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.     

The rotational bands 12+[411]and 12−[541]in 175Lu

In a study of the γ-radiation emitted in the reaction ¹⁷⁶Yb(p, 2n) excited states of the nucleus ¹⁷⁵Lu up to spin I = $\text{13}\text{2}$ have been investigated. The main results concern the rotational bands $\text{1}\text{2}$⁺ [411]and $\text{1}\text{2}$^? [541]with the corresponding band heads found at 626.60 and 370.88 keV, respectively. The half-life of the $\text{1}\text{2}$⁺[411] level has been determined to be $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 10.7±0.5}\text{ns}$. Furthermore, the band heads $\text{3}\text{2}$^?[532]and $\text{3}\text{2}{}^{\mathrm{+}}$[411]are proposed at energies of 999.0 and 1150.8 keV, respectively. Experimental E1 transition probabilities between both $\text{K =}\text{1}\text{2}$ bands are compared with calculations including the Coriolis and pairing effects, as well as theoretically deduced quadrupole deformation parameters.     

AES,photoemission and work function study of the deposition of Cs on (100) and (111)B GaAs epitaxial layers

Work function, photoemission and AES measurements have been made on (100) and (111)B epitaxial GaAs layers as a function of caesium coverage. It has been shown that the photoemission maximum and work function minimum occur at a coverage of $\text{2}\text{3}$ of a monolayer. The reduction of the work function takes place in distinct stages with changes in the rate of fall occurring at $\text{1}\text{8}$ and $\text{1}\text{2}$ of a monolayer for the (111)B face and $\text{1}\text{8}$, $\text{1}\text{4}$, $\text{1}\text{3}$ and $\text{1}\text{2}$ of a monolayer for the (100) face. This indicates the presence of specific adsorption sites which have not been observed in previous work on these faces.     

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.     

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.     

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.     

Semi-leptonic decays of charmed baryons

We present estimates of semi-leptonic decays of the charmed $\text{1+}\text{2}$ baryons, members of the SU(3) 3¹ and 6 multiplets, into ordinary $\text{1+}\text{2}\text{and}\text{3+}\text{2}$ baryons. We give general expressions for decay rates and the mass M(B⁺?) spectra. We relate the relevant form factors for the $\text{1+}\text{2}\text{→}\text{1+}\text{2}$ transitions to the electromagnetic ones by means of CVC and SU(4). The form factors for $\text{1+}\text{2}\text{→}\text{3+}\text{2}$ transitions are related through SU(4) to those measured in Δ production. We discuss the dependence of the results on the masses of charmed baryons. The $\text{1+}\text{2}\text{→}\text{1+}\text{2}$ and $\text{1+}\text{2}\text{→}\text{3+}\text{2}$ transitions turn out to be dominant for the decays of the multiplets 3¹ and 6, respectively. The partial lifetimes are O(10^?10 ? 10^?14) sec as the masses of the decaying baryons are varied from 2 to 2.9 GeV. Possible ways of getting an idea about the masses of the charmed baryons are given.     

The antiferroelectric phase transition in TlH2PO4 and TlD2PO4

It is shown by X-ray diffraction measurements that the transitions at 230 K in TlH₂PO₄ and at ≈ 350 K in TlD₂PO₄ are structurally equivalent. In both cases, on cooling through the transition, new reflections appear at points ($\text{h +}\text{1}\text{2}$, $\text{k +}\text{1}\text{2}$, l) referred to the primitive monoclinic unit cell of the high-temperature phase. In TlH₂PO₄ some distinct but broadened scattering remains at the ($\text{h +}\text{1}\text{2}$, $\text{k +}\text{1}\text{2}$, l) points up to 10 K, or more, above the transition temperature.     

The (d,t) and (d,t) reactions on 18O and the 1p spin-orbit splitting

The reactions ¹⁸O(d, t)¹⁷O and ¹⁸O(d, τ)¹⁷N have been investigated at ifE_{d = 52 MeV}. Energy spectra of tritons and τ particles have been measured up to excitation energies of 25 MeV in ¹⁷O and 12 MeV ¹⁷N, respectively, and spectroscopic factors have been obtained by a DWBA analysis of the measured angular distributions. From a comparison of the t-and τ-spectra the distribution of $\text{T =}\text{1}\text{2}\text{and}\text{3}\text{2}$ spectroscopic strengths in ¹⁷O could be deduced and analog relations between $\text{T =}\text{3}\text{2}$ states in ¹⁷N and ¹⁷O could be established. Nearly the total $\text{T =}\text{3}\text{2}$ strengths of the $\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{and}\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ shells and nearly the complete $\text{T =}\text{1}\text{2}$ strength of the $\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ shell have been found, whereas only one third of the $\text{T =}\text{1}\text{2}$ strength of the $\text{1}\text{p}\text{3}\text{2}$. Shell could be clearly identified. The observed centroid energies are understood from the different $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$$\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?}}\text{1)}$ and $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ effective residual interactions. This supports a strong isospin dependence of the 1p spin-orbit splitting.     

The parallel magnetic susceptibility and specific heat of the antiferromagnetic Ising linear-chain system with spin S = 2, 52, and 3

The parallel magnetic susceptibility and specific heat of the antiferromagnetic Ising linear-chain system with spin S = 2, $\text{5}\text{2}$, and 3 are calculated using the matrix approach. The results for spin $\text{S =}\text{1}\text{2}$, 1, $\text{3}\text{2}$, and 2 are checked against known results for these cases.     

Multilevel description of the Rh isotopes in the interacting boson-fermion model

We present a multilevel calculation within the framework of the interacting boson-fermion model (IBFM-1) of the odd-mass ^101–109Rh isotopes. We calculate both positive- and negative-parity states of the same hamiltonian, starting from the $\text{1g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$, $\text{2p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{2p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, $\text{lf}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ and $\text{2d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ single-particle orbitals. We discuss energy spectra, electromagnetic E2 transition rates and one-nucleon transfer properties. We also discuss the influence of the $\text{1f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ orbital on the one-nucleon transfer properties. The results of the calculation for the negative-parity states are compared with the results of the $\text{U(}\text{6}\text{12}$) supersymmetry scheme of the interacting boson model.     

Absence of the second-order phase transitions in the dimerized Ising chains with spin larger than 12

A general spin S Ising chain interacting with a single phonon mode of the harmonic lattice is studied. The thermodynamics of the spin system is calculated exactly for S = 1, $\text{1}\text{2}$ and $\text{3}\text{2}$, while self-consistent equations for the induced lattice distortions are derived. It is demonstrated that for S >$\text{1}\text{2}$ there is no second-order phase transition, in contrast to the case S = $\text{1}\text{2}$ which was proved to have a tricritical point. This is found to cohere with the previous studies of the dimerized magnetic model chains.     

Intrinsic and rotational excitations in 175Lu

The γ-ray cascades following the ¹⁷⁶Yb(p, 2n)¹⁷⁵Lu reaction are studied with Ge(Li) detectors and interpreted within the level scheme of ¹⁷⁵Lu. According to this interpretation the $\text{1}\text{2}$⁺[411], $\text{1}\text{2}$^?[541], $\text{5}\text{2}$⁺[402], $\text{7}\text{2}$⁺[404] and $\text{9}\text{2}$^?[514] rotat $\text{15}\text{2}$⁺, $\text{21}\text{2}$^?, $\text{13}\text{2}$⁺, $\text{19}\text{2}$⁺ and $\text{19}\text{2}$^? members, respectively. Fu band head is determined to be 626.6 keV. The data for the rotational bands are discussed within the particle-rotor model and compared with the available information on the corresponding bands in the adjacent Lu isotopes.     

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.     

Magnetic structure of the compound CeIn3

Neutron diffraction measurements on the CeIn₃ compound show that the magnetic ordered phase is an antiferromagnetic one with a propagation vector ($\text{1}\text{2}$, $\text{1}\text{2}$, $\text{1}\text{2}$) and a weak value of the magnetic moment 0.48±0.08 μ_B. Comparison are made with the CeAl₂ and CeSn₃ cases.     

The energy spectra and electromagnetic transitions of odd-a titanium isotopes

The isotopes ^{55, 47, 49, 51}Ti are studied in the framework of the deformed configuration mixing shell model. The calculated spectra and electromagnetic properties agree well with the observed ones. The calculations suggest the existence of an excited $\text{K =}\text{1}\text{2}$ band of states in ^{45, 47, 49}Ti and a $\text{K =}\text{7}\text{2}$ band in ⁵¹Ti. In ⁴⁹Ti this excited $\text{K =}\text{1}\text{2}$ band is more deformed than the “ground state band”. On the basis of the overall agreement between the calculated and experimental spectra and decay properties we suggest the spin assignments $\text{J =}\text{5}\text{2}$, $\text{7}\text{2}$, $\text{9}\text{2}$, $\text{5}\text{2}$ and $\text{7}\text{2}$ to the states in ⁴⁷Ti observed at 2.168, 2.97, 2.408, 2.835 and 3.223 MeV, respectively.     

Relative Cl 2p:P 2s photoionization intensities in transition metal complexes

X-ray photoelectron spectra of the Cl 2p_{$\text{1}\text{2}$, $\text{3}\text{2}$}, P 2s region were obtained for nine transition metal complexes. The Cl:P atom ratios ranged from 1:3 to 3:2 and exhibited a linear relationship with the Cl 2p_{$\text{1}\text{2}$, $\text{3}\text{2}$} : P 2s intensities. Using AlKα radiation, the ratio of the Cl 2p: P 2s photoionization intensities was found to be 2.5: 1.0 with the McPherson ESCA-36 Photoelectron Spectrometer operated in its standard configuration.     

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.     

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.