An effective method of investigation of positive maps on the set of positive definite operators

Let $\text{A}$₁ be the algebra of linear operators on the n-dimensional Hilbert space $\text{H}$₁, and let $\text{A}$₂ be the algebra of linear operators of the m-dimensional Hilbert space $\text{H}$₂. Let $\text{L}$($\text{A}$₁, $\text{A}$₂) denote the complex space of linear maps from $\text{A}$₁ to $\text{A}$₂. By a positive map we mean an element of the space $\text{L}$($\text{A}$₁, $\text{A}$₂) (superoperator with respect to $\text{H}$₁) which maps positive definite operators in $\text{A}$₁ into positive definite operators in $\text{A}$₂. The aim of this paper is to present an effective method which allows to verify whether a given superoperator Λ∈$\text{L}$($\text{A}$₁, $\text{A}$₂) is a positive map. Besides that necessary and sufficient conditions for the positive definiteness of even-degree forms in many variables are given.     

Resonance structure of 32S + n from transmission and differential elastic scattering experiments

Neutron transmission experiments were performed on ³²S between 0.18 MeV and 19 MeV and differential elastic scattering experiments up to 2 MeV. The resonance parameters, including spin and parity, were determined up to 1.7 MeV. The distribution of neutron strength was determined for s_{$\text{1}\text{2}$}, P_{$\text{1}\text{2}$}, P_{$\text{3}\text{2}$}, d_{$\text{3}\text{2}$}, d_{$\text{5}\text{2}$} and f-wave levels, and is compared to recent model calculations. The isotopic purity of some possible $\text{T =}\text{3}\text{2}$ isobaric analog states was deduced from their neutron widths.     

The structure of the solid electrolyte Li1.6Ag0.4SO4 AT 565°C

The structure of the high-temperature solid solution Li_1.6Ag_0.4SO₄ has been determined from neutron and X-ray powder diffraction data. The sulphate groups form a fcc lattice where the lithium ions are found to occupy the ±($\text{1}\text{4}$, $\text{1}\text{4}$, $\text{1}\text{4}$) tetrahedral sites. The silver ions partly occupy the same sites and partly the larger ($\text{1}\text{2}$, $\text{1}\text{2}$, $\text{1}\text{2}$) octahedral site. The results strongly support earlier conclusions for the fcc phase of Li₂SO₄. Exceptionally high temperature factors are found. The consistency of the structural model with other characteristic properties of the high-temperature fcc phase is briefly discussed.     

Systematics of core line asymmetries in XPS spectra of Ni

Core line asymmetries have been observed in the 3p_{$\text{1}\text{2}$}, 3p_{$\text{3}\text{2}$}, 3s, 2p_{$\text{1}\text{2}$} and 2p_{$\text{3}\text{2}$} XPS spectra of Ni. The asymmetry parameters are the same for all lines within the experimental accuracy. The absence of exchange splitting in the 3s line indicates a 3d¹⁰ configuration for the fully screened final state of Ni.     

Inelastic scattering and satellite fine structure in the high-resolution uv photoelectron spectrum of CS2

The outer valence region in CS₂ has been studied by high-resolution UV photpelectron Spectroscopy. The spectra reveal detailed vibrational structure in the X$\text{\$}\text{?}$²Π_g, A$\text{\$}\text{?}$²Π_u, B$\text{\$}\text{?}$²Σ⁺_u and C$\text{\$}\text{?}$²Σ⁺_g bands. Some of the fine-structure peaks in the X$\text{,}\text{?}$B$\text{\$}\text{?}$and C$\text{\$}\text{?}$bands are shown to be pressure-dependent. The reason for the pressure dependence is assumed to be inelastic scattering of electrons emitted in the adiabatic transitions. It is established that the two CI satellite bands present in the He(I)-excited spectrum contain vibrational structure.     

Sodium resonances in fluorescence from wide-range laser scan in H2-O2-Ar flame

Several resonances and underlying continua were observed in the excitation profiles of sodium atoms in an H₂-O₂-Ar flame, irradiated by the focused beam of a tunable, pulsed dye layer. These profiles are obtained by tuning the laser through the spectral range of Rhodamine 6G and detecting the ensuing fluorescence signals from the 3D-3P and 4D-3P transitions. We observed resonances corresponding to the 3S_{$\text{1}\text{2}$}-3P_{$\text{1}\text{2}$}, 3S_{$\text{1}\text{2}$}-3P_{$\text{3}\text{2}$}, 3P_{$\text{1}\text{2}$}-5S_{$\text{1}\text{2}$}, 3P_{$\text{3}\text{2}$}-5S_{$\text{1}\text{2}$} one-photon transitions and resonances corresponding to the 3S_{$\text{1}\text{2}$}-5S_{$\text{1}\text{2}$}, 3S_{$\text{1}\text{2}$}-4D_{$\text{3}\text{2}$}, _{$\text{5}\text{2}$} two-photon transitions. The observed resonances result from different sequences of radiative and collisional excitation. The presence of the continua is explained by consecutive absorption of laser photons in the collisionally broadened wings of absorption lines. The spatial inhomogeneity of the laser beam and hence of the saturation causes submerging of some resonances into continua.     

Analysis of the high-temperature spin-glass susceptibility: Determination of the local magnetic exchange

New measurements are reported of the magnetic susceptibility above the freezing temperature T_f for noble-metal spin-glasses with $\text{1}\text{2}$ to 6 at.% Fe or Mn. The susceptibility for T_f<T?5 T_f is not Curie-Weiss, but local magnetic correlations manifest themselves and provide a key for the determination of the exchange interactions in spin-glasses. The exchange parameters J_n are resolved up to 5 neighbors for $\text{Au}$Fe, $\text{Cu}$Mn, $\text{Au}$Mn and $\text{Pt}$Mn through a configuration ensemble calculation which includes atomic short range order.     

Domain Structures and anisotropy constant in the compound Dy2Fe17

The domain structure of the compounds Dy₂Fe₁₇ was determined by the powder pattern method. The dependence of the mean domain width $\text{D}$ on the mean grain thickness $\text{L}$ is described by $\text{D = 0.32}\text{2}\text{34}$. The magnetic anisotropy constant K₁, the Bloch wall energy γ and the Bloch wall width δ for polycrystalline Dy₂Fe₁₇ compounds are also determined.     

Acoustic phonon anomalies and superstructure of two NbZr alloys

The anomalous dispersion of the [001] transverse phonon branch of Nb_0.9Zr_0.1 and Nb_0.8Zr_0.2 has been measured by neutron inelastic scattering. The anomaly is found to become less pronounced as the Zr content of the alloy is increased. Although the anomaly is strongly temperature-dependent it is not obviously affected by the superconducting transition. Diffraction measurements with the Nb_0.9Zr_0.1 sample show the diffuse scattering which Wakabayashi has recently reported to occur at wave-vectors around [$\text{3}\text{4}$,$\text{3}\text{4}$,$\text{3}\text{4}$] in a 12% alloy. The Nb_0.8Zr_0.2 crystal however displays unbroadened superlattice peaks at wavevectors [$\text{3}\text{4}$,$\text{3}\text{4}$,$\text{3}\text{4}$ in some Brillouin zones.     

Resonant absorption in LiNdP4O12 lasers

The resonant loss in LiNdP₄O₁₂ (LNP) lasers has been investigated. The effective resonant loss coefficient for the 1.047(7) μm laser emission was measured to be 0.042 cm^-1. This value can be explained by resonant absorption due to the ⁴I_{1$\text{1}\text{2}$}→⁴F_{$\text{3}\text{2}$} transition including the reabsorption effect of the fluorescence resulting from the ⁴I_{$\text{9}\text{2}$}→⁴F_{$\text{3}\text{2}$} transition.     

Relaxation of the 4G92 state of Nd3+ in LaCl3 and Nd3+ in La(Cl99.6Br0.4)3

The decay of the ⁴G_{$\text{9}\text{2}$} state of Nd³⁺ in LaCl₃ and La(Cl_99.6 Br_0.4)₃ was measured after pulsed laser excitation as a function of temperature. The decay rate is shown to depend besides the radiative transition on single-phonon relaxation between the states ⁴G_{$\text{9}\text{2}$} ($\text{μ =}\text{1}\text{2}$) and ⁴G_{$\text{9}\text{2}$} ($\text{μ =}\text{3}\text{2}$) and on multiphonon orbit-lattice relaxation from ⁴G_{$\text{9}\text{2}$} to ²G_{$\text{9}\text{2}$}. Partial substitution of Cl by Br only alters the radiative lifetime.     

Specific heats of pure and doped polyacetylene

The temperature dependences (0.8 K ? T < 7 K) of the specific heats of pure polyacetylene (both $\text{cis}$ and $\text{trans}$ isomers) and heavily doped metallic [CH(AsF₅)_0.12]_X are reported. Results for undoped $\text{cis}$-(CH)_X indicate behavior typical of crystalline polymers, whereas isomerization to the $\text{trans}$-form leads to a small term linear in temperature signifying increased disorder. Comparison of the data from $\text{cis}$ and $\text{trans}$ starting material indicates that isomerization is induced during doping. The increased coefficient of the linear term in the metallic polymer is discussed in terms of two contributions; an electronic term expected for a metal, and the increased effect of disorder in the doped polymer.     

Annealing studies on the absorption spectrum of 41K-atoms trapped in an argon matrix

Argon crystals were doped with 0.2 ppm of ⁴¹K through the nuclear reaction ⁴⁰Ar (n, β^-) ⁴¹K. The absorption spectrum from 300 nm to 800 nm was measured as a function of the annealing temperature. Absorption ← 4²s_{$\text{1}\text{2}$} transition of the free atom could be bands corresponding to the 4²p_{$\text{1}\text{2}$}, _{$\text{3}\text{2}$} ← 4²s_{$\text{1}\text{2}$} and 5²p_{$\text{1}\text{2}$}, _{$\text{3}\text{2}$} ← 4²s_{$\text{1}\text{2}$} transition of the free atom could be observed. The absorption bands depend strongly on the annealing temperature. An increase in the annealing temperature results in a blue shift of the absorption bands.     

Isomers in the N = 83 nucleus 149Dy

Energy levels in the N = 83 nucleus ¹⁴⁹Dy were studied by the reaction ¹⁵²Gd(α, 7n) at 106 MeV bombarding energy using in-beam γ-ray spectroscopy methods. The measurements identified three isomers in this nucleus, at 1073 keV (13 ± 3 ns), at 2700±150keV (5 μs < T_{$\text{1}\text{2}$} < 0.5 s), and above 3.5 MeV (50 ± 15 ns). The low-lying isomer is interpreted as i_{$\text{13}\text{2}$}. The configuration $\text{27}\text{2}$^?(πh_{$\text{11}\text{2}$}²)₁₀₊ ×vf_{$\text{7}\text{2}$} is suggested for the state at 2.7 MeV.     

Investigation of emission spectra and lifetimes of Cs2NaErCl6 single crystals

The fluorescence spectra and lifetimes of low lying states of Er³⁺ in Cs₂NaErCl₆ single crystals have been investigated at room temperature and at 77 K. The assignments of the ⁴F_{$\text{9}\text{2}$}-⁴I_{$\text{15}\text{2}$} and ⁴I_{$\text{11}\text{2}$}-⁴I_{$\text{15}\text{2}$} phonon-assisted transitions have been proposed. The fluorescence lifetimes of low lying fluorescing levels have been estimated.     

Evidence for assignment of 14.0 MeV state in 11B from 10B(n,n)10B

The differential cross section and polarization for neutrons scattered from ¹⁰B have been measured at E_n = 2.63 MeV (E_x = 13.85 MeV). The results of this experiment and other available neutron scattering data in the range 1 < E_n < 4 MeV are interpreted through a single-level R-matrix calculation over the region 12 < E_x < 15 MeV. Based on this analysis the most probable J^π assignment for the 14.0 MeV level in ¹¹B is $\text{11}\text{2}{}^{\mathrm{+}}$. The anomaly near E_x = 13.1 MeV can only be explained in terms of two overlapping levels having assignments of ($\text{5}\text{2}$, $\text{7}\text{2}$)^? and ($\text{3}\text{2}$, $\text{5}\text{2}$, $\text{7}\text{2}$)⁺.     

Experimental transition probabilities of some Xe(I) lines

Using the light absorption technique in a ¹³²Xe afterglow plasma, we have measured the relative transition probabilities for several xenon lines which have the metastable 6s[$\text{3}\text{2}$]₂ or the resonant 6s[$\text{3}\text{2}$]₁ states as their lowest transition level. Because the transition probabilities of the 8819 Å (6p[$\text{5}\text{2}$]₃ ? 6s[$\text{3}\text{2}$]²) and 8280 Å (6p[$\text{1}\text{2}$]₀ ? 6s[$\text{3}\text{2}$]₁) lines are relatively well known, we have chosen these as reference lines and have thus been able to determine the absolute values of the transition probabilities for 19 xenon lines corresponding to transitions from 6p, 6p′, 7p, 8p, 9p, 4f and 5f to 6s[$\text{3}\text{2}$]₂, and for four lines corresponding to the transitions 6p?6s[$\text{3}\text{2}$]₁.     

Characterization of LiFeCl4 and AgFeCl4 ionic conductors

LiFeCl₄ and AgFeCl₄ are obtained by direct reaction between LiCl or AgCl and FeCl₃ at 300°C and 400°C respectively. Both compounds are monoclinic with $\text{a = 7.02 (1)}\text{A}\text{?}$, $\text{b = 6.33 (1)}\text{A}\text{?}$, $\text{c = 12.72 (4)}\text{A}\text{?}$, β = 92° (30') for LiFeCl₄ and $\text{a = 10.60 (5)}\text{A}\text{?}$, $\text{b = 6.30 (5)}\text{A}\text{?}$, $\text{c = 12.34 (10)}\text{A}\text{?}$, β = 106° (1) for AgFeCl₄.LiFeCl₄ is clearly isotypic of LiAlCl₄. Magnetic measurements characterize in both cases Fe³⁺ ions in a high spin tetrahedral situation. LiFeCl₄ becomes antiferromagnetic at low temperature (T_N?10 K). AgFeCl₄ reveals a more complex situation. On contrary to the silver derivative, LiFeCl₄ is a good ionic conductor with activation energy of 0.78 eV in the solid state below 105°C, and a sharp increase in the lithium mobility at this temperature.     

The p-approximations and inverse problems of expansion and contraction of n-fermion operators

The orthogonal projectors from the space $\text{L}$(n) of n-fermion operators onto its sub-spaces $\text{L}$_p(n) consisting of p-reducible elements of $\text{L}$(n>), as well as those from $\text{L}$(n) onto $\text{L}$_p(n)?$\text{L}$_p?1(n) are constructed. Using the above projectors the inverse problems of contraction and expansion are solved.     

Electrical resistance and magnetoresistance of amorphous alloys Gd67Co33 and Pd80Si20

In search for structural contributions to the low temperature anomaly we report high resolution resistance and magnetoresistance measurements ($\text{0.02}\text{K}\text{? T ? 20}\text{K}$) of amorphous splats of Gd₆₇Co₃₃ and Pd₈₀Si₂₀. For both alloys, the resistivity ?(H = 0, T) has a minimum at T ～ 10 K and increases with decreasing T. The ferromagnetic Gd₆₇Co₃₃ shows a strong negative field dependence of $\text{Δ?}\text{?(0)}$, saturating at H ～ 2T for T = 4.2 K but no measurable change in $\text{??}\text{?}\text{T}$ below 10 K is observed.The diamagnetic Pd₈₀Si₂₀ exhibits a positive field dependent magnetoresistance $\text{[Δ?}\text{?(0)]}\text{(}\text{H}\text{)}$ at low temperatures. Additionally, a field dependent part in $\text{??}\text{?}\text{T}$ is found which is probably due to paramagnetic impurities (～ 1 ppm Fe). However, there is also a field independent contribution in the amorphous state of Pd₈₀Si₂₀, which vanishes after crystallization. We attribute this to non-magnetic scattering induced by the disordered structure.