Super <Emphasis Type="Italic">D</Emphasis>-Differentiation for <Emphasis Type="Italic">R</Emphasis><Superscript> ∞ </Superscript>-Supermanifolds

The concept of ‘D-Differentiation’, which, in the context of smooth manifolds, generalises Lie and covariant differentiation, is extended to R ^∞-supermanifolds under the name of ‘Super D-Differentiation’. This is done by defining new (non-linear) mappings, called ‘μ-mappings’ and by relating their non-linearity to the Leibniz rule that a derivation must satisfy when it acts on a tensor product. The resulting axiomatics, which is basis-independent and coordinate-free, is then expressed in a general basis (not necessarily holonomic). Super Lie and Super covariant differentiation are, amongst others, special cases of Super D-Differentiation. In particular, the transformation rules for the connection coefficients and the commutation coefficients of non-holonomic bases are obtained. These special cases are found to be in agreement with the DeWitt Super covariant and Super Lie derivatives.      

δ/γ transformation in non-equilibrium solidified peritectic Fe-Ni alloy

Through phase transformation kinetic analysis and experimental observation, the δ/γ transformation occurring in the non-equilibrium peritectic Fe-4.33at.%Ni alloys was systematically investigated. According to JMA solid-state transformation kinetic theory, the Time-Temperature-Transformation (TTT) curves of the δ/γ transformation in peritectic Fe-Ni alloy were calculated. On this basis, the physical correlation between the δ/γ transformation and the initial undercooling of melt (△T) was elucidated. The results indicate that the change of △T can alter not only the overall δ/γ transformation pathways but also the transformation fraction with respect to each transformation mechanism.     

<Emphasis Type="Italic">In situ</Emphasis> study of the <Superscript>41</Superscript>Ar plume released from the Ignalina NPP

The ⁴¹Ar gamma ray radiation was registered using the in situ method in the vicinity of the Ignalina nuclear power plant (NPP). The sum of gamma rays, that are reaching the HPGe detector, situated along the wind direction, from a number of plume segments and which are registered in the energy range of about 1.29 MeV, is calculated. An independent technological regime of the operating reactor method of the determination of the ⁴¹Ar emission rate from NPP stack is introduced.      

Magnetic and transport properties of monocrystalline<Emphasis Type="Italic">Fe</Emphasis><Subscript>3</Subscript><Emphasis Type="Italic">O</Emphasis><Subscript>4</Subscript>

A monocrystal ofFe ₃ O ₄ is characterized by resistance, magnetoresistance and magnetic measurements in a temperature range from 4.2 K to 350 K and magnetic field-cycling from −9 T to 9 T. The resistance measurements revealed a metal-insulator Verwey transition (VT) atT _v =123.76 K with activation energy E=92.5 meV at T >T _v and temperature-substitute for the activation energy below the VT,T ₀=E/k _B ≈3800 K within 70 K–110K. The magnetotransport results independently verified the VT at 123.70 K, with discontinuous change in the magnetic moment ΔM≈0.21 ΔM≈0.21μ _B and resistance hysteresis, dependent on the magnetic field in a narrow temperature range of 0.4° around theT _v . The magnetic characterization established self consistentlyT _v as ≈123.67 K, the jump in the magnetization at the VT≈0.25μ _B and confirmed, that the magnetocrystalline anisotropy is the main microscopic mechanism responsible for the magnetization of the monocrystal (88%) with additional natural and imposed defects contributing as 12%.     

Coplanar (<Emphasis Type="Italic">e</Emphasis>, 3<Emphasis Type="Italic">e</Emphasis>) differential cross-section of He atom

We present in this paper the results of our calculation of five-fold differential cross-section (FDCS) for (e,3e) process on He atom in low momentum transfer and high electron impact energy in shake-off mechanism. The formalism has been developed in Born approximation using plane waves, Byron and Joachain as well as Le Sech and correlated BBK-type wave functions respectively for incident and scattered, bound and ejected electrons. The angular distribution of FDCS of our calculation is presented in various modes of coplanar geometry and comparison is made with the available experimental data. We observe that the present calculation is able to reproduce the trend of the experimental data. However, it differs in magnitude from the experiment. The present theory does not predict four-peak structure insummed mutual angle mode for lower excess ejected electron energies. We also discuss the importance of momentum transfer, post-collision interaction (PCI) and ion participation in the (e,3e) process in constant θ₁₂ mode     

The pp→K<Superscript>+</Superscript><Emphasis Type="Italic">Σ</Emphasis><Superscript>+</Superscript>n cross-section from missing-mass spectra

We utilize existing inclusive data on K⁺-meson momentum spectra of the reaction pp→K ⁺ X at T _p = 2.3-2.85GeV to deduce total cross-sections for pp→K ⁺ Σ ⁺ n. The method used to extract those cross-sections is explained and discussed in detail. Our result for T _p = 2.85GeV is consistent with the data point from a direct measurement at the same beam energy. The cross-section obtained for T _p = 2.3GeV is with 13.7±2.3μb considerably smaller than the value found in a recent experiment by the COSY-11 Collaboration at a somewhat lower beam energy, indicating that the pp→K ⁺ Σ ⁺ n reaction cross-section could exhibit a rather unusual energy dependence.     

<Emphasis Type="Italic">Q</Emphasis> kink of the nonlinear <Emphasis Type="Italic">O</Emphasis>(3) <Emphasis Type="Italic">σ</Emphasis> model involving an explicitly broken symmetry

The (1 + 1)-dimensional nonlinear O(3) σ model involving an explicitly broken symmetry is considered. Sphalerons are known to exist in this model. These sphalerons are of a topological origin and are embedded kinks of the sine-Gordon model. In the case of a compact spatial manifold S ¹, sine-Gordon multikinks exist in the model. It is shown that the model admits a nonstatic generalization of the sine-Gordon kink/multikink, Q kink/multikink. Explicit expressions are obtained for the dependence of the Q kink energy and charge on the phase frequency of rotation. The Q kink is studied for stability, and expressions are obtained for the eigenfunctions and eigenfrequencies of the operator of quadratic fluctuations. It is shown that the Q kink is unstable over the entire admissible frequency range ω ∈ [−1, 1]. The one-loop quantum correction to the static-kink mass is calculated, and the Q-kink zero mode is quantized. It is shown that, in a general static case, the field equations of the model are integrable in quadratures.     

Density functional study of structural and electronic properties of Al<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>P (2 ≤ <Emphasis Type="Italic">n</Emphasis> ≤ 12) clusters

Low-lying equilibrium geometric structures of Phosphorus-doped aluminum cluster Al _n P (n = 2–12) clusters obtained by an all-electron linear combination of atomic orbital approach, within spin-polarized density functional theory, are reported. The binding energy, dissociation energy, and stability of these clusters are studied within the local spin density approximation (LSDA) and the three-parameter hybrid generalized gradient approximation (GGA) due to Becke-Lee-Yang-Parr (B3LYP). Ionization potentials, electron affinities, hardness, and static polarizabilities are calculated for the ground-state structures within the GGA. It is observed that symmetric structures with the P atom occupying a peripheral position are lowest-energy geometries of Al _n P (n = 2, 4–11), while the P impurities of Al₃P and Al₁₂P prefer to occupy internal sites in the aluminum clusters. Generalized gradient approximation extends bond lengths as compared to the LSDA lengths. The odd-even oscillations in the dissociation energy, the second differences in energy, the HOMO–LUMO gaps, the ionization potential, the electron affinity, and the hardness are more pronounced within both GGA and LSDA. The stability analysis based on the energies clearly shows the clusters with an even number of valence electrons are more stable than clusters with odd number of valence electrons.     

2<Emphasis Type="Italic">µ</Emphasis>m Laser based on an electro-optical <Emphasis Type="Italic">Q</Emphasis>-switched intracavity KTP optical parametric oscillator

An 2 μm pulse laser based on an intracavity optical parameter oscillator (OPO) pumped by an electrooptical Q-switched 1.064 μm laser is realized. A type-II phase-matched (θ = 51.5° and φ = 0) KTP crystal and a limiting diaphragm with a diameter of 4 mm were used. The parameters of the KTP-OPO tuning curves as a function of the phase matching angles were analyzed for the case of 1.064 μm laser pumping. Experiments based on single and double KTPs for walk-off compensation were performed. An output energy of 26 mJ in the 2 μm wavelength region was obtained with a pump-to-signal conversion efficiency of 26%. The center wavelengths of the signal and idle lights were 2165.4 and 2088.6 nm with a FWHM of 3.8 and 4 nm, respectively.     

Wavelength and oscillator strength of dipole transition 1s<Superscript>2</Superscript>2p—1s<Superscript>2</Superscript><Emphasis Type="Italic">n</Emphasis>d for Mn<Superscript>22+</Superscript> ion

The transition energies, wavelengths and dipole oscillator strengths of 1s²2p—1s² nd (3⩽n⩽9) for Mn²²⁺ ion are calculated. The fine structure splittings of 1s² nd (n</9) states for this ion are also evaluated. In calculating energy, the higher-order relativistic contribution is estimated under a hydrogenic approximation. The quantum defect of Rydberg series 1s² nd is determined according to the quantum defect theory. The results obtained in this paper excellently agree with the experimental data available in literatures. Supported by the National Natural Science Foundation of China (Grant No. 10774063)     

Mixed symmetry states and isospin excitation in <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis> nucleus <Superscript>52</Superscript>Fe

The interacting boson model with isospin (IBM-3) was applied to study the band structure and electromagnetic transition properties of the low-lying states in the even-even N = Z nucleus ⁵²Fe. The isospin excitation states with T = 0, 1 and 2 were identified, and compared with the available data. The study shows that the 2₃⁺ state is the lowest mixed symmetry state in ⁵²Fe. The excitation energy of the second 0₂⁺ state with T = 0 in nucleus ⁵²Fe was identified. The model calculations with the data show a reasonably good agreement. Supported by the National Natural Science Foundation of China (Grant Nos. 10765001 and 10547003), the Natural Science Foundation of Inner Mongolian Autonomous Region of China (Grant No. 200607010111), and the Scientific Research Fund of Inner Mongolian Education Bureau (Grant Nos. NJZY07155 and NJZY07153)     

The exclusive reaction of pion quasi-elastic knockout from nucleon <Emphasis Type="Italic">p(e,e′ π)B</Emphasis> to various states of the final baryon-spectator <Emphasis Type="Italic">B</Emphasis> and the quark models for the pion cloud of nucleon

The pion momentum distributions (MDs) in four channels of virtual decay p→B+π, B = N, Δ, N _1/2-(1535), N _1/2+(1440) are calculated in two models, the microscopic model of ³ P ₀ scalar q−q fluctuation with the pion as a composite q−q-system and the chiral semi-microscopic model of πq interaction with the pion as a structureless Goldstone boson. The results of the above models are similar for the baryon states B = N, Δ, N _1/2-(1535) but are rather different for the Roper resonance N _1/2+(1440) which corresponds to excitation of two oscillator quanta in the nucleon. The experimental investigation of pion MDs by means of the reaction of quasi-elastic knockout of pion by an electron of a few GeV energy p(e, e′ π)B may be very suitable for Jefferson Laboratory, Virginia (JLab).     

1/<Emphasis Type="Italic">N</Emphasis><Superscript>2</Superscript> Correction to Free Energy in Hermitian Two-Matrix Model

Using the loop equations we find an explicit expression for genus 1 correction in hermitian two-matrix model in terms of holomorphic objects associated to spectral curve arising in large N limit. Our result generalises known expression for F¹ in hermitian one-matrix model. We discuss the relationship between F¹, Bergman tau-function on Hurwitz spaces, G-function of Frobenius manifolds and determinant of Laplacian over spectral curve.Mathematics Subject Classifications. 15A52, 34M55.     

<Emphasis Type="Italic">Λ</Emphasis>N scattering length from the reaction <Emphasis Type="Italic">γ</Emphasis>d→K<Superscript>+</Superscript><Emphasis Type="Italic">Λ</Emphasis>n

The prospects of utilizing the strangeness production reaction γd→K ⁺ Λn for the determination of the Λn low-energy scattering parameters are investigated. The spin observables that need to be measured in order to isolate the Λn singlet (¹ S ₀) and triplet (³ S ₁) states are identified. Possible kinematical regions where the extraction of the Λn scattering lengths might be feasible are discussed.     

Fusion Rules for the Vertex Operator Algebras <Emphasis Type="Italic">M</Emphasis>(1)<Superscript>+</Superscript> and <Emphasis Type="Italic">V</Emphasis><Superscript>+</Superscript><Subscript><Emphasis Type="Italic">L</Emphasis></Subscript>

The fusion rules for the vertex operator algebras M(1)⁺ (of any rank) and V⁺_L (for any positive definite even lattice L) are determined completely.Supported by JSPS Research Fellowships for Young ScientistsPartially supported by NSF grants and a research grant from the Committee on Research, UC Santa CruzPartially supported by a NSA grant and a grant from Rutgers University Research Council     

Dual properties of orthogonal polynomials of discrete variables associated with the quantum algebra <Emphasis Type="Italic">U</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>(<Emphasis Type="Italic">su</Emphasis>(2))

We show that for every set of discrete polynomials y _n (x(s)) on the lattice x(s), defined on a finite interval (a, b), it is possible to construct two sets of dual polynomials z _k (ξ(t)) of degrees k = s-a and k = b-s-1. Here we do this for the classical and alternative Hahn and Racah polynomials as well as for their q-analogs. Also we establish the connection between classical and alternative families. This allows us to obtain new expressions for the Clerbsch-Gordan and Racah coefficients of the quantum algebra U _q (su(2)) in terms of various Hahn and Racah q-polynomials. Dedicated to the memory of our teacher and friend Arnold F. Nikiforov (18.11.1930–27.12.2005).     

Leptonic constant of the pseudoscalar <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> meson

We calculate the leptonic constant for the pseudoscalar ground state of the B _c meson in the framework of a QCD-motivated potential model taking into account the two-loop anomalous dimension for the heavy quark current in nonrelativistic QCD as matched with full QCD.     

Enhancement of the defect field of one-dimensional photonic crystals containing <Emphasis Type="Italic">ε</Emphasis>-and <Emphasis Type="Italic">μ</Emphasis>-negative layers

Employing the transfer matrix method, we study the electromagnetic field of one-dimensional photonic crystals with a defect inserted by pairs of μ-negative (MNG) and ε-negative (ENG) material layers. The fields within the pairs of layers and the matrix defect are independent of each other, and the whole field is their superposition. The whole defect field can be significantly enhanced by pairs of ε-negative and μ-negative layers. In contrast to the conventional defect modes, the intensity and volume of the defect field with pairs of ε-negative and μ-negative layers can be precisely adjusted.     

Once more about gauge invariance in <Emphasis Type="Italic">ϕ</Emphasis> → <Emphasis Type="Italic">γπ</Emphasis><Superscript>0</Superscript><Emphasis Type="Italic">π</Emphasis><Superscript>0</Superscript>

It is argued that the realization of gauge invariance condition as a consequent of cancellation between the ϕ → γf ₀ → γπ ⁰ π ⁰ resonance contribution and the ϕ → γπ ⁰ π ⁰ background one, suggested by A.V. Anisovich et al., Yad. Fiz. 68, 1614 (2005), is misleading. The text was submitted by the author in English.     

The <Emphasis Type="Italic">Φ</Emphasis>→K<Superscript>0</Superscript>¯<Emphasis Type="Italic">γ</Emphasis> decay

The scalar contributions to the radiative decay φ→K ⁰ˉ⁰ γ are studied within the framework of the Linear Sigma Model (LσM). Theoretical predictions for the associated subprocesses φ→f ₀ γ and φ→a ₀ γ as well as the ratio φ→f ₀ γ/a ₀ γ are also given.