Angular-anisotropy coefficients for fragment originating from the resonance-neutron-induced fission of <Superscript>235</Superscript>U oriented nuclei

Statistical distributions of the coefficients measured for the angular distribution of fragments originating from the fission of ²³⁵U oriented nuclei that was induced by resonance neutrons obtained by using booster targets at the electron accelerator in Harwell and at a pulsed reactor in Dubna were approximated by a curve that was calculated under the assumption of a normal distribution of partial-wave fission amplitudes. A cutoff from below at a level of one-half of the average partial-wave width was introduced in this distribution. The calculation was performed with allowance for the K = 0, 1 and 2 channels for J = 3 and the K = 1 and 2 channels for J =4. The contributions of the K channels to the total probability were in the ratio 0.15 : 0.53 : 0.32 for J = 3 and in the ratio 0.625 : 0.375 for J = 4. A strong suppression of the K = 0 channel in the J = 3 spin subsystem in contrast to the situation observed in photofission can be interpreted as an indication of the possible partial conservation of K in resonance states formed from the entrance channel, which features only maximum values of K equal to J and J ? 1.     

Precision measurements of optical excitation functions for the mercury atom

We describe a computer-based facility for studying the excitation of atoms by ultramonochromatic electrons and give optical excitation functions for the 12 mercury spectral lines that originate from the n ¹ S ₀, n ¹ P ₁, n ¹ D ₂, n ³ S ₁, n ³ P _j , and n ³ D _j levels. We detected about 100 features in the energy dependences measured from the excitation threshold to 15.5 eV. The previously found positions of the features on the energy scale are in good agreement with our results. Most of the resonant features are shown to be mainly attributable to the decay of short-lived states of the negative mercury ion. We detected a postcollision interaction effect in the optical excitation functions of the lines that originate from the n ¹ S ₀ levels at energies of about 11 eV.     

Ion-pair states of I<Subscript>2</Subscript>, Br<Subscript>2</Subscript>, IBr,and ICl

The experimentally determined energies and rotational constants of the vibrational levels v = 0–20 of the Ion-Pair states Ω = 0⁺, Ω = 1 of the I₂, Br₂, IBr, and ICl molecules are modeled. The model used includes three diabatic states, which correlate to X⁺(3P, 1D) + Y^～(1S₀). These states are coupled by the spin-orbit interaction, which is assumed to be independent of the internuclear distance. For IBr and ICl, as well as for the ungerade states of I₂ and Br₂, satisfactory results are obtained. The model is less applicable to the gerade states of I₂ and Br₂, which is possibly results from the retainment of the asymptotic J _A J _B coupling of the angular momenta at equilibrium internuclear distances.     

Precision measurements of optical excitation functions for the cadmium atom

An experimental setup and a technique for the investigation of excitation of atoms by ultramonoenergetic electrons are described. The optical excitation functions are given for 14 spectral lines of the cadmium atom originating from the n ¹ S ₀, 5¹ P ₁, n ³ S ₁, 5³ P ₁, and n ³ D _j levels. More than 150 specific features are found in the energy dependences of the effective excitation cross sections measured from the excitation threshold to 16 eV. The most pronounced of these features are in good agreement with the fine structure observed previously. The main mechanisms of the initial-level population, namely, the direct transition of an electron from the ground atomic state to the initial level of a spectral line, the population of the initial levels due to the decay of short-lived states of a negative ion, and the cascade population, are separated. In the excitation functions of the lines originating from the n ¹ S ₀ levels, in the energy range from 10.9 to 12.4 eV, we observed for the first time an effect of postcollision interactions of emitted and scattered electrons in the vicinity of the thresholds of four autoionization states of the cadmium atom.     

Solving the relativistic inverse scattering problem with allowance for inelasticity effects on the basis of <Emphasis Type="Italic">N/D</Emphasis> equations and application of the resulting solution to an analysis of nucleon-nucleon interaction

A manifestly Poincaré-invariant approach to solving the inverse scattering problem is developed with allowance for inelasticity effects. The equations of the N/D method are used as dynamical equations in this approach. Two versions of the approach are considered. In the first version (method A), the required equations are constructed on the basis of the maximal-analyticity principle, which constitutes the basis of dynamical S-matrix theory. In formulating the second version of equations (method B), it is assumed that a partial-wave scattering amplitude may develop dynamical singularities that violate the requirement of maximal analyticity. The dynamics of interaction components that violate maximal analyticity is described within the model of a nonlocal separable potential. The method is used to analyze nucleon-nucleon interaction in the ¹S₀ and ³S₁ states. The results obtained by solving the inverse scattering problem for potential functions are compared with the predictions of the one-boson-exchange model.     

Breit-Wigner parameters of the <Emphasis Type="Italic">S</Emphasis><Subscript>11</Subscript>(1535) nucleon resonance

The results of a partial-wave analysis of the angular distributions for the process γp → ηp over the energy range up to 2 GeV are presented. Reliable estimates of the Breit-Wigner parameters of the S₁₁(1535) resonance, as well as the energy dependence of the real and imaginary parts of the electric dipole amplitude E₀₊ and its phase, are derived from the energy dependence of the regression coefficient a₀(W).     

Thermodynamics of the frustrated J<Subscript>1</Subscript>-J<Subscript>2</Subscript> Heisenberg ferromagnet on the body-centered cubic lattice with arbitrary spin

We use the spin-rotation-invariant Green’s function method as well as thehigh-temperature expansion to discuss the thermodynamic properties of the frustratedspin-S J ₁-J ₂ Heisenbergmagnet on the body-centered cubic lattice. We consider ferromagnetic nearest-neighborbonds J ₁<0 and antiferromagnetic next-nearest-neighbor bonds J ₂ ≥ 0 andarbitrary spin S. We find that the transition point\hbox{$J_2^c$}J2cbetween the ferromagnetic ground state and theantiferromagnetic one is nearly independent of the spin S, i.e., it is very closeto the classical transition point\hbox{$J_2^{c,{\rm clas}}= \frac{2}{3}|J_1|$}J2c,clas=23|J1|. At finite temperatures we focus on the parameterregime\hbox{$J_2<J_2^c$}J2<J2cwith a ferromagnetic ground-state. We calculate theCurie temperature T _C (S, J ₂)and derive an empirical formula describing the influence of the frustration parameterJ ₂ and spin S on T _C . We find that theCurie temperature monotonically decreases with increasing frustration J ₂, where veryclose to\hbox{$J_2^{c,{\rm clas}}$}J2c,clasthe T _C (J ₂)-curveexhibits a fast decay which is well described by a logarithmic term\hbox{$1/\textrm{log}(\frac{2}{3}|J_1|-J_{2})$}1/log(23|J1|?J2). To characterize the magnetic ordering below and aboveT _C , we calculate thespin-spin correlation functions ?S ₀ S _R ?, the spontaneous magnetization, the uniform static susceptibilityχ ₀ as well as the correlation lengthξ.Moreover, we discuss the specific heat C _V and the temperaturedependence of the excitation spectrum. As approaching the transition point\hbox{$J_2^c$}J2csome unusual features were found, such as negativespin-spin correlations at temperatures above T _C even though theground state is ferromagnetic or an increase of the spin stiffness with growingtemperature.     

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.     

Role of the Δ-isobar excitation mechanism in the reaction pp → {pp}<Subscript><Emphasis Type="Italic">s</Emphasis></Subscript>π<Superscript>0</Superscript>

The mechanism of Δ-isobar excitation in the intermediate state of the reaction pp → {pp}_sπ⁰, where {pp}_s is a pair of protons in state ¹S₀ at excitation energy E _pp < 3 MeV, is used to calculate the differential cross section of this reaction in the energy range of 0.3–1 GeV. It is shown that the main contribution is made by three partial waves in the pp channel: ³ P ₀, ³ P ₂ and ³ F ₂. The model explains the position of the peak observed at a beam energy of GeV and a zero diproton scattering angle, but cannot describe its absolute value.     

Quark-antiquark composite systems: The Bethe-Salpeter equation in the spectral-integration technique

The Bethe-Salpeter equations for the quark-antiquark composite systems, q\(\bar q\), are written in terms of spectral integrals. For the q\(\bar q\) mesons characterized by the mass M, spin J, and radial quantum number n, the equations are presented for the following (n, M²) trajectories: π _J , η _J , a _J , f _J , ρ _J , ω _J , h _J , and b _J .     

Spin-selective low temperature spectroscopy on single molecules with a triplet-triplet optical transition: Application to the NV defect center in diamond

The spin-selective photokinetics of a single matrix-isolated impurity molecule with a triplet-triplet optical transition, T ₀–T ₁, is considered and the manifestations of the photokinetics in the fluorescence excitation spectra and intensity autocorrelation functions g ⁽²⁾(τ) of the molecule undergoing narrow-band optical excitation is studied to resolve the fine structure of the transition. The rates of intersystem crossings (ISCs) T ₁→S→T ₀ to and from a nonradiating singlet state S of the molecule and the rate of population relaxation among the ground (T ₀) state sublevels can be obtained from the spectra and g ⁽²⁾(τ) using the analytical expressions obtained. New experiments on an individual NV defect center in nanocrystals of diamond, where, for the first time, the fine structure of its triplet-triplet ³ A-³ E zero-phonon optical transition (~637 nm) at 1.4 K was resolved, are interpreted. It is concluded that the rate of the ISC transition from the m _S =0 sublevel of the excited ³ E state to the singlet ¹ A state (~1 kHz) is much slower than the rates from the m _S =±1 substates, while the rates of ISC transitions to different m _S substates of the ground ³ A state are close to each other (~1 Hz). As a result, only the optical transition between m _S =0 sublevels in the ³ A-³ E manifold contributes strongly to the fluorescence. The experimentally observed double-exponential decay of the g ⁽²⁾(τ) function is explained by the two pathways available to the center for it to leave the S state: (i) the S→ T ₀(m _S )=0) transition and (ii) the S→T ⁰(m _S =±1) transitions followed by the slow spin-lattice relaxation T ₀(m _S =±1)→T ₀(m _S =0) (rate ~0.1 Hz). The work is important for studies where the NV center is used as a single photon source or for quantum information processing.     

Diagnosing holographic type dark energy models with the Statefinder hierarchy,composite null diagnostic and <Emphasis Type="Italic">w</Emphasis>-<Emphasis Type="Italic">w′</Emphasis> pair

The main purpose of this work is to distinguish various holographic type dark energy (DE) models, including the ΛHDE, HDE, NADE, and RDE model, by using various diagnostic tools. The first diagnostic tool is the Statefinder hierarchy, in which the evolution of Statefinder hierarchy parmeter S ⁽¹⁾ ₃(z) and S ⁽¹⁾ ₄(z) are studied. The second is composite null diagnostic (CND), in which the trajectories of {S ⁽¹⁾ ₃, ?} and {S ⁽¹⁾ ₄, ?} are investigated, where ? is the fractional growth parameter. The last is w-w′ analysis, where w is the equation of state for DE and the prime denotes derivative with respect to lna. In the analysis we consider two cases: varying current fractional DE density Ω _de0 and varying DE model parameter C. We find that: (1) both the Statefinder hierarchy and the CND have qualitative impact on ΛHDE, but only have quantitative impact on HDE. (2) S ⁽¹⁾ ₄ can lead to larger differences than S ⁽¹⁾ ₃, while the CND pair has a stronger ability to distinguish different models than the Statefinder hierarchy. (3) For the case of varying C, the {w,w′} pair has qualitative impact on ΛHDE; for the case of varying Ω _de0, the {w, w′} pair only has quantitative impact; these results are different from the cases of HDE, RDE, and NADE, in which the {w,w′} pair only has quantitative impact on these models. In conclusion, compared with HDE, RDE, and NADE, the ΛHDE model can be easily distinguished by using these diagnostic tools.     

X-ray photoelectron spectroscopy of FeP phosphide

The structure of the outer and inner electron spectra of iron (2p, 3p, 3s, and 3d) and phosphorus (3s and 3p) atoms in FeP monophosphide is studied in detail by the X-ray photoelectron spectroscopy (XPS) method. On the basis of the analysis of the binding energy of electrons, as well as the parameters characterizing the structure of experimental spectra, a conclusion is made that Fe³⁺ (d ⁵) cations in FeP are stabilized in a state with intermediate value of the total spin (IS, S = 3/2). The range of values of intra-atomic parameters (10Dq, J _H ) is established in which the consideration of the high degree of covalence of Fe–P bonds may lead to the stabilization of (FeP₆)^15– clusters in the IS state.     

Excitation of resonance lines of the cadmium ion by monoenergetic electrons

The excitation of resonance lines at 226.5 and 214.4 nm, corresponding to the transitions 226.5 (5p ² P ₁ ^2/0 →5s ² S _1/2) and 5p ² P ₃ ^2/0 → 5s ² S _1/2, respectively, in the Cd⁺ ion upon collisions with monoenergetic electrons with an energy in the range of 4–130 eV is studied with high precision by a spectroscopic method in crossing beams. It is found that the dependence of the effective excitation cross sections of the resonance doublet components on the energy of the electrons has a distinct resonance structure. It is shown that the dominant mechanism responsible for this structure is the capture of an incident electron by a Cd⁺ ion with the simultaneous excitation of an electron from the subvalence 4d ¹⁰ shell to the autoionizing states of the Cd atom with their subsequent decay (directly or via cascade transitions) to resonance levels of the ion. The results obtained are compared with data from other experiments and with the results of the R-matrix strong-coupling calculation of 15 states and of semiempirical calculation using the Van Regemorter formula.     

Polarization of phosphorescence transitions and probabilities of intramolecular nonradiative deactivation of the lowest triplet state of aromatic molecules

This study continues the experimental testing of the validity of the inductive resonance theory of dipole-dipole energy transfer from the T ₁→S ₀ transition dipole to stretching vibrations of intramolecular CH bonds of naphthalene and its hydroxy derivatives. To this end, in the series of compounds under study, the range of variation of the geometrical parameter [Φ(CH)]² of the Förster theory, which accounts for the mutual orientation of the energy donor and acceptor, is estimated. Preliminarily, the angles between the transition dipole moments of the radiative and absorptive electronic transitions (T ₁→S ₀ and S ₀→S ₁; T ₁→S ₀ and S ₀→S ₂; S ₁→S ₀ and S ₀ →S ₁; and S ₁→S ₀ and S ₀→S ₂) are measured at 77 K by the method of polarization photoselection. From the polarization measurements, the angles between the phosphorescence transition dipole moment and the plane of a molecule are determined. It was found that, upon passage from naphthalene to its β derivatives, the orientation of the dipole moment of the radiative T ₁→S ₀ transition relative to the plane of a molecule markedly changes, with the in-plane component of the dipole moment being increased by an order of magnitude. The experimentally determined rate constants of nonradiative deactivation of the T ₁ state averaged over the CH groups of the naphthalene ring system, k _nr(CH), are compared with the rate constants [Φ(CH)]² of the inductive resonance energy transfer from the dipole of the T ₁→S ₀ transition to the dipole of the CH vibrations polarized in the plane of a molecule, calculated with regard to the orientational factor [Φ(CH)]². This comparison showed that, in the series of compounds under study, a change in the orientation of the dipole moment of the radiative T ₁→S ₀ transition relative to the plane of a molecule does not affect the rate of the nonradiative T ₁?S ₀ transition. This inference is confirmed by the absence of a correlation between the rate constants k _dd(CH) calculated by us (with regard to [Φ(CH)]²) and the well-known rate constants k _nr(CH) of individual sublevels of the T ₁ state measured at T≤1.35 K for a number of organic molecules. The possible sources of discrepancy between the experimental data that k _nr(CH) is independent of [Φ(CH)]² and the predictions of the theory are considered. A conclusion is made that the electronic-vibrational energy transfer between electric dipoles is the most probable mechanism of the T ₁?S ₀ transitions, but the rate constant of the dipole-dipole energy transfer upon interaction of the electronic and vibrational dipoles in a molecule does not depend on their orientations.     

Probabilities of radiative dipole transitions of parahelium in an electric field

Quadratic Stark corrections to the wave functions, matrix elements, and probabilities of transitions between the singlet states ¹ S ₀ and ¹ P ₁ of helium atoms are calculated. The coefficients of the polynomials that depend on the effective principal quantum number of the upper level v _f and that approximate the numerical values of the polarizabilities, the quadratic corrections to the wave functions, and the probabilities of transitions to highly excited Rydberg states with large v _f are determined. The results of calculations testify that the probabilities of all σ transitions n _i ¹ S ₀ → n _f ¹ P ₁ and π transitions to the states with n _f > n _i /2 are decreased with increasing electric field strength, except for the transition 2¹ S ₀ → 2¹ P ₁, whose probability increases both for σ and for π transitions.