Positron annihilation in the MuPs system

The life-time of the four-body atomic system MuPs ($\mu^{+} e^{-}_2 e^{+}$ or muonium-positronium) against positron annihilation has been evaluated as $\tau = \frac{1}{\Gamma} \approx 4.076453 \cdot 10^{-10}$ $sec$. Various annihilation rates for MuPs are determined to a good numerical accuracy, e.g., $\Gamma_{2 \gamma} \approx$ 2.446485$\cdot 10^{9}$ $sec^{-1}$, $\Gamma_{3 \gamma} \approx$ 6.62798$\cdot 10^{6}$ $sec^{-1}$, $\Gamma_{4 \gamma} \approx$ 3.61680$\cdot 10^{3}$ $sec^{-1}$, $\Gamma_{5 \gamma} \approx$ 6.32973 $sec^{-1}$. The hyperfine structure splitting for the ground state in the MuPs system has also been evaluated as $\Delta$ = 23.078 $MHz$

A modified Poisson-Boltzmann theory: Effects of co-solvent polarizability

In this paper within a field-theoretical approach taking into account explicitly a co-solvent with a nonzero dipole and a polarizability tensor, we derive a modified Poisson-Boltzmann equation. Applying the modified Poisson-Boltzmann equation, we formulate a generalized Gouy-Chapman theory for the case when an electrolyte solution is mixed with a polar co-solvent having a large polarizability. We show that an increase of the co-solvent concentration as well as the co-solvent polarizability lead to a significant increase of differential capacitance at sufficiently high surface potentials of the electrode, whereas the profile of the electrostatic potential becomes considerably more long-ranged. On the contrary, an increase in the permanent dipole of the co-solvent only weakly affects the differential capacitance

A flexible polymer chain in a critical solvent: Coil or globule?

We study the behavior of a flexible polymer chain in the presence of a low-molecular weight solvent in the vicinity of a liquid-gas critical point within the framework of a self-consistent field theory. The total free energy of the dilute polymer solution is expressed as a function of the radius of gyration of the polymer and the average solvent number density within the gyration volume at the level of the mean-field approximation. Varying the strength of attraction between polymer and solvent we show that two qualitatively different regimes occur at the liquid-gas critical point. In case of weak polymer-solvent interactions the polymer chain is in a globular state. On the contrary, in case of strong polymer-solvent interactions the polymer chain attains an expanded conformation. We discuss the influence of the critical solvent density fluctuations on the polymer conformation. The reported effect could be used to excert control on the polymer conformation by changing the thermodynamic state of the solvent. It could also be helpful to estimate the solvent density within the gyration volume of the polymer for drug delivery and molecular imprinting applications

On the Ado Theorem for finite Lie conformal algebras with Levi decomposition

We prove that a finite torsion-free conformal Lie algebra with a splitting solvable radical has a finite faithful conformal representation.Comment: 11 page

Stability and hyperfine structure of the four- and five-body muon-atomic clusters a+b+μ−e−a^{+} b^{+} \mu^{-} e^{-} and a+b+μ−e−e−a^{+} b^{+} \mu^{-} e^{-} e^{-}

Based on the results of accurate variational calculations we demonstrate stability of the five-body negatively charged ions $a^{+} b^{+} \mu^{-} e^{-} e^{-}$. Each of these five-body ions contains two electrons $e^{-}$, one negatively charged muon $\mu^{-}$ and two nuclei of the hydrogen isotopes $a, b = (p, d, t)$. The bound state properties of these five-body ions, including their hyperfine structure, are briefly discussed. We also investigate the hyperfine structure of the ground states of the four-body muonic quasi-atoms $a^{+} b^{+} \mu^{-} e^{-}$. In particular, we determine the hyperfine structure splittings for the ground state of the four-body muonic quasi-atoms: $p^{+} d^{+} \mu^{-} e^{-}$ and $p^{+} t^{+} \mu^{-} e^{-}$