Stimulated Raman scattering in natural crystals of SrSO4, BaSO4 and PbSO4: High-order Stokes and anti-Stokes generation with?single-wavelength UV, visible, and near-IR excitation, as?well?as cascaded up-conversion nonlinear �� (3)?�� (3) lasing effects under dual-wavelength picosecond collinear coherent pumping

Orthorhombic crystals of SrSO₄, BaSO₄, and PbSO₄, known as natural crystals celestine, barite, and anglesite, were found to be attractive ?? ⁽³⁾-active nonlinear optical materials. High-order Stokes and anti-Stokes picosecond generation that spans almost two octaves has been recorded with single-wavelength laser excitation in the UV, visible, and near-IR ranges. All recorded Raman induced lasing components were identified and attributed to the SRS-promoting vibration modes of the studied crystals (?? _SRS??999?cm^?1 for SrSO₄,?? _SRS??985?cm^?1 for BaSO₄ and ?? _SRS??977?cm^?1 for PbSO₄). Under dual-wavelength (?? _f1=1.06415???m + ?? _f2=0.53207???m) collinear coherent picosecond pumping several new manifestations of cascaded ?? ⁽³⁾??? ⁽³⁾ nonlinear up-conversion lasing effects were observed in BaSO₄ and SrSO₄ crystals. We classify all three studied sulfate crystals as promising SRS-active materials for Raman laser frequency converters and as efficient ?? ⁽³⁾-crystals that efficiently generate Stokes and anti-Stokes frequency combs, which can enable experiments of ultra-short pulse syntheses.     

Optical absorption spectra of s2 impurity ions in aqueous halide ion glasses

The optical absorption bands of aqueous 0·05 M Sn²⁺ in 7 M LiI at 77°K appear at 361, 352, 325, 310, 300, 292 and 262 nm. They are considered to be the A₁, A₂, B, C₁, C₂, C₃ and D′ bands since the positions and relative intensities lie within the range of those bands for Sn²⁺-doped alkali iodide crystals. Upon warming the glass there is an uncorrelated increase in the B band and a decrease in the A₁ band. In 3·6, 4·1, 4·6 and 5·1 M CaCl₂ glasses with 5×10^?3 M Sn²⁺ the A₁ and A₂ bands show uncorrelated increases with increasing concentration of Cl^?. Comparable observations are reported for Pb²⁺-doped glasses of lithium halides and CaI₂. In general the spectra of the Sn²⁺- and Pb²⁺-doped glasses correlate well with those of the corresponding crystal systems. The effect of temperature and halide-ion concentration are attributed to shifts in chemical equilibria among the well-known halo complexes, MX_n^2?n MX_n?1^1?n+X^?, each having a characteristic, absorption and emission. Absorptions may be attributed to M²⁺(³P₁ ← ¹S₀) and M²⁺(¹P₁ ← ¹S₀) in the complex, shifted by partially covalent bonding of n halide ions.     

Muon Capture on Light Nuclei

This work investigates the muon capture reactions ²H(?? ^?, ?? _?? )nn and ³He(?? ^?, ?? _?? )³H and the contribution to their total capture rates arising from the axial two-body currents obtained imposing the partially-conserved-axial-current (PCAC) hypothesis. The initial and final A = 2 and 3 nuclear wave functions are obtained from the Argonne v ₁₈ two-nucleon potential, in combination with the Urbana IX three-nucleon potential in the case of A?=?3. The weak current consists of vector and axial components derived in chiral effective field theory. The low-energy constant entering the vector (axial) component is determined by reproducting the isovector combination of the trinucleon magnetic moment (Gamow-Teller matrix element of tritium beta-decay). The total capture rates are 393.1(8) s^?1 for A = 2 and 1488(9) s^?1 for A?=?3, where the uncertainties arise from the adopted fitting procedure.     

Muon Capture on Deuteron and 3He

We present the results of a recent simultaneous study of the muon capture reactions ²H(?? ^?, ?? _?? )nn and ³He(?? ^?, ?? _?? )³H. The initial and final A = 2 and 3 nuclear wave functions are obtained from the Argonne v ₁₈ or chiral N3LO two-nucleon potential, in combination with, respectively, the Urbana IX or chiral N2LO three-nucleon potential in the case of A?=?3. The weak current consists of polar- and axial-vector components. The former are related to the isovector piece of the electromagnetic current via the conserved-vector-current hypothesis. These and the axial currents are derived either in a meson-exchange or in a chiral effective field theory (??EFT) framework. In the first case, there is one parameter which is fixed by reproducing the Gamow-Teller matrix element in tritium ??-decay (GT^EXP). In the second case, the low-energy constants, two in the polar and one in the axial-vector current, are fixed, respectively, by reproducing the A?=?3 magnetic moments and GT^EXP. The total rates are found to be 392.0 ± 2.3 s^?1 for A?=?2, and 1484 ± 13 s^?1 for A?=?3, where the spread accounts for the model dependence relative to the adopted interactions and currents (and cutoff sensitivity in the ??EFT currents).     

The number of independent traces and supertraces on symplectic reflection algebras

It is shown that A:= H₁, _η (G), the sympectic reflection algebra over ?, has T_G independent traces, where T_G is the number of conjugacy classes of elements without eigenvalue 1 belonging to the finite group G ? Sp(2N) ? End(?^2N) generated by the system of symplectic reflections.

Simultaneously, we show that the algebra A, considered as a superalgebra with a natural parity, has S_G independent supertraces, where S_G is the number of conjugacy classes of elements without eigenvalue -1 belonging to G.

We consider also A as a Lie algebra A^L and as a Lie superalgebra A^S.

It is shown that if A is a simple associative algebra, then the supercommutant [A^S, A^S] is a simple Lie superalgebra having at least S_G independent supersymmetric invariant non-degenerate bilinear forms, and the quotient [A^L, A^L]/([A^L, A^L] ∩ ?) is a simple Lie algebra having at least T_G independent symmetric invariant non-degenerate bilinear forms.     

Moderate Deviations for Random Field Curie-Weiss Models

The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interestingly rich phase structure. In this setting, we derive moderate deviations principles for the random total magnetization S _n , which is the partial sum of (dependent) spins. A typical result is that under appropriate assumptions on the distribution of the local external fields there exist a real number m, a positive real number ??, and a positive integer k such that (S _n ?nm)/n ^?? satisfies a moderate deviations principle with speed n ^1?2k(1???) and rate function ??x ^2k /(2k)!, where 1?1/(2(2k?1))<??<1.     

EPR study of Fe3+ and Mn2+ in CeO2 and ThO2

Attempts were made to grow CeO₂ and ThO₂ single crystals doped with transition metal ions. Only Fe³⁺ and Mn²⁺ could be detected by the EPR technique. The EPR spectrum of Fe³⁺ in CeO₂ exhibits the well-known fine structure in cubic fields. The parameters areg=2.0044(1) anda=15.6(1)·10^?4 cm^?1. The hyperfine constantA for⁵⁷Fe in hexahedral coordination was found to be 8.9(1)·10^?4 cm^?1. The EPR spectrum of Mn²⁺ in CeO₂ reveals two cubic Mn²⁺ centers. The parameters for center 1 areg=1.9999(1) andA=86.9(1)·10^?4 cm^?1 and for center 2g=1.9984(1) andA=87.0(1)·10^?4 cm^?1. Heating the Mn doped CeO₂ samples in hydrogen, the Mn²⁺ centers transform from cubic into trigonal centers with approximate values ofg=1.9988(2),A=84.5(6)·10^?4 cm^?1 andD=203(1)·10^?4 cm^?1. The two observed Mn²⁺ centers in ThO₂ exhibita priori axial symmetry with approximate values ofg=2.0006(2),A=88.9(4)·10^?4 cm^?1 andD=33(3)·10^?4 cm^?1.     

Phonon coupled cooperative low-spin 1A1high-spin 5T2 transition in [Fe(phen)2(NCS)2] and [Fe(phen)2(NCSe)2] crystals

Heat capacities of [Fe(phen)₂(NCS)₂] and [Fe(phen)₂(NCSe)₂] were measured between 13⁵ and 375 K. A heat capacity anomaly due to the spin-transition from low-spin ¹A₁ to high-spin π₂ electronic ground state was found at 176·29 K for the SCN-compound and at 231·26 K for the SeCN-compound, respectively. Enthalpy and entropy of transition were determined to be ΔH = 8·60 ± 0·14 kJ mol^?1 and ΔS = 48·78 ± 0·71 J K^?1 mol^?1 for the SCN-compound and ΔH = 11·60 ± 0·44 kJ mol^?1 and ΔS = 51·22 ± 2·33 J K^?1 mol^?1 for the SeCN-compound. To account for much larger value of ΔS compared with the magnetic contribution, we suggest that there is significant coupling between electronic state and phonon system. We also present a phenomenological theory based on heterophase fluctuation. Gross aspects of magnetic, spectroscopic, and thermal behaviors were satisfactorily accounted for by this model. To examine closely the transition process, infrared spectra were recorded as a function of temperature in the range 4000 ? 30 cm^?1. The spectra revealed clearly the coexistence of the ¹A₁, and the ⁵T₂ ground states around T_c.     

Absorption spectrum of the Mn2+ ions in crystals of lanthanum manganese double nitrate and praseodymium manganese double nitrate

The optical absorption spectrum of the Mn²⁺ ions in the two double nitrates La₂Mn₃(NO₃)₁₂ ? 24H₂O and Pr₂Mn₃(NO₃)₁₂ ? 24H₂O were measured up to 30000 cm^?1. Uniaxial stress was applied to the crystals to determine the multiplicity of the observed zero phonon lines belonging to the transitions from the groundstate⁶ A ₁ (⁶ S) to the excited states⁴ E(⁴ G) and⁴ T ₂(⁴ D). The Zeeman effect of the states⁴ A ₁(⁴ G) and⁴ E(⁴ G) was measured with magnetic fields up to 6.4T. The effect of covalency and trigonal field, especially to the states⁴ A ₁ (⁴ G) and⁴ E(⁴ G), is briefly discussed.     

Latest Results From the HypHI Experiments at GSI: Hypernuclear Spectroscopy with Heavy Ion Induced Reactions

The HypHI Phase 0 experiment with ⁶Li projectiles at 2 AGeV on a carbon target has been performed at GSI in order to demonstrate the feasibility of hypernuclear spectroscopy with induced reaction of heavy ion beams. Current data analyses have shown peaks in invariant mass distributions of p + π ^? for Λ, ³He+ π ^? for ³ _Λ H and ⁴He + π ^? for ⁴ _Λ H. Lifetime values for the corresponding peaks have been also deduced, which are in good agreement with the former known values.     

Temperature dependence of Mn2+ EPR in Sn2P2S6 near the phase transition

The X-band EPR spectrum of Mn²⁺ in Sn₂P₂S₆ was studied in the temperature rangeT=223–363 K. At room temperature the spin-Hamiltonian constants areg=2.00±0.01,B ₂ ⁰ =(163±3)·10^?4 cm^?1,B ₂ ² =(159±3)·10^?4 cm^?1,A=?(75±1)·10^?4 cm^?1. The effect of the invariance in temperature of the resonance magnetic fields in the narrow temperature rangeT=337–340 K and the model of the paramagnetic centre are discussed. According to EPR data a phase transition occurs atT=337 K. This transition from the paraelectric phase to the ferroelectric one is accompanied by a dramatic change in value of the spin-Hamiltonian constantB ₂ ⁰ .     

Diagnosing ΛHDE model with statefinder hierarchy and fractional growth parameter

Recently, a new dark energy model called ΛHDE was proposed. In this model, dark energy consists of two parts: cosmological constant Λ and holographic dark energy(HDE). Two key parameters of this model are the fractional density of cosmological constant ?_(Λ0), and the dimensionless HDE parameter c. Since these two parameters determine the dynamical properties of DE and the destiny of universe, it is important to study the impacts of different values of ?_(Λ0) and c on the ΛHDE model. In this paper,we apply various DE diagnostic tools to diagnose ΛHDE models with different values of ?_(Λ0) and c; these tools include statefinder hierarchy{S_3~(1), S_4~(1)}, fractional growth parameter ?, and composite null diagnostic(CND), which is a combination of{S_3~(1), S_4~(1)}and ?. We find that:(1) adopting different values of ?_(Λ0) only has quantitative impacts on the evolution of the ΛHDE model, while adopting different c has qualitative impacts;(2) compared with S_3~(1), S_4~(1) can give larger differences among the cosmic evolutions of the ΛHDE model associated with different ?_(Λ0) or different c;(3) compared with the case of using a single diagnostic, adopting a CND pair has much stronger ability to diagnose the ΛHDE model.     

The one-site distribution of Gibbs states on Bethe lattice are probability vectors of period⩽2 for a nonlinear transformation

We prove that the one-site distribution of Gibbs states (for any finite spin setS) on the Bethe lattice is given by the points satisfying the equation π=T ²π, whereT=h·A·?, with?(x)=x ^(q?1/q,h(x)=(x∥x∥ _q ) ^q ,A=(a(r, s)∶r, s∈S), and $$a(r,s) = \exp (K[r,s] + (1/q)[N,r + s])$$ We also show that forA a symmetric, irreducible operator the nonlinear evolution on probability vectorsx(n+1)=Ax(n) ^p ∥Ax(n) ^p ∥₁ withp>0 has limit pointsξ of period?2. We show thatA positive definite implies limit points are fixed points that satisfy the equationAξ ^p=λξ. The main tool is the construction of a Liapunov functional by means of convex analysis techniques.     

EPR study of the Ag6S3O4 compound prepared by two methods

The temperature dependence of the EPR spectra of the recently discovered Ag₆S₃O₄ phase in the Ag-O-S system prepared by two methods, the known method of co-precipitation from aqueous solution and a new method depending on the interaction of Ag₂S and Ag₂SO₄ solid reagents, has been investigated. No EPR spectra were observed at room temperature, while at liquid helium temperature a number of EPR spectra have been recorded, which disappeared upon increasing temperature up to liquid nitrogen temperature. The sample obtained by the co-precipitation method revealed an intense, rich EPR spectrum that has been tentatively interpreted assuming the presence of at least two different Ag²⁺ ion complexes, one monomer resulting in an intense anisotropic, rhombic EPR powder pattern with g₁ = 1.93(1), g₂ = 2.025(3), g₃ = 2.094(5), hyperfine constants A₁ = = A₂ = 60(5) · 10^?4 cm^?1,A ₃ = 90(5) · 10^?4 cm^?1 and one dimer EPR pattern presumably involving a pair of Ag²⁺ ions with internuclear separation of 4.3 Å. However, the presence of larger clusters could not be excluded. On the other hand, the sample obtained by a solid state reaction method has given rise to two rather weak EPR lines centered at g_eff = 2.105(3) and g_eff = 4.213(3), respectively.     

An investigation of theL 2-L 3 Coster-Kronig transition probability for 63≦Z≦96

Nuclear spin polarization in the 4f ¹⁴6s ^{2 1} S ₀ ground state of¹⁷⁵Lu⁺(I=7/2) ions is achieved by optical pumping with the resonance line (¹ S ₀-¹ P ₁,λ=261.5 nm). Nuclear magnetic resonance of the free ions in He buffer gas yields for the magnetic dipole momentμ(¹⁷⁵Lu)=2.2240(11)μ _n (with diamagnetic correction). This value can be used for a more accurate determination of the magnetic dipole moments of other Lu isotopes from knownA factor ratios. A comparison with nuclear induction measurements in solids results in the chemical shiftsδ(LuB₁₂)=?23(5)·10^?4 andδ(LuSb)= ?31(5)·10^?4.     

Theoretical prediction of cosmological constant Λ in Veneziano ghost theory of QCD

Based on the Veneziano ghost theory of QCD, we predict the cosmological constant ??, which is related to energy density of cosmological vacuum by $ \Lambda = \frac{{8\pi G}} {3}\rho _\Lambda $ . In the Veneziano ghost theory, the vacuum energy density ?? _?? is expressed by absolute value of the product of quark vacuum condensate and quark current mass: $ \rho _\Lambda = \frac{{2N_f H}} {{m_{\eta '} }}c|m_q < 0|:\bar qq:|0 > | $ . We calculate the quark local vacuum condensates ??0|: $ \bar q $ q: |0?? by solving Dyson-Schwinger Equations for a fully dressed confining quark propagator S _f (p) with an effective gluon propagator G _???? ^ab (q). The quark current mass m _q is predicted by use of chiral perturbation theory. Our theoretical result of ??, with the resulting ??0|: 471-4 q: |0?? = ?(235 MeV)³ and light quark current mass m _q ? 3.29?C6.15 MeV, is in a good agreement with the observable of the ?? ?? 10^?52 m^?2 used widely in a great amount of literatures.     

Contribution of vector resonances to the \bar{B}_{d}^{0}\to\bar {K}^{*0}\mu^{+}\mu^{-} decay

The fully differential angular distribution for the rare flavor-changing neutral current decay $\bar{B}_{d}^{0} \to\bar{K}^{*0} (\to K^{-} \pi^{+}) \mu^{+}\mu^{-} $ is studied. The emphasis is placed on accurate treatment of the contribution from the processes $\bar{B}_{d}^{0} \to\bar{K}^{*0} (\to K^{-} \pi^{+}) V $ with intermediate vector resonances V=??(770),??(782),?(1020),J/??,??(2S),?? decaying into the ?? ⁺ ?? ^? pair. The dilepton invariant-mass dependence of the branching ratio, longitudinal polarization fraction f _L of the $\bar{K}^{*0}$ meson, and forward?Cbackward asymmetry A _FB is calculated and compared with data from Belle, CDF and LHCb. It is shown that inclusion of the resonance contribution may considerably modify the branching ratio, calculated in the SM without resonances, even in the invariant-mass region far from the so-called charmonia cuts applied in the experimental analyses. This conclusion crucially depends on values of the unknown phases of the B ⁰??K ^?0 J/?? and B ⁰??K ^?0 ??(2S) decay amplitudes with zero helicity.     

Hartree-fock wave functions and oscillator strengths for the helium isoelectronic sequence

Oscillator strengths for 1¹S?n¹P transitions for some members of the helium isoelectronic sequence have been calculated by utilizing the dipole length, velocity and acceleration forms of the transition matrix element with coupled H.F. wave functions. Good agreement has been obtained between the values of the oscillator strengths. The quantities $\text{(?}{}_{\mathrm{A}}\text{??}{}_{\mathrm{L}}\text{)}$ and $\text{(?}{}_{\mathrm{A}}\text{??}{}_{\mathrm{V}}\text{)}$ decrease slowly with nuclear charge Z, whereas $\text{(?}{}_{\mathrm{L}}\text{-?}{}_{\mathrm{V}}\text{)}$ first increase to a maximum value and then decreases slowly.     

Measurement of Ar(I) and Ar(II) transition probabilities in LTE ARC plasmas

The transition probabilities of two Ar(I) lines and one Ar(II) line have been measured in emission on wall-stabilized argon arc plasmas (0·5×10⁵?p, Nm^-2?3×10⁵; 10,000?T, K?20,000; 10²²?N_e, m^-3?5×10²³) using the “method of best fit (MBF)”. The results (without line-wing correction) are for Ar(I) at 714·7 nm, A_nm=5·66×10⁵ s^-1±5%; for Ar(I) at 430·0 nm, A_nm=3·40×10⁵ s^-1±5%; for Ar(II) at 480·6 nm, A_nm=8·82×10⁷ s^-1±7%. These values were not influenced by deviations from LTE, which have been observed at electron number densities n_e?10²³ m^-3. The small uncertainties were achieved after careful corrections of different sources of error.