n-shell Thomas-Fermi model: Coulomb atom

A simple expression for the electron density of then-shell of the Coulomb atom with the nuclear charge Zρ _n(r)=Z ³ π ^?2 n ^?3(2Z ^?1 r ^?1?n ^?2)^1/2 is found in the semi-classical approximation. It is used for the asymptotic estimation of averages 〈r ^a 〉 (?2<a<∞). An explicit dependence of the leading oscillatory contribution to 〈r ^a 〉 due to angular moments on the electron number is also obtained.     

Charge transfer and rapidity gap analysis inp(π+)n interactions at 195GeV/c

We present charge transfer probabilities between CM hemispheres inpn and π⁺ n interactions at 195 GeV/c. The relative probabilities for charge exchanges |ΔQ|>1 as a function of rapidity gap length,r, are given. Both results are compared with those of π^? p interactions at 200GeV/c. The average ofr, viz. <r>, is given as a function of the gap number and of ΔQ for various multiplicities, and the reduced average gap lengths <r>/y _max forpn interactions are compared with data at a lower energy.     

Anisotropy profiles of optical fibers and preforms

An experimental method to measure the optical anisotropy profiles of optical fibers and preforms is presented. The local values of n_z?n_r and n_z?n_?, (r,?,z) being a cylindrical coordinate system associated with the fiber or preform, are obtained.     

Long-range potentials and the electromagnetic polarizabilities

The long-range spin and velocity independent forces of electromagnetic origin which act between any two systems are studied for those cases in which no forces of this type exist to order e². It is shown that they are uniquely determined by the charge, magnetic moment, and polarizabilities of both systems, not only to the dominant order r^?n, but also to the next one r^?(n+1). These potentials provide the link between Compton scattering polarizabilities (response to real photons) and classically defined polarizabilities (response to static electromagnetic field). The two definitions are shown to be equivalent for neutral spinless systems; the problems arising for a neutral particle with magnetic moment are studied in detail. The r^?(n+1) terms have no classical counterpart, since they are due to the relativistic quantum propagation of the system which carries charge or magnetic moment. The results are of general validity with analyticity, crossing, unitarity, and gauge invariance as only inputs. The most general conclusion is that the polarizabilities represent electromagnetic properties of a system at order e², as the charge and magnetic moment do at order e. Thus they give the strength of the response to electric and magnetic fields, independently of the specific characteristics of the electromagnetic agent.     

Tilt of primordial gravitational wave spectrum in a universe with sterile neutrinos

In this work,we constrain the spectral index ntof the primordial gravitational wave power spectrum in a universe with sterile neutrinos by using the Planck temperature data,the WMAP 9-year polarization data,the baryon acoustic oscillation data,and the BICEP2 data.We call this model theΛCDM+r+νs+ntmodel.The additional massive sterile neutrino species can significantly relieve the tension between the Planck and BICEP2 data,and thus can reduce the possible effects of this tension on the fit results of nt.To constrain the parameters of sterile neutrino,we also utilize the Hubble constant direct measurement data,the Planck Sunyaev-Zeldovich cluster counts data,the Planck CMB lensing data,and the cosmic shear data.We find that due to the fact that the BICEP2 data are most sensitive to the multipole～150 corresponding to k～0.01 Mpc-1,there exists a strong anticorrelation between ntand r0.002in the BICEP2 data,and this further results in a strongly blue-tilt spectrum.However,a slightly red-tilt tensor power spectrum is also allowed by the BICEP2 data in the region with larger value of r0.002.By using the full data sets,we obtain meffν,sterile=0.48+0.11-0.13eV,Neff=3.73+0.34-0.37,and nt=0.96+0.48-0.63for theΛCDM+r+νs+ntmodel.     

Intermediate asymptotic expressions for high-order spin correlation functions in a two-dimensional classical ferromagnet

Different-point spin correlation functions are calculated for a two-dimensional classical ferromagnet in a pacerturbative range of distances r: a<r?m ^?1, where a is the lattice parameter and m ^?1 is the correlation length. The expressions for the four-and higher-order correlation functions are presented.     

Indirect interaction of Mössbauer nuclei

An expression is deduced for the operator of the indirect interaction of nuclei via the electromagnetic field. The properties of Mössbauer nuclei are described within the pseudospin formalism, which is usually used in the theory of optical two-level systems. The indirect interaction of pseudospins is derived by a method adopted from the theory of superconductivity. It is found that the potentials of this interaction involve terms decreasing as r ^?3, r ^?2, and r ^?1. The estimates demonstrate that the two-particle interaction can contribute significantly to the width of the resonance line, for example, in crystals whose cells contain thulium nuclei.     

An alternative solution of diatomic molecules

The spectrum of r ^?1 and r ^?2 type potentials of diatomic molecules in radial Schrödinger equation are calculated by using the formalism of asymptotic iteration method. The alternative method is used to solve eigenvalues and eigenfunctions of Mie potential, Kratzer-Fues potential, Coulomb potential, and Pseudoharmonic potential by determining the α, β, γ and σ parameters.     

Correlation inequality in Heisenberg ferromagnet

In a four-spin Heisenberg ferromagnetic system, it is found computationally that Griffiths' second inequality, ?〈σ_r·σ_s〉/?J_mn?0, m, n, r, s distinct, is violated, and conditions are obtained under which it holds.     

Spin-wave resonance in [Co x Ni1 − x ]N and [Co x P1 − x ]N gradient films

Gradient films of ferromagnetic 3d metals with prescribed magnetic potential profile along the film thickness are obtained. It is found that the spin-wave resonance spectrum in these films is characterized by anomalous dependences of resonance fields of spin-wave modes H _r on the mode number: H _r(n) ～ n, H _r(n) ～ n ^2/3.     

A family of angle-moments proportional to r-n,n = 1,2,…, in free space

The moments M_n(r) ≡ 1/2 ∝^2π₀ dθ sinⁿ θ I(r,θ) of the intensity I(r, θ) in free space surrounding a spherical object emitting radiation with an arbitrary directional dependence are shown to be exactly proportional to r^-(n+1), n = 0, 1,….     

On the ground state energy of a two-dimensional electron fluid

A new theory of the ground state energy of a two-dimensional electron fluid is presented. It is shown that the ring diagram contribution changes its analytical behavior atr _s =2^1/2, wherer _s is the usual density parameter defined by r_S = 1/a ₀(π n)^1/2,a ₀ being the Bohr radius andn is the electron density. For smallr _s , a high density series is obtained in agreement with the previous calculation. For larger _s , a hitherto unknown low density series is obtained. In the low density region, the first order exchange energy is completely cancelled out by a term from the ring contribution so that the ground state energy decreases in proportion tor _s ^?2/3 , followed byr _s ^/?4/3 and higher order terms. The energy is found to be minimum atr _s=1.4757, the minimum value being ?0.481915 Rydbergs.     

Effect of Composition on Chain Dimensions of Styrene-Methylmethacrylate Random Copolymers under Theta Condition

Rotational-isomeric-state (RIS)-Metropolis Monte Carlo simulations are performed on poly(styrene-ran-methylmethacrylate) random copolymers to study the intrinsic unperturbed (θ-condition) dimensions. Mean-squared end-to-end distance (?r²?_o ), mean-squared radius of gyration (?s²?_o ), and characteristic ratio (C_n) have been calculated for these copolymers constituted by different overall chemical compositions (styrene fractions 0.29, 0.56, and 0.70). Calculations were carried out with chains of 500 repeating units. With an increase in the styrene content there is an increase in ?r ²? _o, `, and C_n, in agreement with experimental observations. An increase in the fraction of trans conformational states in the backbone torsion angles is found to be responsible for the exhibited chain expansion behavior. The dimensions calculated by the Monte Carlo simulations agree well with experimental values reported in the literature.     

Minimal Lagrangian isotropic immersions in indefinite complex space forms

Let Mⁿ be an n-dimensional (n≥3) minimal Lagrangian isotropic submanifold in an indefinite complex space form. We show that the dimension of Mⁿ satisfies n=3r+2 with r, a positive integer. When n<14, we give a classification of such submanifolds.     

Decay Mechanism of 290,292114* Superheavy Nuclei Formed in 48Ca-Induced Reactions

We calculate the neutron-evaporation residue cross sections σ _3n , σ _4n , and σ _5n in the hot-fusion reactions ⁴⁸Ca+^242,244Pu →^290,292114 ^? over a wide range of compound-nucleus excitation energies ( $E_{\text{CN}}^{*}$ = 34–53 MeV). We work with the dynamical cluster-decay model (DCM), with a single parameter, the neck-length parameter ΔR. To calculate neutron-evaporation cross sections, we choose the superheavy proton magic Z = 126 and neutron magic N = 184. Among the 3n, 4n, and 5n production cross sections for ^{290, 292}114^?, only the 3n decay cross sections of ²⁹²114^? correspond to spherical fragmentation. The 4n and 5n cross sections of ²⁹²114^? and 3n, 4n, and 5n cross sections of ²⁹⁰114^? could only be fitted after the inclusion of quadrupole deformations β _2i within the optimum orientation approach. Changes in the angular momentum and N/Z ratio do not significantly influence the fragmentation paths of ^{290, 292}114^? superheavy nuclei. Larger barrier modification is required for the lower angular momentum states and lighter neutron clusters. The contribution of the fusion–fission component is also computed for the compound nucleus ²⁹²114^? in the energy range $E_{\text{CN}}^{*}$ = 27–47 MeV.     

Franck-Condon factors and R-centroids for the A1∑+-X1∑+ and B3Π(0+)−X1∑+ band system of 63Cu1H and 63Cu2H

The recently reported new RKR potential energy curves for the X¹∑⁺, A¹∑⁺, and B³Π(0⁺) electronic states of ⁶³Cu¹H and ⁶³Cu²H are used to calculate Franck-Condon factors and r-centroids for the A?X and B?X band systems for 0≤v″≤20, 0≤v′≤10 and J = 0, 30, 40. The r-centroid approximation is verified and a physical interpretation of the r-centroid is discussed.     

Negative ion effects in CO2 convection laser discharges

Negative ions are computed to be formed on a time scale and in quantities such that they may be a cause of plasma instability observed in low pressure electrical discharge convection CO₂ lasers. In a typical CO₂?N₂?He?H₂O laser mixture the principal ions are CO ₃ ^? , CO ₄ ^? and H^? with the total negative ion densityn _? given by 0.1n _e <n _?<n _e , wheren _e is the electron density: but if the gases are re-cycled or if there is an air leak NO ₂ ^? and NO ₃ ^? are formed in significant amounts andn _? can become greater thann _e in a time considerably less than the gas dwell time in the electrical excitation discharge. CO is effective in reducingn _? in a system without re-cycling, but is ineffective in a re-cycled system with the oxides of nitrogen present.     

Mössbauer study of the hyperfine and magnetic properties of organo-di-iron electron reservoirs containing a polyaromatic bridging ligand

Organo di-iron electron reservoirs Fe(CP^*)₂(Ar) ⁿ⁺ withn=2, 1, 0, where Cp^* is C₅(CH₃)₅ and where Ar are the following bridges: biphenyl, dihydrophenanthrene, triphenylene, have been studied by Mössbauer spectroscopy in the solid state. Complexes withn=2, with 36e^? in the coordination spheres of the metals, exhibit the usual diamagnetic behaviour of 18e^?, Fe^II mono-iron systems. Complexes withn=1, 37e^?, are delocalized mixed valence (Fe^IIFe^I) with a spin 1/2; the magnetic hyperfine interaction, measured under an external field, shows equal delocalization of the 37^th e^? on the two iron centers and the two bridging carbon atoms of the biphenylene. Complexes withn=0, formally with 38e^?, have a practically temperature-independent quadrupole splitting, and isomer shift values which constrast with the expected behaviour of independent Fe^I, 19e^? centers. This indicates that the 37^th and 38^th electrons are mostly located on the polyaromatic bridge. Spectra obtained in an external field show a negligible magnetic hyperfine interaction and support this conclusion. In the case of biphenyl and dihydrophenanthrene bridges, this electron localization can be related to a strong intramolecular chemical coupling, evidenced by other spectroscopic and X-ray data [1].     

The formation of the superheavy hydrogen isotope <Superscript>6</Superscript>H in the absorption of stopped π<Superscript>−</Superscript>-mesons by nuclei

An experimental search for the superheavy hydrogen isotope ⁶H was conducted through studying the absorption of stopped π^?-mesons by ⁹Be and ¹¹B nuclei. A structure in the missing mass spectrum caused by the resonance states of ⁶H was observed in three reaction channels, namely, ⁹Be(π^?, pd)X, ¹¹B(π^?, d³He)X, and ¹¹B(π^?, p⁴He)X. The parameters of the lowest state E_r=6.6±0.7 MeV and Γ=5.5±2.0 MeV (E_r is the resonance energy with respect to the disintegration into the triton and three neutrons) are evidence that ⁶H is a more weakly bound system than ⁴H and ⁵H. Three excited states of ⁶H were observed. Their resonance levels (E_1r=10.7±0.7 MeV, Γ_1r=4±2 MeV, E_2r=15.3±0.7 MeV, Γ _2r=3±2 MeV, and E_3r=21.3±0.4 MeV, Γ_3r=3.5±1.0 MeV) are energetically capable of disintegrating into six free nucleons.