Dynamical connections between quark fragmentation functions

Assuming that the quark kicked by a virtual photon emits pions one by one, integral equations connecting the fragmentation functions D_u^π+ (z) and D_u^π? (z) are obtained. It is shown that they have a plateau the height of which can be determined from the multiplicity difference N_p^π+ (z) ? N_p^π? (z). Comparison with experiment is made.     

Classical stability of direct products of spheres in gravitational systems

Classical stability of Einstein spaces S^d₁ ×?×S^d_n(d_j ? 2) against all fluctuations is investigated in euclidean gravity with a cosmological constant. It is shown that S^d is classically stable, while S^d₁ ×?× S^d_n(n ? 2) is classically unstable. As a generalization of this analysis it is proved that a compact Einstein space B₁ ×?× B_n(n ? 2) which is a direct product of each Einstein space is classically unstable. Non-Einstein spaces M² × S⁴ (M² × S² × S²) are also considered in six- dimensional Einstein-Maxwell theory and are shown to be classically stable (unstable).     

Selective laser spectroscopy of Mn4+-Mn4+ pair centers in SrTiO3 crystal

Zero-phonon lines of a pair center of Mn⁴⁺ ions are observed in the luminescence and luminescence-excitation spectra of SrTiO₃:Mn crystal. Based on the experimental data, the energy-level structure of the ground state ∣⁴ A _2g ,⁴ A _2g 〉 and excited state ∣⁴ A _2g ,² E _g 〉 of the Mn⁴⁺-Mn⁴⁺ pair center is constructed. It is shown that the exchange interaction in the ground state of the Mn⁴⁺-Mn⁴⁺ pair is antiferromagnetic. Energies of the levels are calculated assuming that the pair is formed by Mn⁴⁺ ions occupying neighboring octahedral positions of Ti⁴⁺ ions along the [110] axis. Experimental values of the exchange integral in the ground state ∣⁴ A _2g ,⁴ A _2g 〉 and energies of spin multiplets in the excited state ∣⁴ A _2g ,² E _g 〉 agree well with calculation of the exchange interaction carried out within the framework of the channel model with the parameters J _ξη = 32 cm^4-1 and J _ζζ = ?45.5 cm^4-1. Experimental data and calculations unambiguously demonstrate that zero-phonon lines in the luminescence and luminescence-excitation spectra have magnetic-dipole nature.     

Influences of La3+ substitution on the structure and magnetic properties of M-type strontium ferrites

M-type strontium ferrites with substitution of Sr²⁺ by rare-earth La³⁺, according to the formula Sr_1−xLa_xFe₁₂O₁₉, are prepared by the ceramic process. Influences of the substituted amount of La³⁺ on structure and magnetic properties of Sr_1−xLa_xFe₁₂O₁₉ compounds have systematically been investigated by XRD, VSM and Mössbauer spectrum. When the substituted amount x is below 0.30, X-ray diffraction shows that the samples are single M-type hexagonal ferrites. It is found that the suitable amount of La³⁺ substitution may remarkably increase saturation magnetization σ_s and intrinsic coercivity H_cJ. With the La³⁺ addition for the same sintering temperature, σ_s and H_cJ increase at first, then decrease gradually. However, the substituted amount x at the maximum value of H_cJ is bigger than that of σ_s. Mössbauer spectroscopy of ⁵⁷Fe in Sr_1−xLa_xFe₁₂O₁₉ has shown that the substitution of Sr²⁺ by La³⁺ is associated with a valence change of Fe³⁺ to Fe²⁺ at 2a or 4f₂ site. The magnetic properties are reflected in the Mössbauer spectra which indicate that the magnetic hyperfine field (H_hf) is detected with the highest value at x=0.20. The different exchange paths between the iron sublattices are discussed according to the increased hyperfine fields of the 12k- and 2b-site. The Curie temperature of Sr_1−xLa_xFe₁₂O₁₉ decreases linearly with increasing La³⁺ substitution.     

The near-ultraviolet spectrum of diacetylene trapped in solid argon at 9 K

The absorption spectra of normal and deuterated diacetylene trapped in solid argon at 9 K were investigated in the near-ultraviolet region between 2000 and 3000 Å. The vibrational structure observed at low temperature for the band system at 2448 Å, which was previously reported by Haink and Jungen in the gas phase, and identified as a ¹Δ_u ← X¹Σ_g⁺ transition, was analyzed. A comparison between the spectra for C₄H₂ and C₄D₂ suggests some revisions in the upper-state vibrational assignments. The possibility that the upper state assumes a C_2htrans configuration of ¹A_u symmetry is examined. The matrix spectra also appear to indicate that the absorption spectrum observed at 2576 Å in the gas phase and which has been assigned to a ¹Σ_u^? ← X¹Σ_g⁺ transition may not originate in the ground state of C₄H₂.     

Isotropic and anisotropic exchange interactions in the Orbitally degenerate excited (4 A 2×2 T 2) state of a Cr3+ ion pair possessing D 3h symmetry

Experimentally observed optical absorption spectra of isolated pairs of chromium ions in Cs₃Cr₂Br₉ corresponding to transitions of pairs from the ground (⁴ A ₂ײ A ₂) state to a singly excited (⁴ A ₂ײ T ₂) state are theoretically interpreted. It is shown that the position of the exchange multiplets in the excited (⁴ A ₂ײ T ₂) state is determined mainly by the resonance exchange interactions removing the degeneracy with respect to the exchange by an excitation within the pair. It is established that the observed fine structure of the pair in the (⁴ A ₂ײ T ₂) state is due to a superposition of the contributions from the one-and two-center spin-orbit interaction and resonance antisymmetric exchange.     

The missing mass squared dependence of the average charged particle multiplicity in the reaction K+p → KoX++ from 5–16 GeV/c

The average charged particle multiplicity, 〈n_ch(M_X²)〉, in the reaction K⁺p→K^oX⁺⁺ is studied as a function of the mass squared, M_X², of the recoil system X and also as a function of the K^o transverse momentum, p_T, at incident momenta of 5.0, 8.2 and 16.0 GeV/c. The complete data samples yield distributions which are not independent of c.m. energy squared, s, They exhibit a linear dependence on log (M_X²_X/M_o²)[M_o²=1 GeV²] with a change in slope occurring for M_X²≈s/2, and do not agree with the corresponding distributions of 〈n_ch〉 as a function of s for K⁺ p inelastic scattering. Sub-samples of the data for which K^o production via beam fragmentation, central production and target fragmentation are expected to be the dominant mechanisms show that, within error, the distribution of 〈n_ch(M_X²)〉 versus M_X² is independent of incident momentum for each sub-sample separately. In particular in the beam fragmentation region the 〈n_ch(M_X²)〉 versus M_X² distribution agrees rather well with that of 〈n_ch〉 versus s for inelastic K⁺p interactions. The latter result agrees with recent results on the reactions pp → pX and π^?p → pX in the NAL energy range. Evidence is presented for the presence of different production mechanisms in these separate regions.     

High-resolution photofragment spectroscopy of the O2+b4Σg− (v′ = 3, 4, 5) ← a4Πu (v′ = 3, 4, 5) First Negative system using coaxial dye-laser and velocity-tuned ion beams

A new photofragment spectrometer employing coaxial tunable single-mode laser and velocity-tuned fast-ion beams has been used to measure transition energies in the O₂⁺b⁴Σ_g^? ← a⁴Π_u First Negative system to an accuracy and precision that are an order of magnitude better than was previously possible in Doppler-limited emission spectroscopy. The technique consists of velocity-tuning a beam of metastable O₂⁺a⁴Π_u ions such that a set of First Negative rotational transitions can be sequentially brought into resonance with the laser wavelength. The subsequent absorption transitions promote the ions to predissociating levels of the b⁴Σ_g^? state and observation of the O⁺ photofragments is the signal that denotes that each absorption transition has occurred. Repetition of the velocity tuning at different dye-laser frequencies provides a scan of the First Negative spectrum for predissociating upper-state vibrational levels, which are inaccessible to emission spectroscopy. The O⁺ photofragment ions have a kinetic energy that depends on the height of the predissociating rotational level above the separatedatom limit. The present apparatus incorporates a photofragment energy analyzer that can often be used to separately record the wavenumbers of transitions to different upper-state rotational levels, but whose wavenumbers could not otherwise be resolved. A set of 359 wavenumbers involving the (4,4), (4,5), (5,5), and (3,3) bands were recorded with an estimated accuracy of ±0.0032 cm^?1 and a precision of 0.0028 cm^?1, the latter being estimated precisely with a statistical technique. These data were fitted to ⁴Σ and ⁴Π Hamiltonians used in recent studies of the First Negative emission spectrum to determine molecular constants for the v′ = 4, 5 and v″ = 4, 5 levels. The former represent an extension of the b⁴Σ_g^? state to new levels and the latter represent substantial improvements over the constants that were available from previous moderate-resolution emission studies. These photofragment molecular constants were merged with those from the previous emission studies to yield a new consistent set of molecular constants and Dunham coefficients for the O₂⁺b⁴Σ_g^? and a⁴Π_u states. In the fit to the photofragment bands, it was found that the Hamiltonians, which were sufficient for the emission data, are inadequate to describe these states within the precision of the present measurements.     

Magnetic anisotropy and saturation of LaFe12O19 and some related compounds

The saturation magnetization σ_s and uniaxial anisotropy constants K₁ and K₂ are measured on a polycrystalline, crystal-oriented sample of LaFe₁₂O₁₉ contaminated with known amounts of Fe₃O₄ and LaFeO₃. K₁ and K₂ increase strongly with decreasing temperature and the value of K₁ = (19–24) × 10⁵ erg/g at T = 0 shows that the substance is considerably more anisotropic than BaFe₁₂O₁₉ (K₁ ? 8·5 × 10⁵ erg/g) at low temperatures. The σ_s-T curve is more convex than that of BaFe₁₂O₁₉, so that σ_s is 11 per cent higher at room temperature but lower at T = 0. The value σ_s(T = 0) = 96·2 G cm³/g (19·2 μ_B/molecule) and the anisotropic behaviour are attributed to the presence of 1 Fe²⁺/molecule occupying the octahedral 2a sites in the magnetoplumbite lattice and having a uniaxial anisotropy of 10–15 cm^?1/ion.From measurements on polycrystalline, crystal-oriented samples of BaFe_10·8Fe²⁺_0·6Ti⁴⁺_0·6O₁₉ and BaFe_10·5Fe²⁺_1·0Sb⁵⁺_0·5O₁₉ it was found that, in comparison with LaFe₁₁Fe²⁺O₁₉, σ_s (T = 0) is smaller and K₁ is much smaller and much less temperature-dependent. The difference in anisotropic behaviour is attributed to a different distribution of the Fe²⁺ ions among the lattice sites due to the effective positive charge of the Ti⁴⁺ and Sb⁵⁺ ions.     

Comparative study of the semiempirical three-parameter potential energy functions for diatomic molecules

A comparative study is made of four three-parameter semiempirical potential energy functions for 32 electronic states of diatomic molecules and their ions:n ₂:X¹gS _g ⁺ ,B ³π_g,A ³ gS_u,C ³ _u,B′ ³ gS_u.a ¹ π_g, a′gS _u ^? ,Ω ¹δ_u N ₂ ⁺ :X ² gS _g ^gS +A ² π,C ² gS _u ⁺ ,B ² gS _u ⁺ CO:X¹gS⁺,a ³ π, a′³ gS_u,e ³ gS^?,d ³gD₁,A ¹π CO⁺:X²gS⁺,A ² π,B ²gS⁺ O₂:X³gS _g ^? ,B ³ gS_u,c ¹ gS _u ^? ,b ¹gS _g ^s ,a ¹ δ_g,c ³ δ_u O ₂ ⁺ :X ²π_g,A ² π_g, a¹ π_g,b ⁴ gS _g ^? A program for numerically integrating the radial Schrödinger equation by the Cooley method is worked out. Certain additional units are introduced to conserve computer time. The resulting vibrational levels are compared with the experimental levels for all the electronic states studied. It is concluded on the basis of this analysis that it is not possible to describe equally well all the electronic states of various molecules on the basis of any single three-parameter potential function. A method for choosing a potential function for describing some particular electronic state of a diatomic molecule is proposed.     

Analysis of transverse momentum distributions forpp interactions at 360 GeV/c in the framework of a quark-diquark fragmentation model

Using a quark-diquark fragmentation model, in which either the Field-Feynman or the Lund model is coupled with a quark-diquark distribution function, we study transverse momentum distributions,p _T, for the inclusive reactionspp→hadron +anything at 360 GeV/c. We find that a primordial mean transverse momentum 〈k _T〉?0.4 GeV/c can well reproduce thep _T ² distributions of charged hadrons, π⁰,K _s ⁰ , Λ⁰,K ^* and Σ^* and the Feynmanx?p _T correlations. We confirm that a diquark in a proton plays an important rôle in reproducing thex?p _T correlation of Λ⁰.     

Observation of the c3Πu-X1Σg+ intersystem transition in the absorption spectrum of P2

The observation of the c³Π_u-X¹Σ_g⁺ intersystem transition of P₂ is reported. The 6-0 band of the system was identified on high resolution absorption plates teken on the NRC 10-m vacuum spectrograph at Ottawa. A rotational analysis of the band is given together with that of the adjacent 5-0 band of the C¹Σ_u⁺-X¹Σ_g⁺ system, the upper level of which is involved in a mutual perturbation with the c³Π_u, v = 6 level. The interaction parameters for the perturbation are derived. It is proposed that the appearance of the 6-0 band of the c³Π_u-X¹Σ_g⁺ transition is due to intensity borrowing from the strong, allowed C¹Σ_u⁺-X¹Σ_g⁺ system. Accurate values for the energies of the c³Π_u, b³Π_g, and a³Σ_u⁺ states relative to the ground state are given. The analysis of two other bands, 2-0 and 7-0, of the C¹Σ_u⁺-X¹Σ_g⁺ system whose upper levels likewise interact strongly with the c³Π_u state are also given.     

Isospin and density waves in asymmetric nuclear matter

The excitation of small density oscillations (zero sound) and isospin oscillations (isospin sound) in cold asymmetric nuclear matter (in the ground state ?⁰_n> ?⁰_p, ?⁰ = ?⁰_n+?⁰_p = 0.17 nucleons/fm³) is investigated within the framework of the Landau theory of normal Fermi liquids. There is only one undamped mode of excitation, which consists predominantly of isospin oscillations, with some admixture of density oscillations. The phase velocity of this undamped wave depends very weakly on the neutron excess and is close to that of a pure isospin wave (isospin sound) in symmetric nuclear matter of the same density. At the neutron excess corresponding to that existing in heavy nuclei the amplitude of the density oscillations constitutes about 30 % of the amplitude of the neutron excess density oscillations. Calculation with a suitably parametrized charge dependent quasiparticle interaction in asymmetric nuclear matter shows that for (?⁰_n??⁰_p)/?⁰ > 0.63 both zero sound and isospin sound are strongly damped.     

A XPS study of Fe1-χCuχCr2S4

The X-ray photoelectron spectroscopy is applied for a chalcogen chromite system Fe_{1 ? x}Cu_xCr₂S₄ to obtain microscopic information about valence states of the constituting atoms. The features of the Cu 2p spectra show that copper is always in a monovalent state in this system. This supports a model Fe³⁺_{1 ? x}Cu¹⁺_xCr³⁺₂S^1-_{2x ? 1}S^2-_{5 ? 2x} for a compositional range 0.5 < x < 1.     

Mössbauer study of new vanadate glass with large charge-discharge capacity

Charge-discharge capacity and cyclicity of lithium ion battery (LIB) was evaluated in which 15Li₂O·10Fe₂O₃·xSnO₂·5P₂O₅·(70–x)V₂O₅ glass (x?=?0 and 20 in mol%, abbreviated as xLFSPV) was used as a cathode. A local structure of xLFSPV glass before and after charging was investigated by ⁵⁷Fe- and ¹¹⁹Sn-Mössbauer spectroscopies. ⁵⁷Fe-Mössbauer spectrum of xLFSPV glass with ‘x’ of 20 was composed of a doublet with isomer shift (δ) of 0.35_±0.02 mm s^???1 and quadrupole splitting (Δ) of 0.88_±0.03 mm s^???1 due to distorted Fe^IIIO₄ tetrahedra. ¹¹⁹Sn-Mössbauer spectrum of this glass consisted of a doublet with δ of 0.08_±0.01 and Δ of 0.52_±0.01 mms^???1 due to distorted Sn^VIO₆ octahedra. After discharging the battery from 4.5 to 1.0 V, larger δ of 0.40_±0.03 mm s^???1 and Δ of 0.94_±0.04 mm s^???1 were obtained, indicating that both iconicity of Fe-O bonds and local distortion of Fe^IIIO₄ tetrahedra were increased. On the contrary, identical δ of 0.09_±0.01 mm s^???1 and Δ of 0.50_±0.01 mm s^???1 were observed in the ¹¹⁹Sn-Mössbauer spectrum of 20LFSPV glass after the discharge, indicating that chemical environment of Sn^IVO₆ octahedra was not affected after the discharge. Charge-discharge curve of LIB containing 20LFSPV glass as a cathode active material recorded under the current density of 8.3 mA g^???1 (0.011 mA cm^???2) between 1.0 and 4.5 V showed a large initial charge capacity of 431.1 mAh g^???1 and discharge capacity of 382.3 mAh g^???1, respectively. These results indicate that 20LFSPV glass could be a new cathode active material for LIB.     

Anisotropy of hexagonal ferrites with M,W and Y structures containing Fe3+ and Fe2+ as magnetic ions

The ferrimagnetic saturation moment and hexagonal anisotropy constant K₁ have been measured at 4K on a Zn₂Y single crystal and on polycrystalline BaFe²⁺₂W and SrFe²⁺₂W samples. The moment of Fe₂W is in agreement with a collinear spin coupling and with the known site occupation for the Fe²⁺ ions. The moment of Zn₂Y is 9% lower than the value for a collinear configuration.The uniaxial anisotropy of Fe²⁺ in hexagonal ferrites is discussed and compared with that of Co²⁺. No noticeable Fe²⁺ anisotropy is found in Fe₂W in contrast to LaM = LaFe²⁺Fe³⁺₁₁O₁₉, in which the Fe²⁺ anisotropy is strong. The difference is attributed to the symmetry difference of the sites occupied by the Fe²⁺ ions in both compounds. The current theory does not satisfactorily explain the anisotropy and quadrupole splitting of Fe²⁺ in LaM. From this it is concluded that admixing of ⁵E states and (or) the influence of a dynamical Jahn-Teller effect cannot be neglected.The dipole-dipole anisotropy is computed for the M, W and Y structure and some deviation from the literature data is found. Using these results, a mean anisotropy of 1.3 to 2.3 cm^?1 per Fe³⁺ ion is found for the three structures.     

4 T 2→4 A 2 transition in the luminescence spectra of Mn4+ ion in gadolinium gallium garnet at intense laser pumping

The Mn^{4+ 4} T ₂→⁴ A ₂ transition was observed in the luminescence spectrum of Gd₃Ga₅O₁₂:Mn⁴⁺ at intense laser pumping. It is shown that the ⁴ T ₂ → ⁴ A 2 transition becomes more intense than ² E→⁴ A ₂ because of an increase in the role of induced transitions with increasing pump power. This process is most efficient in the region of strongest overlap between the ² E→⁴ A ₂ and ⁴ T ₂→⁴ A ₂ bands, where it leads to strengthening of the zero-phonon line of the latter at 694 nm. It is assumed that GGG:Mn⁴⁺ can be used as an active material in tunable lasers.     

Observation of the 5pΠu Rydberg state of Li2

Some weak, collisionally induced transitions in ⁷Li₂ have been recorded by Fourier transform spectrometry in the near infrared, following excitation of the 5d¹Π_g state by optical-optical double resonance. They have been assigned as transitions to the 1 ¹Δ_g state from levels v=0 and 1 of a new ungerade Rydberg state, 5p¹Π_u. Quantum defect considerations indicate that the principal quantum number for this new state is 5, and that the assignment to 5p is compatible with a Rydberg series of which the lowest members would be the B¹Π_u and C¹Π_u states.     

Theory of nonstoichiometric ordering of Pb-containing relaxors with perovskite structure

Conditions that are imposed on the interatomic interaction and under which a certain ordered state of AB _x ^′ B _1?x ^″ perovskites arises are determined with allowance for effectively pairwise interactions and the configuration entropy of interchanges of B′ and B″ ions. It is shown that, for the interaction potential u(R) = u ₀/R ⁶, the highest temperature of ordering of the 1: 2 type (T _ord (1: 2)) corresponds to a structure observed at A ≡ Ba. The highest temperature of ordering of the 1: 1 type (T _ord (1: 1)) corresponds to a structure that typically occurs in the case of A ≡ Pb. Within the approximation used, it is found that T _ord (1: 1) > T _ord (1: 2) for all compositions and that the 1: 1-ordered phase is most stable. For models with u(R) = u ₀/R ⁿ (n = 1–6) including the interaction in the first m coordination shells (m = 3, 6, 8, 11), it is shown that the ground state of AB _x ^′ B _1?x ^″ O₃ corresponds either to a decomposed solid solution or to an ordered state similar to that observed in PbMg_1/3Nb_2/5O₃.