Comment on "New Methods for Old Coulomb Few-Body Problems"

In this Comment on the above mentioned paper by F. E. Harris, A. M. Frolov, and V. H. Smith, we briefly review our contributions to development of new methods for solution of the Coulomb four-body problem. We show that our research group, headed by Prof. T. K. Rebane, had a priority in using the fully correlated exponential basis for variational calculations of four-body systems. We also draw attention to the fact that our group subsequently implemented a more advanced method, which uses highly efficient exponential-trigonometric basis functions for solution of the same problem.Comment: Accepted by the International Journal of Quantum Chemistr

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 $MHz$

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

Stationary strings near a higher-dimensional rotating black hole

We study stationary string configurations in a space-time of a higher-dimensional rotating black hole. We demonstrate that the Nambu-Goto equations for a stationary string in the 5D Myers-Perry metric allow a separation of variables. We present these equations in the first-order form and study their properties. We prove that the only stationary string configuration which crosses the infinite red-shift surface and remains regular there is a principal Killing string. A worldsheet of such a string is generated by a principal null geodesic and a timelike at infinity Killing vector field. We obtain principal Killing string solutions in the Myers-Perry metrics with an arbitrary number of dimensions. It is shown that due to the interaction of a string with a rotating black hole there is an angular momentum transfer from the black hole to the string. We calculate the rate of this transfer in a spacetime with an arbitrary number of dimensions. This effect slows down the rotation of the black hole. We discuss possible final stationary configurations of a rotating black hole interacting with a string.Comment: 13 pages, contains additianal material at the end of Section 8, also small misprints are correcte

Planckian AdS2×S2AdS_2 \times S_2 space is an exact solution of the semiclassical Einstein equations

The product space configuration $AdS_2\times S_2$ (with $l$ and $r$ being radiuses of the components) carrying the electric charge $Q$ is demonstrated to be an exact solution of the semiclassical Einstein equations in presence of the Maxwell field. If the logarithmic UV divergences are absent in the four-dimensional theory the solution we find is identical to the classical Bertotti-Robinson space ($r=l=Q$) with no quantum corrections added. In general, the analysis involves the quadratic curvature coupling $\lambda$ appearing in the effective action. The solutions we find are of the following types: i) (for arbitrary $\lambda$) charged configuration which is quantum deformation of the Bertotti-Robinson space; ii) ($\lambda >\lambda_{cr}$) Q=0 configuration with $l$ and $r$ being of the Planck order; iii) ($\lambda<\lambda_{cr}$) $Q\neq 0$ configuration ($l$ and $r$ are of the Planck order) not connected analytically to the Bertotti-Robinson space. The interpretation of the solutions obtained and an indication on the internal structure of the Schwarzschild black hole are discussed.Comment: 14 pages, latex, 1 figure; v2: a note on S2*S2 type solutions adde