κ-generalized statistics in personal income distribution

Starting from the generalized exponential function , with exp ₀(x)=exp (x), proposed in reference [G. Kaniadakis, Physica A 296, 405 (2001)], the survival function P_>(x)=exp _κ(-βx^α), where x∈R⁺, α,β>0, and , is considered in order to analyze the data on personal income distribution for Germany, Italy, and the United Kingdom. The above defined distribution is a continuous one-parameter deformation of the stretched exponential function P_> ⁰(x)=exp (-βx^α) to which reduces as κ approaches zero behaving in very different way in the x→0 and x→∞ regions. Its bulk is very close to the stretched exponential one, whereas its tail decays following the power-law P_>(x)∼(2βκ)^-1/κx^-α/κ. This makes the κ-generalized function particularly suitable to describe simultaneously the income distribution among both the richest part and the vast majority of the population, generally fitting different curves. An excellent agreement is found between our theoretical model and the observational data on personal income over their entire range.     

Analysis of Ωb? (bss) and Ωc0 (css) with QCD sum rules

We calculate the masses and the pole residues of the heavy baryons Ω _c ⁰(css) and Ω _b ⁻(bss) with the QCD sum rules. The numerical values  GeV (or  GeV) and  GeV (or  GeV) are in good agreement with the experimental data.     

Amplitude-squared squeezing in superposed coherent states

We study amplitude-squared squeezing of the Hermitian operator Z_θ=Z₁ cosθ+Z₂ sin θ, in the most general superposition state , of two coherent states and . Here operators Z_1,2 are defined by , a is annihilation operator, θ is angle, and complex numbers C_1,2 , α, β are arbitrary and only restriction on these is the normalization condition of the state . We define the condition for a state to be amplitude-squared squeezed for the operator Z_θ if squeezing parameter , where N=a⁺a and . We find maximum amplitude-squared squeezing of Z_θ in the superposed coherent state with minimum value 0.3268 of the parameter S for an infinite combinations with α- β= 2.16 exp [±i(π/4) + iθ/2], and with arbitrary values of (α+β) and θ. For this minimum value of squeezing parameter S, the expectation value of photon number can vary from the minimum value 1.0481 to infinity. Variations of the parameter S with different variables at maximum amplitude-squared squeezing are also discussed.     

NLO contributions to <Emphasis Type="Italic">B</Emphasis>→<Emphasis Type="Italic">KK</Emphasis><Superscript>*</Superscript> decays in the pQCD approach

We calculate the important next-to-leading-order (NLO) contributions to the B→KK ^* decays from the vertex corrections, the quark loops, and the magnetic penguins in the perturbative QCD (pQCD) factorization approach. The pQCD predictions for the CP-averaged branching ratios are , , and Br(B ⁰→K ⁺ K ^*−+K ⁻ K ^*+)≈1.3×10⁻⁷, which agree well with both the experimental upper limits and the predictions based on the QCD factorization approach. Furthermore, the CP violating asymmetries of the considered decay modes are also evaluated. The NLO pQCD predictions for and decays are and .     

Separated cross-sections in \pi^{0}_{} electroproduction at threshold at Q2 = 0.05GeV2/c2

The differential cross-sections σ₀ = σ_T + εσ_L , σ_LT , and σ_TT of electroproduction from the proton were measured from threshold up to an additional center-of-mass energy of 40MeV, at a value of the photon four-momentum transfer of Q ² = 0.05 GeV²/c² and a center-of-mass angle of θ = 90^° . By an additional out-of-plane measurement with polarized electrons σ_LT' was determined. This showed for the first time the presence of an imaginary part of the s -wave above the threshold, which is usually interpreted as a unitary cusp. The predictions of the Heavy Baryon Chiral Perturbation Theory (HBChPT) are in disagreement with these data. On the other hand, the data are somewhat better predicted by the MAID phenomenological model and are in good agreement with the dynamical model DMT.     

Lifetime vibrational interference during the NO 1s-1π* resonant excitation studied by the NO+(A 1Π → X 1Σ+) fluorescence

Dispersed fluorescence from fragments formed after the de-excitation of the 1s^-1π^* resonances of N^*O and NO^* has been measured in the spectral range of 118–142 nm. This range is dominated by lines of atomic nitrogen and oxygen fragments and by the bands in the NO⁺ ion which result from the participator Auger decay of the 1s^-1π^* resonances. Ab-initio calculations of the transition probabilities between vibrational levels during the reaction NO N^*O ⇒ NO were used to explain the observed intensity dependence for the fluorescence bands on the exciting-photon energy across the resonances and on both v^′ and v^′′ vibrational quantum numbers. The multiplet structure of the 1s^-1π^* resonance and lifetime vibrational interference explain the observed exciting-photon energy dependence of the fluorescence intensity. A strong spin-orbit coupling between singlet and triplet states of NO⁺ is proposed to reduce additional cascade population of the state via radiative transitions from the and states and to explain remaining differences between measured and calculated integral fluorescence intensities.     

Two-step laser excitation of the highly excited even-parity states of atomic mercury

We report term energies and quantum defects of highly excited even-parity states of mercury in the 83 876–84 140 cm^-1 energy range, employing a two-step laser excitation scheme via the S₀↦6s6p³P₁ inter-combination transition. Two dye lasers, pumped by a common Nd:YAG laser, were frequency doubled by BBO crystals and used to record the spectra in conjunction with a thermionic diode ion detector. Our new observations include the much extended D₂ (22 ≤n ≤52) series and a few members of the S₁ (24 ≤n ≤30) Rydberg series. Members of the D₂ Rydberg series with such a high n value are reported for the first time. The relative intensities of the D₂ and S₁ transitions (m = 4, 5 and 6) of group II-B elements excited from the P₁ inter-combination states are also discussed.     

Soft end-point and mass corrections to the η′g*g* vertex function

Power-suppressed corrections arising from end-point integration regions to the space-like vertex function of the massive η^′-meson virtual gluon transition are computed. Calculations are performed within the standard hard-scattering approach (HSA) and the running coupling method supplemented by the infrared renormalon calculus. Contributions to the vertex function from the quark and gluon contents of the η^′-meson are taken into account and the Borel resummed expressions for (Q²,ω,η), as well as for (Q²,ω=±1,η) and (Q²,ω=0,η) are obtained. It is demonstrated that the power-suppressed corrections ∼(Λ²/Q²)ⁿ, in the explored range of the total gluon virtuality 1≤Q²≤25 GeV², considerably enhance the vertex function relative to the results found in the framework of the standard HSA with a fixed coupling. Modifications generated by the η^′-meson mass effects are discussed. PACS 12.38.Bx; 14.40.Aq; 11.10.Hi     

Semiclassical analysis of edge state energies in the integer quantum Hall effect

Analysis of edge-state energies in the integer quantum Hall effect is carried out within the semiclassical approximation. When the system is wide so that each edge can be considered separately, this problem is equivalent to that of a one dimensional harmonic oscillator centered at x = x_c and an infinite wall at x = 0, and appears in numerous physical contexts. The eigenvalues E_n(x_c) for a given quantum number n are solutions of the equation S(E,x_c)=π[n+ γ(E,x_c)] where S is the WKB action and 0 < γ < 1 encodes all the information on the connection procedure at the turning points. A careful implication of the WKB connection formulae results in an excellent approximation to the exact energy eigenvalues. The dependence of γ[E_n(x_c),x_c] ≡γ_n(x_c) on x_c is analyzed between its two extreme values as x_c ↦-∞ far inside the sample and as x_c ↦∞ far outside the sample. The edge-state energiesE_n(x_c) obey an almost exact scaling law of the form and the scaling function f(y) is explicitly elucidated.     

Beam-helicity asymmetry in photon and pion electroproduction in the Δ(1232)-resonance region at Q2 = 0.35(GeV/c)2

The beam-helicity asymmetry has been measured simultaneously for the reactions p→epγ and p→epπ ⁰ in the Δ(1232)-resonance region at Q ² = 0.35(GeV/c)². The experiment was performed at MAMI with a longitudinally polarized beam and an out-of-plane detection of the proton. The results are compared with calculations based on dispersion relations for virtual Compton scattering and with the MAID model for pion electroproduction. There is an overall good agreement between experiment and theoretical calculations. The remaining discrepancies may be ascribed to an imperfect parametrization of some γ ^(*) N→πN multipoles, mainly contributing to the non-resonant background. The beam-helicity asymmetry in both channels (γ and π ⁰) shows a good sensitivity to these multipoles and should allow future improvement in their parametrization.     

On the fluctuations of the force exerted by a lipid nanotubule

After deriving the projected stress tensor in cylindrical geometry for a fluid membrane described by the Helfrich Hamiltonian, we calculate the average force f exerted by a thermally fluctuating nanotubule of radius R , and its standard deviation f . We obtain f and f in terms of the internal membrane tension , the bending rigidity , the temperature k _B T and a molecular cutoff . We find for f a shift ∼ 1/ with respect to the mean field behavior ∼ . We obtain ( f )² ∼ R ln(R/b) where b is a molecular length, f being typically small compared to f . Taking into account the difference between the internal tension and the actual mechanical tension applied to the membrane from which the tubule is drawn, we discuss the amplitude of the fluctuation-induced corrections to the average force. Our results, obtained in the harmonic approximation, hold for tubules with aspect ratio not larger than 200 , of radius significantly smaller than 100nm, that are connected to a large membrane reservoir, e.g., a giant vesicle.     

Determination of the gluon polarization at RHIC and COMPASS

The most recent determinations of the gluon polarization in the nucleon, , obtained at RHIC and COMPASS experiments, are reviewed. The former accesses the gluon polarization mainly through the production of neutral pions (PHENIX) or jets (STAR) in polarized proton collisions. The latter uses the photon-gluon fusion in polarized lepton-nucleon scattering, tagged either by open charm or high-p_T hadrons production. All the results are in good agreement, and favour values of ΔG roughly between 0 and 0.5 at a few (GeV/c)² , thus in contradiction with what could be derived from the Ellis-Jaffe sum rule and the axial anomaly. Much stronger constraints will be obtained in a near future by both programs, helping us to clarify the role of gluons in the nucleon spin.     

Odd autoionizing 2p<Subscript>1/2</Subscript><Superscript>5</Superscript>n(s<Superscript>′</Superscript>/d<Superscript>′</Superscript>) resonances of Ne excited from the 2p<Superscript>5</Superscript>3p[K]<Subscript>J</Subscript> states

Absolute photoionization cross sections for Ne atoms in the excited levels (Paschen notation ) were calculated at near threshold energies within the configuration interaction Pauli-Fock approach including core polarization. The computed spectra and the lineshape parameters of the odd parity 2p_1/2 ⁵ns^′/d^′ autoionizing resonances are found to be in good agreement with high resolution laser spectroscopic results. Guided by the theoretical results, improved analyses of the measured spectra by superimposed Fano-type profiles were achieved. Theoretical predictions are presented for resonances which have not yet been studied experimentally. In addition, we report the absolute partial photoionization cross sections for the ²P_3/2 and ²P_1/2 channel at photoelectron energies up to 7 eV. Except for the highest lying 2p₁(¹S₀) level, these cross sections monotonically decrease with energy (as reported earlier in single-electron calculations for the Ne(2p⁵3p) configuration) with branching ratios which essentially reflect the core composition of the 2p_x levels. For the 2p₁ level the resonance structure and the partial cross sections are strongly influenced by a Cooper-Seaton minimum in the d_3/2 ^′ channel,located just above the ²P_1/2 ionization limit.     

The photoresponse of <Superscript>45</Superscript>Sc up to 7 MeV

High-resolution photon scattering experiments have been performed on the nucleus ⁴⁵Sc at the Darmstadt superconducting electron accelerator S-DALINAC using bremsstrahlung beams with end point energies of 5.0 and 7.0MeV. Energies, absolute cross-sections and decay widths of 50 states, most of them previously unknown, have been determined. The results are compared to (γ, ) experiments on the neighbouring closed proton shell isotope ⁴⁴Ca .     

Combinatorial entropies and statistics

We examine the combinatorial or probabilistic definition (“Boltzmann’s principle”) of the entropy or cross-entropy function H ∝ or D ∝ - , where is the statistical weight and the probability of a given realization of a system. Extremisation of H or D, subject to any constraints, thus selects the “most probable” (MaxProb) realization. If the system is multinomial, D converges asymptotically (for number of entities N ↦∞) to the Kullback-Leibler cross-entropy D_KL; for equiprobable categories in a system, H converges to the Shannon entropy H_Sh. However, in many cases or is not multinomial and/or does not satisfy an asymptotic limit. Such systems cannot meaningfully be analysed with D_KL or H_Sh, but can be analysed directly by MaxProb. This study reviews several examples, including (a) non-asymptotic systems; (b) systems with indistinguishable entities (quantum statistics); (c) systems with indistinguishable categories; (d) systems represented by urn models, such as “neither independent nor identically distributed” (ninid) sampling; and (e) systems representable in graphical form, such as decision trees and networks. Boltzmann’s combinatorial definition of entropy is shown to be of greater importance for “probabilistic inference” than the axiomatic definition used in information theory.     

Thermal neutron capture cross-section of <Superscript>76</Superscript>Ge

The thermal neutron capture cross-sections of the ⁷⁶Ge(n,)⁷⁷Ge and the ⁷⁶Ge(n,)^77m Ge reactions have been measured by activating targets of isotopically enriched GeO₂ through cold neutrons. The -decay spectra after the -decay of ⁷⁷Ge and ^77m Ge were measured with HPGe detectors. From these spectra the cross-sections for the ⁷⁶Ge(n,) reactions were derived relative to the cross-section of ¹⁹⁷Au using the absolute emission probabilities of the observed -ray energies. The methods used in this work result in smaller systematic uncertainties than those obtained in previous experiments.     

Measurement of the LT-asymmetry in πelectroproduction at the energy of the Δ(1232)-resonance

The reaction p(e, e'p)π⁰ has been studied at Q² = 0.2 (GeV/c)² in the region of W = 1232MeV. From measurements left and right of , cross-section asymmetries ρ_LT have been obtained in forward kinematics ρ_LT( = 20^°) = (- 11.68±2.36_stat±2.36_sys) and backward kinematics ρ_LT( = 160^°) = (12.18±0.27_stat±0.82_sys) π⁰. Multipole ratios {S₁₊ ^* M₁₊}/| M₁₊|² and {S₀₊ ^* M₁₊}/| M₁₊|² were determined in the framework of the MAID2003 model. The results are in agreement with older data. The unusally strong negative {S₀₊ ^* M₁₊}/| M₁₊|² required to bring also the result of Kalleicher et al. in accordance with the rest of the data is almost excluded.     

Variable-range hopping in 2D quasi-1D electronic systems

A semi-phenomenological theory of variable-range hopping (VRH) is developed for two-dimensional (2D) quasi-one-dimensional (quasi-1D) systems such as arrays of quantum wires in the Wigner crystal regime. The theory follows the phenomenology of Efros, Mott and Shklovskii allied with microscopic arguments. We first derive the Coulomb gap in the single-particle density of states, g(ε), where ε is the energy of the charge excitation. We then derive the main exponential dependence of the electron conductivity in the linear (L), i.e. σ(T) ∼exp [-(T_L/T)^γL], and current in the non-linear (NL), i.e. , response regimes ( is the applied electric field). Due to the strong anisotropy of the system and its peculiar dielectric properties we show that unusual, with respect to known results, Coulomb gaps open followed by unusual VRH laws, i.e. with respect to the disorder-dependence of T_L and and the values of γ_L and γ_NL.     

Transition energies of atomic lawrencium

Transition energies of the superheavy element lawrencium, including the ionization potential, excitation energies and electron affinities, are calculated by the intermediate Hamiltonian coupled cluster method. A large basis set (37s31p26d21f16g11h6i) is used, as well as an extensive P space (6s5p4d2f1g). The outer 43 electrons are correlated. Accuracy is monitored by applying the same approach to lutetium, the lighter homologue of Lr, and comparing with experimentally known energies. QED corrections are included. The main goal is to predict excitation energies, in anticipation of planned spectroscopy of Lr. The ground state of Lr is , unlike the of Lu. Predicted Lr excitations with large transition moments in the prime range for the planned experiment, 20 000–30 000 cm^-1, are 7p→8s at 20 100 cm^-1 and 7p→7d at 28 100 cm^-1. The average absolute error of 20 excitation energies of Lu is 423 cm ^-1, and the error limits for Lr are put at 700 cm^-1. The two electron affinities measured recently for Lu are reproduced within 55 cm^-1, and a third bound state of Lu^- is predicted.