pseudospin symmetry.     

Scalar σ meson at a finite temperature in a nonlocal quark model

The properties and temperature behavior of the π and σ bound states are studied in the framework of the nonlocal model with a separable interaction kernel, based on the quark Dyson-Schwinger and meson Bethe-Salpeter equations. M _π(T), f _π(T), M _σ(T), and Γ_{σ → ππ}(T) are considered above and below the deconfinement and chiral restoration transitions. Talk at the Round-Table Discussion “Searching for a Mixed Phase of Strongly Interacting Matter at the JINR Nuclotron,” Dubna, July 7–9, 2005. The text was submitted by the authors in English.