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.     

PDM creation and annihilation operators of the harmonic oscillators and the emergence of an alternative PDM-Hamiltonian

The exact solvability and impressive pedagogical implementation of the harmonic oscillator's creation and annihilation operators make it a problem of great physical relevance and the most fundamental one in quantum mechanics. So would be the position-dependent mass (PDM) oscillator for the PDM quantum mechanics. We, hereby, construct the PDM creation and annihilation operators for the PDM oscillator via two different approaches. First, via von Roos PDM Hamiltonian and show that the commutation relation between the PDM creation ${\hat{A}}^{+}$ and annihilation $\hat{A}$ operators, $[\hat{A},{\hat{A}}^{+}]=1\iff \hat{A}{\hat{A}}^{+}-1/2={\hat{A}}^{+}\hat{A}+1/2$, not only offers a unique PDM-Hamiltonian ${\hat{H}}_1$ but also suggests a PDM-deformation in the coordinate system. Next, we use a PDM point canonical transformation of the textbook constant mass harmonic oscillator analog and obtain yet another set of PDM creation ${\hat{B}}^{+}$ and annihilation $\hat{B}$ operators, hence an “apparently new” PDM-Hamiltonian ${\hat{H}}_2$ is obtained. The “new” PDM-Hamiltonian ${\hat{H}}_2$ turned out to be not only correlated with ${\hat{H}}_1$ but also represents an alternative and most simplistic user-friendly PDM-Hamiltonian, $\hat{H}={(\hat{p}/\sqrt{2m\left(x\right)})}^2+V\left(x\right)$; $\hat{p}=-iħ{\partial }_x$, that has never been reported before.     

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.     

Conserved spin current with a perpendicular magnetic field

Previous theoretical studies show that the spin current in spin-orbit coupled systems can be effectively conserved. In this study, we show that in the presence of an external magnetic field B perpendicular to the surface without causing Landau levels, the spin-Hall conductivity, including the conventional spin and spin-torque Hall currents exhibit an interesting symmetry, ${\sigma }_{xy}^c(B)={\sigma }_{xy}^c(-B)$ valid for k-linear and k-cubic Rashba systems. The phenomenon where the electric field generated spin z component is unaltered under $B\to -B$ is attributed to the fact that the spin precession is locked in spin-orbit coupled systems. The perpendicular magnetic field generates spin x and y components, which are linear to B, and thus, there is no time-reversal symmetry. This result provides evidence for the detection of the bulk spin-Hall current. Furthermore, the applied magnetic field breaks the degenerate point of the two-band model, and the resulting spin-Hall conductivity does not vanish even for systems with linear momentum, which implies that the Berry phase is not the principal mechanism in k-linear systems. The non-zero charge-Hall conductivity generated by the perpendicular magnetic field is discussed here.     

Novel electron holes of Gaussian type due to second order,non-perturbative electron trapping and the general loss of identifiability of hole structures in experiments

A second order non-perturbative trapping scenario is employed to show the existence of a new Gaussian type of solitary electron holes. Use is thereby made of Schamel's pseudo-potential method, the only method that can guarantee the completeness of an equilibrium solution of the Vlasov-Poisson system in addition to its existence. The new potential is of the form $e^{-X{(x)}^2}$ where $X(x)=sinh(x)$ and is hence reminiscent of the Gaussian potential appearing in its “second generation”. The simultaneous presence of both trapping generations hence establishes a one-parametric continuum spectrum of solitary electron holes all of them being, through appropriate fitting, potential candidates for identifying structures in experimental observations and numerical simulations. Taking into account the possibility of many more trapping scenarios moreover, a unique identification of structures, the desired goal expressed in the current literature when interpreting structure formation, is therefore not achievable. Origin of this intrinsic ambiguity is the loss of mathematical stringency in the kinetic regime through chaos triggered by the ergodic particle trajectories in the resonant region of phase space in the single particle – coherent wave interaction process.     

Thermodynamic calculation of spin scaling functions

Critical phenomena theory centers on the scaled thermodynamic potential per spin $?(\beta ,h)=|t{|}^{p}Y(h|t{|}^{?q})$, with inverse temperature $\beta =1/T$, $h=?\beta H$, ordering field H, reduced temperature $t=t(\beta )$, critical exponents p and q, and function $Y(z)$ of $z=h|t{|}^{?q}$. I discuss calculating $Y(z)$ with the information geometry of thermodynamics. Scaled solutions are found to obtain with three admissible functions $t(\beta )$: 1) $t=e^{?J\beta }$, 2) $t={\beta }^{?1}$, and 3) $t={\beta }_C?\beta$, where J and ${\beta }_C$ are constants. For $p=q$, information geometry yields $Y(z)=\sqrt{1+z^2}$, consistent with the one-dimensional (1D) ferromagnetic Ising model.     

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.     

PDM-charged particles in PD-magnetic plus Aharonov–Bohm flux fields: Unconfined “almost-quasi-free” and confined in a Yukawa plus Kratzer exact solvability

Using azimuthally symmetrized cylindrical coordinates, we consider some position-dependent mass (PDM) charged particles moving in position-dependent (PD) magnetic and Aharonov–Bohm flux fields. We focus our attention on PDM-charged particles with $m\left(\overrightarrow{r}\right)=g\left(\rho \right)=\eta f\left(\rho \right)\exp (-\delta \rho )$ (i.e., the PDM is only radially dependent) moving in an inverse power-law-type radial PD-magnetic fields $\overrightarrow{B}=B_{\circ }(\mu /{\rho }^{\sigma })\widehat{z}$. Under such settings, we consider two almost-quasi-free PDM-charged particles (i.e., no interaction potential, $V\left(\overrightarrow{r}\right)=0$) endowed with $g\left(\rho \right)=\eta /\rho$ and $g\left(\rho \right)=\eta /{\rho }^2$. Both yield exactly solvable Schrödinger equations of Coulombic nature but with different spectroscopic structures. Moreover, we consider a Yukawa-type PDM-charged particle with $g\left(\rho \right)=\eta \exp (-\delta \rho )/\rho$ moving not only in the vicinity of the PD-magnetic and Aharonov-Bohm flux fields but also in the vicinity of a Yukawa plus a Kratzer type potential force field $V\left(\rho \right)=-V_{\circ }\exp (-\delta \rho )/\rho -V_{{}_1}/\rho +V_{{}_2}/{\rho }^2$. For this particular case, we use the Nikiforov-Uvarov (NU) method to come out with exact analytical eigenvalues and eigenfunctions. Which, in turn, recover those of the almost-quasi-freePDM-charged particle with $g\left(\rho \right)=\eta /\rho$ for $V_{\circ }=V_{{}_1}=V_{{}_2}=0=\delta$. Energy levels crossings are also reported.