The effect of Cu substitution on the A1g mode of La0.7Sr0.3MnO3 manganites

We report on the first Raman data of Cu substituted La_1−ySr_yMn_1−xCu_xO₃ (0≤x≤0.10 and 0.17≤y≤0.3, accordingly in order to have the same Mn⁴⁺/[Mn⁴⁺+Mn³⁺] ratio), collected in the frequency range 100-900 cm⁻¹ and at room temperature, with parallel (e_i∥e_s) and crossed (e_i⊥e_s) polarizations of the incident (e_i) and scattered (e_s) light. Spectra were fitted with a Drude-Lorentz model, and peaks at 190-220 and 430 cm⁻¹, together with two broad structures centered at near 500 and 670 cm⁻¹, have been found. We also have observed that the A_1g mode is substantially shifted with increasing Cu substitution. The A_1g phonon shift is a linear function of the tolerance factor t and the rhombohedral angle α_r, thus following the structural changes of the MnO₆ octahedra in the system.     

Optical-Optical Double Resonance Spectroscopy of the 1g(P1)-AΠ (1u)-XΣg Transition of I2

Optical-optical double resonance spectroscopy was used to study the 1_g(³P₁) ion-pair state of I₂ correlating to I⁻(¹S)+I⁺³P₁) at the dissociation limit. We gained access to the 1_g(³P₁) state though the A³Π (1_u) state in the (1+1) photon-excitation scheme. The pump laser excited the A³Π (1_u)-X¹Σ_g⁺ transition at a fixed frequency for state selection. The probe laser was scanned to detect the 1_g(³P₁)-A³Π (1_u) resonance by monitoring the ultraviolet emission from the 1_g(³P₁) state at 278 nm. The 1_g(³P₁) state was observed in a vibrational progression consisting of P and R doublets. An energy level analysis was carried out for the 1_g(³P₁) state in the 0≤ v ≤ 14 and 12≤J≤135 range, which led to a set of molecular parameters including the Ω-doubling constant. The Ω-doubling of the 1_g(³P₁) state was discussed by the pure precession model and interpreted to occur through the heterogeneous coupling with the 0_g⁻(³P₁) state correlating to the same ionic asymptote.     

Calculation of Coefficients of Fractional Parentage for Large-Basis Harmonic-Oscillator Shell Model

A new procedure for large-scale calculations of the coefficients of fractional parentage (CFPs) for a single j-orbit with isospin is presented. The approach is based on a simple enumeration scheme for antisymmetric A-particle states and an efficient method for constructing the eigenvectors of an idempotent matrix. We investigate the characteristics of the introduced CFP basis and the application of this procedure to the ab initio harmonic-oscillator shell-model approach. The results of CFP calculations for the j=1/2,…,41/2 orbits are presented (the full sets of one-particle and two-particle CFPs up to the j=9/2 orbit are obtained). The new computer code for calculation of the CFPs proves to be very quick, efficient, and numerically stable and produces results possessing only small numerical uncertainties.     

Determination of theg j -factor in the72 P 3/2-state of133Cs by optical double resonance in a strong magnetic field

The hfs in the 7² P _3/2-state of¹³³Cs has been investigated by optical double resonance in a strong magnetic field. From the positions of the magnetic dipole transitions Δm _j =± 1, Δm _i =0 the magnetic hfs coupling con slanta (7² P _3/2)=16.591(25) MHz and theg _j -factorg _j (7² P _3/2)=1.33410(15) could be derived. Contrarily to recent measurements,g _j agrees well with the value calculated from the Lande formula.     

Level-crossing-Untersuchung der Hyperfeinstruktur des angeregten 32 P 3/2- und 42 P 3/2-Zustands von Na23

The hyperfine structure of the excited 3² P _3/2- and 4² P _3/2-state of Na²³ has been investigated in a level-crossing-experiment by means of a detailed analysis of the dependence of the scattered resonance light as a function of the magnetic field. From the experimental curves the following results for the hyperfine structure constantsA andB and for the lifetimesΤ were deduced 3² P _3/2-state: 4² P _3/2-state:A=18.65(10)Mc/sA=6.006(30)g _j/1.334Mc/sB=2.82(30)Mc/sB=0.86 (9)g _j/1.334Mc/sΤ=1.60 (3) · 10^?8sΤ=6.56 (25)1.334/g_j·10^?8 s. The nuclear electric quadrupolemoment of Na²³ derived from these values isQ=0,097 · 10^?24 cm², where the Sternheimer-correction has been applied.     

Effect of quadrupole and octopole vibrations of206Pb on the 1j 15/2 neutron particle state of207Pb

The quadrupole as well as the octopole vibrational states of²⁰⁶Pb are coupled to the 2g _9/2, 1i _11/2 and 1j _15/2 neutron states to explain the fragmentation of 1j _15/2 state in²⁰⁷Pb as observed in the²⁰⁶Pb(d,p) reaction. The structures of weak fragmented 1j _15/2 states are deduced through the particle-core coupling scheme.     

g J -Faktoren der tiefsten3 P 1-Zustände von Strontium und Barium

Theg _J -values of the lowest³ P ₁-states of Sr and Ba have been determined with optical double resonance. The measurement has been carried out by observation of radiofrequency transitionsΔm _j =± 1 between Zeeman levels of the even isotopes. Calibration of the magnetic field has been done by optical pumping of the 3²S_1/2 ground state of the sodium atom. The results are:g _j ^exp (5s 5p ³ P ₁, Sr)=1.50065(4)g _j ^exp (6s 6p ³ P ₁, Ba)=1.49651(7).     

Non-spherical magnetic moment in MnAlGe

The magnetic structure factors of MnAlGe (space groupP4/nmm) measured with polarised neutrons have been expressed in terms of the magnetic moment of the Mn atom (site symmetry tetrahedral with tetragonal distortion), the Bessel transforms 〈j _n〉 of the Mn radial functions and the fractional occupancies of the moment density in the various crystal field orbitals. The measured structure factors were least-squares fitted with the theoretical expression involving 〈j _n〉 appropriate to the Mn⁰, Mn⁺ and Mn²⁺ atoms. The best fit was got using Mn⁰ transforms, yielding 1·45µ _B as the Mn magnetic moment. The fractional occupancies of the moment density in the crystal field orbitalsA _1g,B _1g E _g andB _2g were obtained. This analysis shows the magnetic moment to be highly non-spherical with a large fractional occupancy (38%) in theA _1g orbital directed along the tetragonal axis while the fractional occupancies ofB _1g andB _2g are found to be 31% and 30% respectively. The fractional occupancy of the moment in theE _g orbital directed towards the Ge and Al atoms is very low (1%). The spatially averaged moment density of Mn in MnAlGe is more diffuse than that of Mn I and Mn II in isostructural Mn₂Sb.     

Crystal field parameters for Yb ions at orthorhombic centers in garnets—Revisited

The major purpose of this paper is to clarify the deficiencies identified in the recent paper by Liu et al. (J. Lumin. 130 (2010) 103) as well as to reanalyze the available data and provide corrected results for the orthorhombic crystal field parameters (CFPs) for selected rare-earth ions in garnets. It appears that Liu et al., when utilizing the computer package for standardization of CFPs, have inadvertently confused the properties of CFPs expressed in the Wybourne notation with those in the extended Stevens operator notation. This confusion has led to misinterpretations concerning the orthorhombic standardization transformations and incorrect labeling of the CFP sets as supposedly ‘standardized’ for Yb³⁺, Pr³⁺, Nd³⁺, and Er³⁺ ions in various garnets. These deficiencies have prompted us to reconsider the CFP sets determined earlier by matching the experimental data, i.e. the orthorhombic spin Hamiltonian parameters (g factors, g_i, and hyperfine structure constants, A_i; i=x, y, z) and available optical spectral band positions, with the theoretical data calculated using the complete diagonalization method. To further verify the correctness of the present results the CFPs for orthorhombic Yb³⁺ centers in Yb₃Al₅O₁₂ and Yb₃Ga₅O₁₂ garnets are calculated using the superposition model (SPM), which requires adoption of a well-defined symmetry-adapted axis system (SAAS). Hence, the SPM calculations enable reanalysis of available CFP sets based on the correct standardization procedure and establishing the correspondence between the SAAS and the ‘nominal’ axis systems assigned to fitted CFP sets. Using the proper SAAS and general transformations of the axis systems, the relations between the calculated g_i and/or A_i values and the respective principal values determined by EPR experiments can be established. The consistent methodology utilized here may be helpful for proper reanalysis of spectroscopic data for rare-earth and transition-metal ions at orthorhombic symmetry sites in various crystals.     

The 250 nm absorption spectrum of benzene: Vibronic analysis

The supporting details for assignment of band maxima (see paper I) in the one-photon ${}^1\text{B}{}_{\mathrm{2u}}\text{←}{}^1\text{A}{}_{\mathrm{1g}}$ absorption spectra of benzene vapor are given. By the criteria of band separations and Franck-Condon intensities, maxima are first sorted into ν₁ progressions (Table II). The progressions are then assigned by systematic search for allowed first-, second-, and third-order Herzberg-Teller transitions as set forth in Table II of Paper II. Much attention is given to vibrational angular momentum as it affects band contours and component splittings. Over 90% of the intensity is assigned and a consistent pattern of Herzberg-Teller activity is found. Both the list of modes observed to be active in vibronically inducing the transition (ν₄, ν₅, ν₆, ν₇, ν₉, ν₁₀, ν₁₁, ν₁₆, ν₁₇) and the relative intensities of various types of transitions found in absorption match well that seen in SVL fluorescence. Third-order transitions are comparatively few in number, but are equivalent in intensity to many second-order transitions. Variation in the separation between progression members suggests that small (and unidentified) perturbations of upper state vibronic levels are ubiquitous. Revised or new values of nine fundamentals in the ¹B_2u state and two in the ¹A_1g state are given (Table IV). Some of the excited and ground state anharmonic constants x_i⁰, x_i,i⁰, x_i,j⁰, g_i,i, and g_i,j are deduced for ν₅, ν₆, ν₁₀, ν₁₁, ν₁₆, and ν₁₇ (Table V).     

Fragmentation of the high spin discrete neutron and proton states of209Pb and209Bi

The distribution of the discrete 1h _9/2, 2f _7/2, 1i _13/2 and 2f _5/2 proton states of²⁰⁹Bi and 2g _9/2, 1i _11/2, 1j _15/2 and 2g_7/2 neutron states of²⁰⁹Pb have been obtained within the particle-vibration coupling model calculation and compared with the experimental datas baising on the most recent high resolution stripping reaction on²⁰⁸Pb using 480 MeV¹²C projectile. The optimised shell model energies arising from the core-polarisation effect have profound influence for both the study of the structures of the high spin continuum shell model states of²⁰⁸Pb and stability of superheavy nuclei.     

Minimal number of operators for observability ofN-level quantum systems

This paper discusses the minimal numbern _min of operatorsA ₁,...,A _n , whose expectation values at some instants determine the statistical state of anN-level quantum system. We assume that the macroscopic information about the system in question is given by the mean values Tr[ρ(t _j )A _i ]=m _i (t _j ) ofn self-adjoint operatorsA ₁,...,A _n at some instantst ₁<t ₂t _s , wheres ²?1.     

Atomic beam magnetic resonance investigations in the 2p 2 3 P ground multiplet of the stable carbon isotopes12C and13C

The hyperfine structure seperations Δv andg _J -factors have been measured in the 2p ^{2 3} P states of¹³C(I=1/2) and¹²C(I=0), respectively, using the atomic beam magnetic resonance method. The results are Δv(³ P ₁,¹³C)=4.200 (25) MHz, Δv(³ P ₂,¹³C)=372.593 (25) MHz,g _J (³ P ₁,¹²C)=1.501052 (13), andg _J (³ P ₂,¹²C)=1.501039 (15). After applying corrections due to perturbations by neighbouring fine structure levels one deduces the constants of the magnetic dipole interactionA(³ P ₁,¹³C)=+2.838 (17) MHz, A(³ P ₂,¹³C)=+149.055 (10) MHz. No signs of theA-factors were determined by the experiment; they follow from the known positive sign of the nuclear magnetic moment μ _I of¹³C. CombiningA(³ P ₂,¹³C) with the results of other measurements on¹¹C, yields μ _I (¹¹C)=?0.964 (1) nm.     

Coordinate-dependent 3 + 1 formulation of the general relativity field equations

This paper presents a coordinate-dependent 3+ 1 decomposition of the general relativity field equations in terms of a scalar potentialc ²[(–g ₄₄)^1/2–1], a vector potentialA _icg _4i/(–g₄₄)^1/2, and the three-space metric _ijg _ij–g_4i g _4j/g ₄₄. The equations are exact and the form of the decomposed equations is valid in any coordinate system.     

Studies of local phase transition behavior for Co2+ in CsCaCl3 crystals from EPR data

In this paper, we establish the calculation formulas ofg factorsg _∥,g _⊥ and the hyperfine structure constantsA _∥,A _⊥ for 3d⁷ ions in tetragonal octahedral field from a cluster approach. In these formulas, besides the configuration interaction, the covalency effect due to the admixture between d electrons of 3d⁷ ion and the p electrons of ligands is considered. The parameters used in these formulas (except the core polarization constantsk in the calculation ofA _i) can be obtained from optical spectra of the studied crystal. From these formulas, the local release (or elongation) factork, which is introduced to characterize the release effect of impurity-ligand bond along C₄ axis at the cubic to tetragonal phase transition, is estimated for CsCaCl₃:Co²⁺ crystal by calculating the electronic paramagnetic resonance (EPR) parametersg _i andA _i . These EPR parameters are therefore explained reasonably and the results are discussed.     

Semiempirical study of perturbations of the Landé g factors of electronic-vibrational-rotational levels of hydrogen: II. i 3 g − and j 3Δ g − states of the H2, HD,and D2 molecules

The values of the Landé g factors of the i ³Π _g ⁻ , v, N and j ³Δ _g ⁻ , v, N states of the H₂, HD, and D₂ molecules have been found semiempirically for the following vibrational and rotational quantum numbers: v≤3; N≤7 for H₂; N≤5 for HD; and N≤11 for D₂. These values were obtained in terms of the nonadiabatic model, which takes into account the interaction between the 3dπ³Π_g and 3dδ³Δ_g states with the same values of v and N in the approximation of pure precession, with the use of semiempirical values of the expansion coefficients of the wave functions in the Born-Oppenheimer basis determined by us previously and the results of numerical calculation of the overlap integrals of the vibrational wave functions of these states. The results obtained for the H₂ molecule are in good agreement with the data in the literature. For the i ³Π _g ⁻ and j ³Δ _g ⁻ states of the HD and D₂ molecules, the g factors were found for the first time. This made it possible to study for the first time the role of the isotopic effect in the perturbation of the dependences of the g factors of rovibrational levels on v and N for the triplet electronic states of the hydrogen molecule. It was found that the interference effects of interaction between the 3dπ³Π_g and 3dδ³Δ_g states lead both to significant differences—up to 8, 6, and 11 times for H₂, HD, and D₂, respectively (the i ³Π _g ⁻ state), 20 times for H₂ and HD, and two orders of magnitude for D₂ (the j ³Δ _g ⁻ state)—between the nonadiabatic values of the g factors and the corresponding adiabatic values for some isotopomers of the hydrogen molecule and to significant differences—up to 9 and 1.5 times for the j ³Δ _g ⁻ and i ³Π _g ⁻ states, respectively—in the nonadiabatic values of the g factors of rovibrational levels of different isotopomers of the hydrogen molecule. __________ Translated from Optika i Spektroskopiya, Vol. 96, No. 1, 2004, pp. 42–54. Original Russian Text Copyright ? 2004 by Astashkevich.     

An inequality for Hilbert-Schmidt norm

For the absolute value |C|=(C*C)^1/2 and the Hilbert-Schmidt norm ∥C∥_HS=(trC*C)^1/2 of an operatorC, the following inequality is proved for any bounded linear operatorsA andB on a Hilbert space $$|| |A|---|B| ||_{HS} \leqq 2^{1/2} ||A - B||_{HS} $$ . The corresponding inequality for two normal state ? and ψ of a von Neumann algebraM is also proved in the following form: $$d(\varphi ,\psi ) \leqq ||\xi (\varphi ) - \xi (\psi )|| \leqq 2^{1/2} d(\varphi ,\psi )$$ . Here ξ(χ) denotes the unique vector representative of a state χ in a natural positive coneP ^? forM, andd(?, ψ) denotes the Bures distance defined as the infimum (which is also the minimum) of the distance of vector representatives of ? and ψ. In particular, $$||\xi (\varphi _1 ) - \xi (\varphi _2 )|| \leqq 2^{1/2} ||\xi _1 - \xi _2 ||$$ for any vector representatives ξ _j of ? _j ,j=1, 2.     

An analytic approach to the measurement of nestedness in bipartite networks

We present an index that measures the nestedness pattern of bipartite networks, a problem that arises in theoretical ecology. Our measure is derived using the sum of distances of the occupied elements in the incidence matrix of the network. This index quantifies directly the deviation of a given matrix from the nested pattern. In the simplest case the distance of the matrix element a_i,j is d_i,j=i+j, the Manhattan distance. A generic distance is obtained as d_i,j=(i^χ+j^χ)^1/χ. The nestedness index is defined by ν=1−τ, where τ is the “temperature” of the matrix. We construct the temperature index using two benchmarks: the distance of the complete nested matrix that corresponds to zero temperature and the distance of the average random matrix where the temperature is defined as one. We discuss an important feature of the problem: matrix occupancy ρ. We address this question using a metric index χ that adjusts for matrix occupancy.     

A phenomenological theory of possible sequences of ferrotoroidal phase transitions in boracites

A phenomenological theory of the sequence of two second-order phase transitions with close temperatures is considered; such transitions occur in the Ni-Br boracite. The thermodynamic potential is written as a function of polarization P _i, magnetization M _i, and toroidal moment T _i vectors and fields E _i and H _i; T _i is treated as an order parameter. It is assumed that only one coefficient of T _i ² passes through zero as T decreases. The possibility of a sequence of two proper ferrotoroidal phase transitions along the T ₁ and T ₂ components is demonstrated. Spontaneous T _i, P _i, and M _i vector values and equations for susceptibility tensors (dielectric χ _ij = dP _i/dE _j, magnetic k _ij = dM _i/dH _j, and magnetoelectric α_ij = dP _i/dH _j = dM _j/dE _i) were obtained for three phases. Some of these values have well-defined anomalies in the vicinity of transitions. All possible sequences of ferrotoroidal phase transitions in boracites are considered. Depending on two potential coefficient values, these sequences may consist of one, two, or three such transitions.