Resonance studies using the contour deformation method in the complex momentum plane

A contour deformation method (CDM) in the complex momentum plane has been successfully extended and implemented to probe resonances in atomic and molecular systems. Specifically, solution of the Schrödinger equation is performed in momentum space with momentum deformed on a contour in the complex plane. The bound, resonant, and complex continuum states could be directly revealed from the eigenvalues of the Schrödinger equation in the complex momentum plane. The calculations of shape resonances in electron scattering with Na⁺ in Debye plasmas (one channel), and in the charge transfer process ${\mathrm{H}}^{?}(1s^2)+\mathrm{Li}(1s^{2}2s)$ ($1^2{\Sigma }^{+}$) $\to \mathrm{H}(1s)+{\mathrm{Li}}^{?}(1s^{2}2s^2)$ ($2^2{\Sigma }^{+}$) (coupled channels) are given as illustrative examples. It is shown that calculated results from CDM agree very well with those extracted from the eigenphase sum of scattering theories. The effectiveness of CDM is also demonstrated by comparing its results with those obtained by the complex rotation scaling and exterior complex scaling methods. The convergence of CDM results can be obtained by increasing the momentum integration region and the number of integration points. The studied examples demonstrate that CDM could be a powerful tool for studies of resonances in complex atomic and molecular systems.     

On the redox reactions between allyl radicals and NOx

NO_x mitigation is a central focus of combustion technologies with increasingly stringent emission regulations. NO_x can also enhance the autoignition of hydrocarbon fuels and can promote soot oxidation. The reaction between allyl radical (C₃H₅) and NO_x plays an important role in the oxidation kinetics of propene. In this work, we measured the absolute rate coefficients for the redox reaction between C₃H₅ and NO_x over the temperature range of 1000–1252 K and pressure range of 1.5–5.0 bar using a shock tube and UV laser absorption technique. We produced C₃H₅ by shock heating of C₃H₅I behind reflected shock waves. Using a Ti:Sapphire laser system with frequency quadrupling, we monitored the kinetics of C₃H₅ at 220 nm. Unlike low-temperature chemistry, the two target reactions, C₃H₅ + NO → products (R1) and C₃H₅ + NO₂ → products (R2), exhibited a strong positive temperature dependence for this radical-radical type reaction. However, these reactions did not show any pressure dependence over the pressure range of 1.5–5.0 bar, indicating that the measured rate coefficients are close to the high-pressure limit. The measured values of the rate coefficients resulted in the following Arrhenius expressions (in unit of cm³/molecule/s):$k_1\left({\mathrm{C}}_3{\mathrm{H}}_5+\text{NO}\right)=1.49\times {10}^{?10}\exp \left(?6083.6\frac{\mathrm{K}}{T}\right)\left(1017?1252K\right)$$k_2\left({\mathrm{C}}_3{\mathrm{H}}_5+\mathrm{N}{\mathrm{O}}_2\right)=1.71\times {10}^{?10}\exp \left(?3675.7\frac{\mathrm{K}}{T}\right)\left(1062?1250K\right)$To our knowledge, these are the first high-temperature measurements of allyl + NO_x reactions. The reported data will be highly useful in understanding the interaction of NO_x with resonantly stabilized radicals as well as the mutual sensitization effect of NO_x on hydrocarbon fuels.     

Experimental determination of interfacial energy for solid Al in the Al-Sn-Mg eutectic system with Bridgman-type apparatus

The equilibrated grain boundary groove shape of solid Al in equilibrium with Al-Sn-Mg eutectic liquid was observed by using a Bridgman type directional solidification apparatus. The ratio of the thermal conductivity of the equilibrated liquid to the thermal conductivity of solid Al has been obtained as 0.91. In addition, the average Gibbs-Thomson coefficient, $\bar{\mathrm{\Gamma }}=(4.20\pm 0.35)\times {10}^{-8}\mathrm{Km}$, the solid-liquid interfacial energy, ${\sigma }_{SL}=180.68\pm 23.48\text{mJ}/{\text{m}}^2$ and the grain boundary energy, ${\sigma }_{GB}=309.30\pm 29.47\text{mJ}/{\text{m}}^2$, in the Al/Al-Sn-Mg system have been calculated from the measured grain boundary shapes.     

Investigation of the kinetics of conjugated diolefins using UV absorption spectroscopy

Conjugated diolefins are not only crucial intermediates in larger hydrocarbon pyrolysis and oxidation, but also key species in the formation and growth of polycyclic aromatic hydrocarbons (PAHs). In this work, we employed a sensitive UV laser diagnostic to measure absorption cross-sections and decomposition rates of three conjugated diolefins, namely 1,3-butadiene, 2-methyl-1,3-butadiene (isoprene), and 2,3-dimethyl-1,3-butadiene. The single-pass UV absorption diagnostic achieved a ppm-level detection limit between the wavelengths of 212.5 and 220.5 nm. The use of dilute conditions (119 – 500 ppm fuel in argon) enabled nearly isothermal measurements despite reaction enthalpy. Temperature-dependent absorption cross-sections were measured from room temperature to 1850 K and pressures ranging 0.75 – 1.50 bar in a shock tube. Decomposition of the molecules was observed at temperatures above ∼ 1350 K, and all three molecules exhibited similar activation energy. Around 1800 K, 2,3-dimethyl-1,3-butadiene decomposed twice as fast as isoprene and 4 times faster than 1,3-butadiene. Our measured overall decomposition rate coefficients are given as (unit of s ^− 1, ± 20% uncertainty):$\begin{array}{ccc}& & k_1\left(1,3-\text{butadiene}\right)=9.65\times {10}^9{e}^{\left(\frac{-24,338K}{T}\right)}(1411-1823\mathrm{K})\hfill \\ & & k_2\left(\text{isoprene}\right)=1.86\times {10}^{10}{e}^{\left(\frac{-24,341K}{T}\right)}(1464-1829\mathrm{K})\hfill \\ & & k_3\left(2,3-\text{dimethyl}-1,3-\text{butadiene}\right)=8.64\times {10}^{10}{e}^{\left(\frac{-25,845K}{T}\right)}(1401-1822\mathrm{K})\hfill \end{array}$1,3-Butadiene decomposition rate coefficients agree well with previous measurement at similar pressures. To our knowledge, this work reports first measurements of the decomposition rate coefficients of isoprene and 2,3-dimethyl-1,3-butadiene. As an additional application of the current UV diagnostic, we measured 1,3-butadiene decay time-histories during fuel-lean oxidation and compared our data with the predictions of AramcoMech 3.0. We updated the model with our measured 1,3-butadiene decomposition rate coefficients, which significantly improved the model prediction of fuel oxidation.     

Exchange bias behavior and magnetocaloric effect in Ni2In-type Mn7Sn4 alloy

In this work, the exchange bias behavior and magnetocaloric effect have been studied in Mn₇Sn₄ alloy. The X-ray powder diffraction pattern recorded at room temperature indicates that the sample crystallizes in a single phase with Ni₂In-type hexagonal structure (space group $P{6}_3/\mathit{mmc}$). The maximum magnetic entropy change value across paramagnetic/ferrimagnetic transition is about 3.3 J kg⁻¹ K⁻¹ under the magnetic field change of ${\mu }_0\mathrm{\Delta }H=0\text{-}5\text{T}$. With further cooling, the reentrant spin-glass-like state is obtained below 150 K, for which the exchange bias effect has been observed. The exchange bias field is ∼7.8 mT and ∼6.7 mT at $T=10\text{K}$ when the cooling field is ${\mu }_0{H}_{\mathrm{CF}}=0.1\text{T}$ and 0.5 T, respectively. The magnetic behavior and the origin of exchange bias in Mn₇Sn₄ are discussed.     

New findings for two new type sine hyperbolic potentials

We propose two new type sine hyperbolic potentials $V(x)=a^2{\sinh }^2?(x)?k{\tanh }^2?(x)$ and $V(x)=c^2{\sinh }^4?(x)?k{\tanh }^2?(x)$. They may become single- or double-well potentials depending on the potential parameters $a,c$ and k. We find that its exact solutions can be written as the confluent Heun functions $H_c(\alpha ,\beta ,\gamma ,\delta ,\eta ;z)$, in which the energy level E is involved inside the parameter η. The properties of the wave functions, which is strongly relevant for the potential parameters $a,c$ and k, are illustrated.     

A Family-nonuniversal U(1)′ Model for Excited Beryllium Decays

Excited beryllium has been observed to decay into electron-positron pairs with a $6.8\sigma$ anomaly. The process is properly explained by a 17 MeV proto-phobic vector boson. In present work, we consider a family-nonuniversal $U{\left(1\right)}^{\prime }$ that is populated by a $U{\left(1\right)}^{\prime }$ gauge boson $Z^{\prime }$ and a scalar field $S,$ charged under $U{\left(1\right)}^{\prime }$ and singlet under the Standard Model (SM) gauge symmetry. The SM chiral fermion and scalar fields are charged under $U{\left(1\right)}^{\prime }$ and we provide them to satisfy the anomaly-free conditions. The Cabibbo-Kobayashi-Maskawa (CKM) matrix is reproduced correctly by higher-dimension Yukawa interactions facilitated by $S$. The vector and axial-vector current couplings of the $Z^{\prime }$ boson to the first generation of fermions do satisfy all the bounds from the various experimental data. The $Z^{\prime }$ boson can have kinetic mixing with the hypercharge gauge boson and $S$ can directly couple to the SM-like Higgs field. The kinetic mixing of $Z^{\prime }$ with the hypercharge gauge boson, as we show by a detailed analysis, generates the observed beryllium anomaly. We find that beryllium anomaly can be properly explained by a MeV-scale sector with a minimal new field content. The minimal model we construct forms a framework in which various anomalous SM decays can be discussed.     

The investigation of structural,electronic, elastic and thermodynamic properties of Gd1−xYxAuPb alloys: A first principle study

First principle calculations have been employed to investigate the effects of Y concentration, pressure and temperature on various properties of ${\mathrm{Gd}}_{1?x}{\mathrm{Y}}_x\mathrm{AuPb}$ ($x=0,0.25,0.5,0.75,1$) alloys using density functional theory (DFT). The full potential linearized augmented plane wave (FP-LAPW) method within a framework of the generalized gradient approximation (GGA) is used to perform the calculated results of this paper. Phase stability of ${\mathrm{Gd}}_{1?x}{\mathrm{Y}}_x\mathrm{AuPb}$ alloys is studied using the total energy versus unit cell volume calculations. The equilibrium lattice parameters of these alloys are in good agreement with the available experimental results. The mechanical stability of ${\mathrm{Gd}}_{1?x}{\mathrm{Y}}_x\mathrm{AuPb}$ alloys is proved using elastic constants calculations. Also, the influence of Y concentration on elastic properties of ${\mathrm{Gd}}_{1?x}{\mathrm{Y}}_x\mathrm{AuPb}$ alloys such as Young's modulus, shear modulus, Poisson's ratio and anisotropy factor are investigated and analyzed. By considering both Pugh's ratio and Poisson's ratio, the ductility and brittleness of these alloys are studied. In addition, the total density of states and orbital's hybridizations of different atoms are investigated and discussed. Moreover, the effect of pressure and temperature on some important thermodynamic properties is investigated.     

Exploring new insights in BAlN from evolutionary algorithms ab initio computations

BN-AlN alloys are potential candidates to achieve wide band gap material for ultraviolet device applications. By combing density functional theory and evolutionary structure predictions, we systematically explore the thermodynamic, mechanical, dynamical and optical properties of ${\mathrm{B}}_x{\mathrm{Al}}_{1?x}\mathrm{N}$ alloys. Through structure search, three compounds (cubic ($\mathrm{B}{\mathrm{Al}}_3{\mathrm{N}}_4$, and ${\mathrm{B}}_3\mathrm{Al}{\mathrm{N}}_4$, space group P-43m), and tetragonal ($\mathrm{B}\mathrm{Al}{\mathrm{N}}_2$, space group P-42m)) have been predicted. The calculated relative large formation enthalpies suggest that large miscibility gap exists in BAlN alloys. In addition, computed elastic constants and phonon show that these structures are mechanically and dynamically stable. From the state of the art LDA-1/2 we show that the direct band gap of BN-AlN evinces strong deviation from a linear dependence on B composition. We found -in particular- giant direct band gap bowing parameter of $b～11.6$ eV for the entire range of composition, where b parameter is found to be sensitive to composition x. From a detailed analysis of the physical origin of the optical gap bowing b, we found that structural and chemical contributions play the most significant effects behind the huge optical band gap bowing parameter of BAlN alloys.     

Asymptotic behavior of two-electron expectation values in two-electron excited states

Singly-excited states of the two-electron atom cease being bound when $Z\to 1$ (from above), the outer orbital becoming infinitely diffuse. The asymptotic relations$\underset{Z\to 1}{\lim }?{(Z?1)}^k〈{(1sns)}^{1,3}S\left|r_{12}^k\right|{(1sns)}^{1,3}S〉=〈(n?1)s^{(0)}\left|r^k\right|(n?1)s^{(0)}〉,$ where $k=?1,1,2,3,?$, are demonstrated to hold. Here, $(n?1)s^{(0)}$ is a hydrogenic s orbital with principal quantum number $(n?1)$. New, more nuanced light is shed on the already challenged dogma that the Pauli principle keeps the electrons further apart in the triplet than in the corresponding singlet.