Mean square number fluctuation for a fermion source and its dependence on neutrino mass for the universal cosmic neutrino background

Using the general formulation for obtaining chemical potentialμ of an ideal Fermi gas of particles at temperature T, with particle rest mass m₀ and average density 〈N〉/V, the dependence of the mean square number fluctuation 〈ΔN ²〉/V on the particle mass m₀ has been calculated explicitly. The numerical calculations are exact in all cases whether rest mass energym ₀c² is very large (non-relativistic case), very small (ultra-relativistic case) or of the same order as the thermal energy k_BT. Application of our results to the detection of the universal very low energy cosmic neutrino background (CNB), from any of the three species of neutrinos, shows that it is possible to estimate the neutrino mass of these species if from approximate experimental measurements of their momentum distribution one can extract, someday, not only the density 〈N _v〉/V but also the mean square fluctuation 〈Δ _v ² 〉/V. If at the present epoch, the universe is expanding much faster than thermalization rate for CNB, it is shown that our analysis leads to a scaled neutrino massm _v instead of the actual massm _0v .     

Orientation dependence of electrical properties of 0.96Na<Subscript>0.5</Subscript>Bi<Subscript>0.5</Subscript>TiO<Subscript>3</Subscript>-0.04BaTiO<Subscript>3</Subscript> lead-free piezoelectric single crystal

In this paper, a single crystal of 0.96Na_0.5Bi_0.5TiO₃-0.04BaTiO₃ with dimensions of Φ 30×10 mm was grown by the top-seeded-solution growth method. X-ray powder diffraction results show that the as-grown crystal possesses the rhombohedral perovskite-type structure. The dielectric, piezoelectric and electrical conductivity properties were systematically investigated with 〈001〉, 〈110〉 and 〈111〉 oriented crystal samples. The room-temperature dielectric constants for the 〈001〉, 〈110〉 and 〈111〉 oriented crystal samples are found to be 650, 740 and 400 at 1 kHz. The (T _m, ε _m) values of the dielectric temperature spectra are almost independent of the crystal orientations; they are (306°C, 3718), (305°C, 3613) and (307°C, 3600) at 1 kHz for the 〈001〉, 〈110〉 and 〈111〉 oriented crystal. The optimum poling conditions were obtained by investigating the piezoelectric constants d ₃₃ as a function of poling temperature and poling electric field. For the 〈001〉 and 〈110〉 crystal samples, the maximum d ₃₃ values of 146 and 117 pC/N are obtained when a poling electric field of 3.5 kV/mm and a poling temperature of 80°C were applied during the poling process. The as-grown 0.96Na_0.5Bi_0.5TiO₃-0.04BaTiO₃ crystal possesses a relatively large dc electrical conductivity, especially at higher temperature, having a value of 1.98×10⁻¹¹ Ω⁻¹⋅m⁻¹ and 3.95×10⁻⁹ Ω⁻¹⋅m⁻¹ at 25°C and 150°C for the 〈001〉 oriented crystal sample.     

The total yields of K *(892)+, Σ+(1385), and Σ0 in neutrino-induced reactions at ? E v? ≈ 10 GeV

Using the data obtained with the SKAT bubble chamber, the total yields of K*(892)⁺, Σ⁺(1385), and Σ⁰ are estimated for the first time in neutrino-induced reactions at moderate energy 〈E _v〉 = 10.4 GeV. It is shown that the recently observed enhancement of the K ⁰ and Λ yields in vA interactions as compared to vN interactions is contributed only slightly by the K*(892)⁺ and Σ⁺(1385) production. The contribution of resonances to the K ⁰ and Λ yields is found to be in qualitative agreement with higher energy (〈E _v〉 ≳ 40 GeV) data. It is shown that the energy dependence of the K*(892)⁺ mean multiplicity in vN interactions is approximately linear in the range of 〈E _v〉 ≈ 10−60 GeV, while that for Σ⁰ in vA interactions (A = 20−21) is approximately logarithmic in the range of 〈E _v〉 ≈ = 10−150 GeV. The text was submitted by the authors in English.     

Superparamagnetism in the 1D Ising model

The temperature dependence of the order parameter (〈M ²〉, the mean-square spin excess per spin) for a system with a finite number of spins of the 1D Ising model was investigated. It was shown that there is a nonzero temperature T _s below which 〈M ²〉 rapidly tends to unity. The analogy between the 1D ensemble of a finite number of spins and a system of superparamagnetic particles is discussed.     

Using the full Raman depolarisation in the determination of the order parameters in liquid crystal systems

The depolarisation ratio for the Raman-active phenyl stretching mode has been measured over the whole of the mesophase range, and the orientational order parameters deduced, in the uniaxial nematic liquid crystal octylcyanobiphenyl (8CB). Linearly polarised light was incident normally on a homogeneously aligned sample and a χ² minimisation routine performed on the 360^° depolarisation ratio profile. The order parameters 〈P ₂₀₀〉 and 〈P ₄₀₀〉 , together with the differential polarisability ratio, r , are used as fitting parameters and measured as a function of temperature. Interestingly, we show that the value for r , conventionally measured in the isotropic phase and assumed to remain constant, has a clear temperature dependence, ranging from -0.032±0.008 in the isotropic phase through to -0.245±0.015 at the nematic-to-smectic A phase transition. The measured order parameters 〈P ₂₀₀〉 and 〈P ₄₀₀〉 varied from 0.35- 0.55±0.02 and 0.180- 0.245±0.02 , respectively, across the 8 ^° C wide nematic phase range. The values of both 〈P ₂₀₀〉 and 〈P ₄₀₀〉 are in excellent agreement with theory, but it is noteworthy that 〈P ₄₀₀〉 shows a much better quantitative match than has been reported in previous work. Crucially the temperature dependence of r is shown to be a contributing factor in the low 〈P ₄₀₀〉 values that have been conventionally reported from Raman scattering measurements. The potential for fitting the entire angular depolarisation ratio distribution in liquid crystalline systems that are described by more order parameters, specifically biaxial materials, is discussed.     

Lattice mechanical properties of noble and transition metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is used to study the interatomic interactions, phonon dispersion curves (inq and r-space analysis), phonon density of states, mode Grüneisen parameters, dynamical elastic constants (C ₁₁,C ₁₂ andC ₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C ₁₂–C ₄₄), Poisson’s ratio (σ), Young’s modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y ₁), limiting value in the [110] direction (Y ₂), degree of elastic anisotropy (A), maximum frequencyω _max, mean frequency 〈ω〉, 〈ω ²〉^1/2=(〈ω〉/〈ω ⁻¹〉)^1/2, fundamental frequency 〈ω ²〉, and propagation velocities of the elastic constants in Cu, Ag, Au, Ni, Pd, and Pt. The contribution of s-like electrons is calculated in the second-order perturbation theory for the model potential while that of d-like electrons is taken into account by introducing repulsive short-range Born-Mayer like term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has proved the ability of our model potential for predicting a large number of physical properties of transition metals.     

Double-beta decay: Present status

The present status of double-beta-decay experiments (including the search for 2β ⁺, ECβ ⁺, and ECEC processes) are reviewed. The results of the most sensitive experiments are discussed. Average and recommended half-life values for two-neutrino double-beta decay are presented. Conservative upper limits on effective Majorana neutrino mass and the coupling constant of the Majoron to the neutrino are established as 〈m _ν 〉 < 0.75 eV and 〈g _ee 〉 < 1.9 × 10⁻⁴, respectively. Proposals for future double-betadecay experiments with a sensitivity for the 〈m _ν 〉 at the level of 0.01–0.1 eV are considered.     

Plastic-strain localization in barium fluoride single crystals at elevated temperatures

The strain distribution is studied in BaF₂ crystals subjected to compression tests along [110] and [112] at a constant strain rate in the temperature range T = (0.22–0.77)T _m. At T > 0.5T _m, the plastic strain in deformed samples is found to be strongly localized in narrow bands, where the shear strain reaches several hundred percent. The degree of localization increases with temperature. Localized-shear microbands are shown to be oriented along {001}〈110〉 slip systems. The phenomenon of serrated yielding is detected, and stress jumps (serrations) are established to correlate with the formation of shear zones.     

Anisotropy of the upper critical field and specific heat in V3Si — a superconductor with cubic symmetry

The specific heat of a V₃Si single crystal (T _c=17 K, H _c2=20 T) in magnetic fields up to 8 T isinvestigated experimentally for three orientations of the field relative to the crystallographic directions — H∥〈001〉, H∥〈110〉, and H∥〈111〉. Both the upper critical magnetic field and the specific heat of the mixed state are observed to depend on the orientation of the magnetic field relative to the crystallographic directions (anisotropy): The critical field reaches its maximum value and the specific heat its minimum value in a field along the 〈001〉 direction. The anisotropy scale in both phenomena increases as the magnetic field and reaches 3% in a 6 T field. The interrelationship of the upper critical field anisotropy and the specific-heat anisotropy in type-II superconductors is studied. It is shown that the anisotropy of the specific heat in the mixed state in weak fields can serve as a criterion for nontrivial pairing. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 26–29 (10 January 1999)     

Evidence of an intermediate phase in ternary Ge<Subscript>7</Subscript>Se<Subscript>93-x</Subscript>Sb<Subscript>x</Subscript> glasses

The compositional dependence of thermal properties, such as glass transition temperature (T_g), non-reversing enthalpy change (ΔH_NR) and the specific heat capacity change (ΔC_p) of melt quenched Ge₇Se_93-xSb_x (21 ≤ x ≤ 31) glasses, has been studied using alternating differential scanning calorimetry (ADSC) which is analogous to modulated differential scanning calorimetry (MDSC). The glass transition temperature, T_g, which is a measure of global connectivity of the glass, has been found to increase with the addition of Sb. In addition, a change in slope has been observed in the composition dependence of T_g at an average coordination 〈r〉 = 2.40. The experimentally observed compositional variation of glass transition temperature, has been compared with the theoretical predictions from the stochastic agglomeration theory (SAT) and has been found to be consistent. Further, a narrow thermally reversing window is seen in the compositional variation of the relaxation enthalpy (ΔH_NR), which is centered around 〈r〉 = 2.40. The change in specific heat capacity (ΔC_p) at T_g is also found to exhibit a distinct minima at 〈r〉 = 2.40, suggesting that the structural rearrangements for the liquid in the glass transition region are minimized around 〈r〉 = 2.4.     

Bell Inequalities as Constraints on Unmeasurable Correlations

The interpretation of the violation of Bell-Clauser-Horne inequalities is revisited, in relation with the notion of extension of QM predictions to unmeasurable correlations. Such extensions are compatible with QM predictions in many cases, in particular for observables with compatibility relations described by tree graphs. This implies classical representability of any set of correlations 〈A _i 〉, 〈B〉, 〈A _i B〉, and the equivalence of the Bell-Clauser-Horne inequalities to a non void intersection between the ranges of values for the unmeasurable correlation 〈A ₁ A ₂〉 associated to different choices for B. The same analysis applies to the Hardy model and to the “perfect correlations” discussed by Greenberger, Horne, Shimony and Zeilinger. In all the cases, the dependence of an unmeasurable correlation on a set of variables allowing for a classical representation is the only basis for arguments about violations of locality and causality.     

Electron paramagnetic resonance of deep boron acceptors in 4H-SiC and 3C-SiC crystals

EPR spectra of deep boron in 4H-SiC and 3C-SiC crystals have been observed and studied. Two sites in 4H-SiC produced deep-boron EPR signals, quasi-cubic k and hexagonal h. In both cases the deep-boron center symmetry is close to axial along the c crystal axis, and the g factor anisotropy is about an order of magnitude larger than that for shallow boron centers. In the 3C-SiC crystal, the deep-boron symmetry is also close to axial along one of the four 〈111〉 directions. The model proposed for the deep boron center with acceptor properties is B_Si-v _C, where B_Si is the boron substituting for silicon, and v _C is the carbon vacancy, with the B_Si-v _C direction coinciding in 4HSiC with the hexagonal axis of the crystal for both k and h positions. In the cubic 3C-SiC crystal, there are four equivalent deep boron centers, which represent B_Si-v _C pairs with the bond directed along one of the four 〈111〉 crystal directions. Fiz. Tverd. Tela (St. Petersburg) 40, 36–40 (January 1998)     

Vacancy formation energy related to liquid structure in a nonlinear scaled potential theory

Summary A scaling relation is derived for the vacancy formation energyE _v in a family of homologous systems at their melting temperatureT _m, using a pair potential theory which relatesE _v atT _m to liquid structure under the assumption that atomic relaxation round the vacancy can be neglected.

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Riassunto Il lavoro deriva una relazione di scala per l’energiaE _v di formazione di un posto vacante in una famiglia di sistemi omologhi alla loro temperatureT _m di fusione, nell’ambito di una teoria a potenziale di coppia che legaE _v aT _m alla struttura della fase liquida nell’ipotesi che rilassamenti atomici attorno al posto vacante possano essere trascurati.

     

Bilepton contributions to the neutrinoless double beta decay in the economical 3-3-1 model

A new bound of the mixing angle between charged gauge bosons (the standard-model W and the bilepton Y) in the economical 3-3-1 model is given. Possible contributions of the charged bileptons to the neutrinoless double beta ((ββ)_0ν) decay are discussed. We show that the (ββ)_0ν decay in this model is due to both the Majorana 〈M _ν〉 _L and Dirac 〈M _ν 〉_D neutrino masses. If the mixing angle is in the range of the ratio of neutrino masses 〈M _ν 〉 _L /〈M _ν 〉_D, the Majorana and Dirac masses are comparable to each other and both may give the main contribution to the decay. As a result, constraints on the bilepton mass are given. The article is published in the original.     

Swelling of two-dimensional polymer rings by trapped particles

The mean area of a two-dimensional Gaussian ring of N monomers is known to diverge when the ring is subject to a critical pressure differential, p _c ∼ N ^-1. In a recent publication (Eur. Phys. J. E 19, 461 (2006)) we have shown that for an inextensible freely jointed ring this divergence turns into a second-order transition from a crumpled state, where the mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N ². In the current work we extend these two models to the case where the swelling of the ring is caused by trapped ideal-gas particles. The Gaussian model is solved exactly, and the freely jointed one is treated using a Flory argument, mean-field theory, and Monte Carlo simulations. For a fixed number Q of trapped particles the criticality disappears in both models through an unusual mechanism, arising from the absence of an area constraint. In the Gaussian case the ring swells to such a mean area, 〈A〉 ∼ NQ, that the pressure exerted by the particles is at p _c for any Q. In the freely jointed model the mean area is such that the particle pressure is always higher than p _c, and 〈A〉 consequently follows a single scaling law, 〈A〉 ∼ N ² f (Q/N), for any Q. By contrast, when the particles are in contact with a reservoir of fixed chemical potential, the criticality is retained. Thus, the two ensembles are manifestly inequivalent in these systems. An erratum to this article is available at .     

Properties of a magnetic impurity in a metal

The effect of a polarized conduction-electron cloud back on a magnetic impurity dissolved in a metal is studied. It is shown that at a temperature T _c much higher than the Kondo temperature the system becomes unstable against symmetry breaking and that a state with 〈S _z 〉 ≠ 0 is established. The behavior of 〈 S _z 〉 is derived for all temperatures and magnetic fields except for a very narrow region around T _c and for very low temperatures. The minute role of Kondo-type processes in establishing the symmetry-broken state is pointed out. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 184–189 (10 August 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The Landauer resistance of a one-dimensional metal with periodically spaced random impurities

We find the dependence of the ensemble-averaged resistance, 〈ρ _L〉, of a one-dimensional chain consisting of periodically spaced random delta-function potentials of the chain length L, the incident-electron energy, and the chain disorder parameter w. We show that generally the 〈ρ _L〉 vs L dependence can be written as a sum of three exponential functions, two of which tend to zero as L℩∞. Hence the asymptotic expression for 〈ρ _L〉 is always an exponential function of L. Such an expression for 〈ρ _L〉 means that the electronic states are indeed localized and makes it possible (which is important) to find the dependence of the localization radius on the incident-electron energy and the force with which an electron interacts with the sites of the chain. We also derive a recurrence representation for 〈ρ _L〉, which proves convenient in numerical calculations. Zh. éksp. Teor. Fiz. 111, 575–584 (February 1997)     

On certain correspondences among various coupled-cluster theories for closed-shell systems

In this paper certain correspondences have been shown among various formulations of coupled-cluster theories for many electron closed-shell systems. Specifically it is shown that (i) the energy functional using unitary ansatz of the form exp (T−T ⁺) is exactly sameorder by order inT with the size-consistent energy functional 〈ψ|H|ψ〉/〈ψ|ψ〉 recently obtained by us in coupled-cluster framework; (ii) in the framework of unitary ansatz of the form exp (T−T ⁺), both non-variational and variational approaches lead to identical equations upto any given order inT andT ⁺ inT∼T ₂ approximation; (iii) variational procedure using our size-consistent energy functional or using the functional obtained in the framework of unitary ansatz (as envisaged by Kutzelnigg) leads to energy in both cases, inT∼T ₂ approximation, for a total of quadratic powers inT andT ⁺, same as Cizek’s linearised coupled pair many electron theory energy; (iv) in case of practical calculation of the energy through the variational procedures using our size-consistent energy functional and the functional in unitary ansatz framework, there is a loss of upper bound.     

A study of neutrinoless double-beta decay in the framework of QRPA

A study concerning the valence space dependence of neutrinoless doubleβ ⁻ decay observables is performed for several nuclei in the framework of QRPA using the multiple commutator method (MCM). Calculations and comparison to earlier results show that at least for the ground state to ground state transition the dependence is much weaker than in the two neutrino doubleβ ⁻ decay. It is still a difficult task to extract the parameters of the neutrinoless doubleβ ⁻ decay since the half-life expression contains products of the parameters 〈m _ν 〉 〈η〉 and 〈λ〉. Presented by M. Aunola at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

The neutrino mass matrix and (selected) variants of <Emphasis Type="Italic">A</Emphasis><Subscript>4</Subscript>

Recent neutrino oscillation experiments have measured leptonic mixing angles with considerable precision. Many theoretical attempts to understand the peculiar mixing structure, observed in these measurements, are based on non-Abelian flavour symmetries. This talk concentrates exclusively on models based on the non-Abelian symmetry A ₄. A ₄ is particularly well suited to describe three family mixing, and allows to explain the near tri-bimaximal mixing observed. Special emphasis is put here on the discussion of the neutrinoless double beta decay observable 〈:m _ν 〉. Different models based on A ₄ with very similar predictions for neutrino angles can yield vastly different expectations for 〈m _ν 〉. Neutrinoless double beta decay can thus serve, in principle, as a discriminator between different neutrino mass models.