Transition probabilities in Nd(II) and the solar neodymium abundance

We have measured branching ratios for all the known transitions from nine levels in Nd⁺. We use the known mean lifetimes of four of these levels to compute transition probabilities for 60 transitions. We have measured the solar equivalent widths of 12 of these lines on the Preliminary Edition of the Kitt Peak Solar Atlas and compute a photospheric Nd abundance $\text{log}\text{(}\text{N}{}_{\mathrm{<mtext>Nd</mtext>}}\text{N}{}_{\mathrm{<mtext>H</mtext>}}\text{)+12 = 1.26±0.14}$, using the solar model parameters of Righini and Rigutti based on the Mutschlecner model. The solar lines used in this computation are weak ($\text{W}\text{λ}$<3×10^-6), and the derived abundance has little dependence on the uncertainties of the solar model.     

Transition probabilities in Sm(II) and the solar abundance of Samarium

We have measured branching ratios for all of the known transitions from nine levels in Sm(II). We use the known mean radiative lifetime for three of these levels to compute the transition probability for 65 transitions from these upper levels. Using the equivalent widths from the Utrecht Atlas and the Preliminary Edition of the Kitt Peak Atlas for four weak solar lines with $\text{W}\text{λ}\text{? 5 × 10}{}^{-6}$, we compute a photospheric Sm abundance log $\text{N}{}_{\mathrm{Sm}}\text{N}{}_{\mathrm{H}}\text{+ 12 = 0.80 ± 0.11}$.     

Phase structure and critical behavior of multi-Higgs U(1) lattice gauge theory in three dimensions

We study the three-dimensional (3D) compact U(1) lattice gauge theory coupled with N-flavor Higgs fields by means of the Monte Carlo simulations. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in easy plane, inflational cosmology, etc. It is known that there is no phase transition in the N = 1 model. For N = 2, we found that the system has a second-order phase transition line in the c₂ (gauge coupling)-c₁ (Higgs coupling) plane, which separates the confinement phase and the Higgs phase. Numerical results suggest that the phase transition belongs to the universality class of the 3D XY model as the previous works by Babaev et al. and Smiseth et al. suggested. For N = 3, we found that there exists a critical line similar to that in the N = 2 model, but the critical line is separated into two parts; one for c₂<c_2tc=2.4±0.1 with first-order transitions, and the other for c_2tc<c₂ with second-order transitions, indicating the existence of a tricritical point. We verified that similar phase diagram appears for the N = 4 and N = 5 systems. We also studied the case of anistropic Higgs coupling in the N = 3 model and found that there appear two second-order phase transitions or a single second-order transition and a crossover depending on the values of the anisotropic Higgs couplings. This result indicates that an “enhancement” of phase transition occurs when multiple phase transitions coincide at a certain point in the parameter space.     

Calculation of collisional and radiative transition probabilities between excited argon levels

Average radiative transition probabilities for argon atoms have been calculated for transitions between 24 levels in two groups characterized by the atomic core terms ²P_1/2 and ²P_3/2 by using the method of Bates and Damgaard. The results are compared with data in the NBS tables (Wiese et al.) and with those of Katsonis and Drawin. We find satisfactory agreement for the order of magnitude, even for transitions between lower lying levels. Parameters, which appear in Drawin's semiempirical cross-section expressions for electronic excitation of optically allowed and parity-forbidden transitions, are determined with the multipole expansion method proposed by Sobel'man for transitions between the specified levels. Most of these are easily obtained, but the method must be improved for transitions between levels having the same azimuthal quantum number because the summation over the constituent terms does not converge.     

Infrared spectrum involving forbidden transitions & coriolis interaction and identification of optically pumped far infrared laser lines in asymmetrically mono-deuterated methanol (Methanol-D1)

In this paper new type of ΔK = 2 and 0 transitions have been identified in the Fourier Transform spectrum of Methanol-D₁ (CH₂DOH). These transitions are normally forbidden but a “Coriolis” type interaction with nearby states is believed to be contributing sufficient transition strength through intensity borrowing effect. This is the first time such forbidden transitions are reported to be identified in the excited states, in this molecule. The present conjecture is supported by observation of a many strong allowed transitions to upper terminating levels which are seen to be highly perturbed. This conclusion has been reached by comparing calculated energy levels using known molecular parameters (Pearson et al., 2012; Coudert et al., 2014; El Hilali et al., 2011; Quade et al., 1998; Richard Quade, 1998, 1999; Mukhopadhyay, 1997) and the actually observed FIR lines. The upper levels are seen to be upshifted from expected position. A closer look at the calculated energy values seems to indicate a possible interaction between the above states and other proximate torsional–rotational states could occur. The possible candidates for the interacting level manifolds are narrowed down through the presence of the forbidden transition. We also take the opportunity to propose alternate rotational quantum numbers for some of the assignments recently reported in the literature (El Hilali et al., 2011). Some ambiguities are pointed out on the data and the reported analysis. There remain too many such irregularities and we propose to gather a large body assigned transitions in a future catalog. Assignments and relevant comments on optically pumped FIR laser radiation are also made.     

Magnetic phases of bismuth ferrite

We have recently shown that BiFeO₃ has at least four different magnetic phases, contrary to the conventional wisdom. Below room temperature it undergoes spin reorientation transitions at T₂=200 K and T₁=140 K analogous to those in orthoferrites; and above room temperature it undergoes a structural transition near 185°C first reported by Polomska et al. This may help explain the apparent linear magnetoelectric effect at 20°C reported by D. Lebeugle et al. [Phys. Rev. Lett. 100, 227602 (2008)] which is nominally forbidden due to the long wavelength cycloidal spin structure assumed. We also find evidence of an unusual acentric spin glass below ca. 200 K, related not to T_N but to T₁ and T₂.     

Lattice effects in singlet ground state systems

We have investigated elastic, magnetic, thermal and structural properties of systems which exhibit induced magnetic behavior (TbP, PrSn₃, Pr₃Se₄, Pr₃Te₄). Particular emphasis is given to phonon effects due to the crystalline electric field, phase transitions, and magnetic fields. TbP has a first order magnetic phase transition and both TbP, PrSn₃ show a temperature dependence of the elastic constants, which can be explained with the known crystal field level scheme. The compounds Pr₃S₄, La₃S₄, Pr₃Se₄ exhibit structural instabilities at much higher temperatures than the magnetic or superconducting transition temperatures. Pr₃Te₄ does not exhibit a structural transition, but a strong elastic softening in a magnetic field. This effect is due to strong field dependent quadrupole transitions. All these systems are analyzed with respect to typical induced moment parameters.     

Optical absorption and emission properties of Pr and Er in lithium cesium mixed alkali borate glasses

This article presents the optical absorption and emission properties of Pr³⁺ and Er³⁺ in mixed alkali borate glasses of the type 68B₂O₃·xLi₂O·(32-x)Cs₂O (where x=8, 12, 16, 20 and 24). The variation of Judd-Ofelt intensity parameters (Ω_λ), the peak wavelength of the hypersensitive transitions, radiative transition probabilities (A_rad) and peak emission cross-sections (σ_p) with x in the glass matrix have been discussed in detail. The changes in position of hypersensitive transition and intensity parameters with x are correlated to the structural changes in the host matrix. The estimated radiative lifetimes (τ_R) of certain excited states of both Pr³⁺ and Er³⁺ in lithium cesium mixed alkali borate glasses are reported. Branching ratios (β) and integrated absorption cross-sections (Σ) for certain important transitions are presented. Peak stimulated emission cross-sections (σ_p) are calculated for the observed emission peaks of Pr³⁺ and Er³⁺ ions in this glass matrix.     

Reunion Probability of N Vicious Walkers: Typical and Large Fluctuations for Large N

We consider three different models of N non-intersecting Brownian motions on a line segment [0,L] with absorbing (model A), periodic (model B) and reflecting (model C) boundary conditions. In these three cases we study a properly normalized reunion probability, which, in model A, can also be interpreted as the maximal height of N non-intersecting Brownian excursions (called “watermelons” with a wall) on the unit time interval. We provide a detailed derivation of the exact formula for these reunion probabilities for finite N using a Fermionic path integral technique. We then analyze the asymptotic behavior of this reunion probability for large N using two complementary techniques: (i) a saddle point analysis of the underlying Coulomb gas and (ii) orthogonal polynomial method. These two methods are complementary in the sense that they work in two different regimes, respectively for $L\ll O(\sqrt{N})$ and $L\geq O(\sqrt{N})$ . A striking feature of the large N limit of the reunion probability in the three models is that it exhibits a third-order phase transition when the system size L crosses a critical value $L=L_{c}(N)\sim\sqrt{N}$ . This transition is akin to the Douglas-Kazakov transition in two-dimensional continuum Yang-Mills theory. While the central part of the reunion probability, for L～L _c (N), is described in terms of the Tracy-Widom distributions (associated to GOE and GUE depending on the model), the emphasis of the present study is on the large deviations of these reunion probabilities, both in the right [L?L _c (N)] and the left [L?L _c (N)] tails. In particular, for model B, we find that the matching between the different regimes corresponding to typical L～L _c (N) and atypical fluctuations in the right tail L?L _c (N) is rather unconventional, compared to the usual behavior found for the distribution of the largest eigenvalue of GUE random matrices. This paper is an extended version of (Schehr et al. in Phys. Rev. Lett. 101:150601, 2008) and (Forrester et al. in Nucl. Phys. B 844:500–526, 2011).     

Energies and widths of atomic core-levels in liquid mercury

High-resolution measurements of the photoinduced X-ray emission of liquid mercury were performed, using a transmission DuMond-type crystal spectrometer for transitions above 11 keV and a reflection von Hamos-type crystal spectrometer for transitions below 11 keV. The target X-ray fluorescence was produced by irradiating the sample with the Bremsstrahlung from X-ray tubes. The energies and natural linewidths of 6 K-shell, 26 L-shell and 2 M-shell X-ray transitions were determined. Using a least-squares-fit method to solve the two sets of equations derived from the observed transition energies and transition widths the binding energies of the subshells K to M₅ and O₁ and the level widths of the subshells K to N₅ and O₁ could also be determined.     

Probabilities for electronic transitions of molecular systems of high-temperature air components—I. The schumann-runge system of the O2-molecule and the first positive system of the N2-molecule

The results for absolute and relative probabilities for electronic transitions of the Schumann-Runge system of the O₂-molecule and the first positive system (1+) of the N₂-molecule published elsewhere have been critically analyzed. For the S-R system, statistical processing of the experimental results for absolute and relative probabilities on a joint basis made it possible to establish a new dependence of the electronic transition strength on the internuclear separations S_e(r_v′v″), which reliably describes the behaviour of S_e over the whole spectral range. For the (1+) system of the N₂-molecule, it has been shown that none of the published dependences S_e(r_v′v″) provide acceptable fits to the measured results on absolute intensities and life-times. In practical calculations, one should use the dependence given in Ref. 41, which is derived from relative intensities and corroborated by absolute intensity measurements.     

Supersymmetry and electromagneticE2 transitions

We discuss the quadrupole electric transitions in the frame of the supersymmetric model for light nuclei (s —d shell). We present the construction of an isoscalar transition operator based on the assumption of the dynamicalSO ^BF (6) symmetry. Theoretical transition probabilities for nuclei belonging to the supermultiplet characterized by a particle numberN=5 show quite a good agreement with experimental data.     

Luminescent properties of trivalent praseodymium-doped lanthanum aluminum germanate LaAlGe2O7

The luminescent characteristics of Pr³⁺-activated LaAlGe₂O₇ were investigated. In response to excitement using 448 nm blue light, the emission spectra involved most of the ³P₀→³H_J transitions. The dominant emission came from the ³P₀→³H₄ transition at 487 nm. ¹D₂ fluorescence quenching was observed in highly doped samples and is related to the cross-relaxation processes among neighboring Pr³⁺ ions. In contrast with conventional Pr³⁺-activated phosphors, the extraordinary excitation spectra showed only intense f-f transition of Pr³⁺ ions, while the 4f-5d transition was eliminated. This is ascribed to photoionization. By analyzing absorption and excitation spectra, it is recognized that no efficient energy transfer occurs between Pr³⁺ and the host lattice in LaAlGe₂O₇.     

Absorption and emission spectra of yttria-stabilized zirconia and magnesium oxide

We have investigated the luminescence and absorption spectra of doped and undoped ZrO₂-Y₂O₃ and MgO crystals at room- and low temperatures. The crystals used are partly doped with the transition metals Ni, Co, Cr and the rare earth Pr. The emission spectra were obtained under laser excitation at different wavelengths. The observed optical emission and absorption bands of the MgO crystals doped with Ni, Co and Cr correspond to transitions between spin-orbit split crystal field levels of the transition metals. Luminescence and absorption bands of undoped yttria-stabilized zirconia (YSZ) crystals are due to color centers, absorption bands of the doped YSZ correspond to the well known transitions of the Ni²⁺, Co²⁺ and Pr³⁺ ions, respectively. The emission spectra of the doped YSZ obtained under various laser excitations can be explained by an energy transfer process between the color center and the doping materials. The influence of annealing on the absorption and emission of Pr³⁺/Pr⁴⁺ is investigated.     

Spectroscopic characteristics of praseodymium-doped cubic double sodium-yttrium fluoride crystals Na0.4Y0.6F2.2:Pr3+. Intensities of optical transitions and luminescence kinetics

Using the Bridgman-Stockbarger technique, we have grown a series of cubic crystals Na_0.4Y_0.6F_2.2:Pr³⁺ (NYF:Pr³⁺) with a content of praseodymium in the range of 0.04–9 at %. We have determined the composition of crystals, evaluated their optical quality, and found the incorporation coefficient of Pr³⁺ ions into the Na_0.4Y_0.6F_2.2 matrix (K _Pr ～ 0.9). We have examined optical spectra of NaYF:Pr³⁺ crystals at room and low (7 K) temperatures in the range of 200–2500 nm. The low-temperature absorption spectra of NYF:Pr³⁺ crystals have been shown to consist of broad weakly structured bands. Based on the analysis of low-temperature absorption spectra, the structure of the Stark splitting of praseodymium levels has been represented in terms of a model of “quasi-centers,” which are characterized by an inhomogeneous broadening of Stark components. From experimental absorption cross-section spectra at T = 300 K, we have calculated oscillator strengths for transitions from the ground state ³ H ₄ to excited multiplets ³ H ₅, ³ H ₆, ³ F _j (j = 2, 3, 4), ¹ G ₄, ¹ D ₂, and (³ P _j ,¹ I ₆) (j = 0, 1, 2). Using the Judd-Ofelt method, we have determined intensity parameters Ω _t and found that Ω₂ = 0, Ω₄ = 4.4 × 10^?20, and Ω₆ = 2.28 × 10^?20 cm². With these values, we have calculated the probabilities of radiative transitions, the branching coefficients, and the lifetimes of the radiative levels ¹ D ₂ and ³ P ₀. The probabilities of multiphonon nonradiative transitions in NYF:Pr³⁺ crystals have been estimated. Using the method of kinetic spectroscopy with selective excitation, we have investigated the luminescence decay kinetics of praseodymium from the ³ P ₀ and ¹ D ₂ levels upon their selective resonant excitation by nanosecond laser pulses. The inference has been made that Na_0.4Y_0.6F_2.2:Pr³⁺ crystals are processable; admit doping by praseodymium in high concentrations; and, with respect to all their radiative characteristics, can be potentially considered as active media for converters of optical radiation and solid-state continuously tunable lasers in the visible range.     

Water vapor line width and shift calculations with accurate vibration-rotation wave functions

Calculations of H₂¹⁶O rotation-vibration line broadening and shifting due to N₂ pressure effects are performed using a semi-empirical approach. The calculations are based on impact theory modified by introducing additional parameters to extend the use of empirical data. These model parameters are determined by fitting the broadening and shifting coefficients to experimental data. The method is further developed by using anharmonic wavefunctions in the estimates of the line profiles. The main feature of the present calculation is the use of a complete set of high-accuracy vibration-rotation dipole transition moments calculated for all possible transitions using wavefunctions determined from variational nuclear motion calculations and an ab initio dipole moment surface. This approach explicitly takes into account all scattering channels induced by collisions. Results of these calculations clearly demonstrate improved agreement between observed and calculated parameters for both the line widths and the line shifts.     

An improved mean field approach to the phase structure in ZN gauge theory in four dimensions

We extend the mean field approximation scheme to include the effect of fluctuation of the gauge field. As a consequence, we successfully obtain for the Z_N theory (N > 5) the phase transition which separates the Coulomb phase from the ordered phase, as well as that separating the Coulomb and disordered phases. The former transition shows characteristics of higher-order phase transitions.     

Decay of correlations in vibrational relaxation

We investigate the decay of initial vibrational correlations in a dilute gas mixture of diatomic molecules and structureless particles. We use the techniques of Davis and Oppenheim to derive an equation for vibrational relaxation which is suitable for correlated systems. We then use the Landau-Teller transition probabilities and solve for the one-and two-molecule distribution functions and the two-molecule correlation functions. We find that the correlations decay faster than the distribution functions, which agrees with the results of Oppenheim, Shuler,et al. for other systems.     

Absolute Transition Probabilities and Oscillator Strengths for Kr II Transitions

Absolute transition probabilities and oscillator strengths for 28 lines belonging to Kr II spectrum were measured. The lines were obtained in a highly repetitive pulsed source where a capillar tube (3 mm internal diameter, 80 cm long) is crossed by a high current pulse (700 to 1600 A). Relative transitions probabilities are obtained after measurement of peak intensities and Stark line widths, using a simple relation. Absolute A_ij values were determined by using experimental values of the lifetime of the level 5p ⁴D_7/2 >.