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 $p^{+} t^{+} \mu^{-} e^{-}$

Thermonuclear burn-up in deuterated methane CD4CD_4

The thermonuclear burn-up of highly compressed deuterated methane CD$_4$ is considered in the spherical geometry. The minimal required values of the burn-up parameter $x = \rho_0 \cdot r_f$ are determined for various temperatures $T$ and densities $\rho_0$. It is shown that thermonuclear burn-up in $CD_4$ becomes possible in practice if its initial density $\rho_0$ exceeds $\approx 5 \cdot 10^3$ $g \cdot cm^{-3}$. Burn-up in CD$_2$T$_2$ methane requires significantly ($\approx$ 100 times) lower compressions. The developed approach can be used in order to compute the critical burn-up parameters in an arbitrary deuterium containing fuel

Gauge field theory for Poincar\'{e}-Weyl group

On the basis of the general principles of a gauge field theory the gauge theory for the Poincar\'{e}-Weyl group is constructed. It is shown that tetrads are not true gauge fields, but represent functions from true gauge fields: Lorentzian, translational and dilatational ones. The equations of gauge fields which sources are an energy-momentum tensor, orbital and spin momemta, and also a dilatational current of an external field are obtained. A new direct interaction of the Lorentzian gauge field with the orbital momentum of an external field appears, which describes some new effects. Geometrical interpretation of the theory is developed and it is shown that as a result of localization of the Poincar\'{e}-Weyl group spacetime becomes a Weyl-Cartan space. Also the geometrical interpretation of a dilaton field as a component of the metric tensor of a tangent space in Weyl-Cartan geometry is proposed.Comment: LaTex, 27 pages, no figure

Gluon - W-meson scattering via different renormalization schemes

The one loop gluon - W-meson amplitude is calculated by means of the gauge-invariant generalized Pauli-Villars regularization and with the help of dimensional regularization. It is shown that in the former case the amplitude satisfies Generalized Ward Identities, whereas in the latter case the amplitude differs from the first one by the constant.Comment: Latex, 12 pages, uses linedraw, accepted for publication in Mod.Phys.Lett.

Merger Transitions in Brane--Black-Hole Systems: Criticality, Scaling, and Self-Similarity

We propose a toy model for study merger transitions in a curved spaceime with an arbitrary number of dimensions. This model includes a bulk N-dimensional static spherically symmetric black hole and a test D-dimensional brane interacting with the black hole. The brane is asymptotically flat and allows O(D-1) group of symmetry. Such a brane--black-hole (BBH) system has two different phases. The first one is formed by solutions describing a brane crossing the horizon of the bulk black hole. In this case the internal induced geometry of the brane describes D-dimensional black hole. The other phase consists of solutions for branes which do not intersect the horizon and the induced geometry does not have a horizon. We study a critical solution at the threshold of the brane-black-hole formation, and the solutions which are close to it. In particular, we demonstrate, that there exists a striking similarity of the merger transition, during which the phase of the BBH-system is changed, both with the Choptuik critical collapse and with the merger transitions in the higher dimensional caged black-hole--black-string system.Comment: 9 pages 2 figures; additional remarks and references are added at Section IX "Discussion

Energy flux through the horizon in the black hole-domain wall systems

We study various configurations in which a domain wall (or cosmic string), described by the Nambu-Goto action, is embedded in a background space-time of a black hole in $(3+1)$ and higher dimensional models. We calculate energy fluxes through the black hole horizon. In the simplest case, when a static domain wall enters the horizon of a static black hole perperdicularly, the energy flux is zero. In more complicated situations, where parameters which describe the domain wall surface are time and position dependent, the flux is non-vanishing is principle. These results are of importance in various conventional cosmological models which accommodate the existence of domain walls and strings and also in brane world scenarios.Comment: references added, accepted for publication in JHE

Accretion of non-minimally coupled generalized Chaplygin gas into black holes

The mass evolution of Schwarzschild black holes by the absorption of scalar fields is investigated in the scenario of the generalized Chaplygin gas (GCG). The GCG works as a unification picture of dark matter plus dark energy that naturally accelerates the expansion of the Universe. Through elements of the quasi-stationary approach, we consider the mass evolution of Schwarzschild black holes accreted by non-minimally coupled cosmological scalar fields reproducing the dynamics of the GCG. As a scalar field non-minimally coupled to the metrics, such an exotic content has been interconnected with accreting black holes. The black hole increasing masses by the absorption of the gas reflects some consistence of the accretion mechanism with the hypothesis of the primordial origin of supermassive black holes. Our results effectively show that the non-minimal coupling with the GCG dark sector accelerates the increasing of black hole masses. Meanwhile some exotic features can also be depicted for specific ranges of the non-minimal coupling in which the GCG dynamics is substantially modified.Comment: 13 pages, 03 figure

Bound state spectra of three-body muonic molecular ions

The results of highly accurate calculations are presented for all twenty-two known bound $S(L = 0)-, P(L = 1)-, D(L = 2)-$ and $F(L = 3)-$states in the six three-body muonic molecular ions $pp\mu, pd\mu, pt\mu, dd\mu, dt\mu$ and $tt\mu$. A number of bound state properties of these muonic molecular ions have been determined numerically to high accuracy. The dependence of the total energies of these muonic molecules upon particle masses is considered. We also discuss the current status of muon-catalysis of nuclear fusion reactions.Comment: This is the final version. All `techical' troubles with the Latex-file have been resolved. A few misprints/mistakes in the text were correcte

On the bound state of the antiproton-deuterium-tritium ion

The properties of the weakly-bound $S(L = 0)-$state in the $\bar{p}dt$ ion are investigated with the use of the results of highly accurate computations. The hyperfine structure splitting of this ion is investigated. We also evaluate the life-time of the $\bar{p}dt$ ion against the nuclear $(d,t)-$fusion and discuss a possibility to evaluate the corresponding annihilation rate(s)

Continuous Self-Similarity Breaking in Critical Collapse

This paper studies near-critical evolution of the spherically symmetric scalar field configurations close to the continuously self-similar solution. Using analytic perturbative methods, it is shown that a generic growing perturbation departs from the critical Roberts solution in a universal way. We argue that in the course of its evolution, initial continuous self-similarity of the background is broken into discrete self-similarity with echoing period $\Delta = \sqrt{2}\pi = 4.44$, reproducing the symmetries of the critical Choptuik solution.Comment: RevTeX 3.1, 28 pages, 5 figures; discussion rewritten to clarify several issue