Search for long-lived states in antiprotonic lithium

The spectrum of the (L_i^3 + p-bar + 2e) four-body system was calculated in an adiabatic approach. The two-electron energies were approximated by a sum of two single-electron effective charge two-center energies as suggested in [6]. While the structure of the spectrum does not exclude the existence of long-lived states, their experimental observability is still to be clarified

Global robust controllability of the triangular integro-differential Volterra systems

AbstractA solution of the global controllability problem for a class of nonlinear control systems of the Volterra integro-differential equations is presented. It is proven that there exists a family of continuous controls that solve the global controllability problem for this class. The constructed controls depend continuously on the initial and the terminal states. It makes possible to prove the global controllability of the uniformly bounded perturbations of these systems under the global Lipschitz condition for the unperturbed system with respect to the states and the controls

On Stabilization Problem for Nonlinear Systems with Power Principal Part

In the present paper, the stabilization problem for the uncontrollable with respect to the first approximation nonlinear system with power principal part is solved. A class of stabilizing controls for the nonlinear approximation of this system is constructed by using the Lyapunov function method. It is proved that the same controls solve the stabilization problem for the original nonlinear system. An ellipsoidal approximation of the domain of attraction to the origin is given

On Robust Feedback for Systems with Multidimensional Control

The paper deals with local robust feedback synthesis problem for systems with multidimensional control and unknown bounded perturbations. Using V.I. Korobov's controllability function method, a bounded control which steers an arbitrary initial point to the origin at some finite time is constructed; an estimate from above for the time of motion is given. The range of a segment where the perturbations can vary is found. As an example, the problem of stopping the oscillations of the system of two coupled pendulums is considered

On Robust Feedback for Systems with Multidimensional Control

The paper deals with local robust feedback synthesis problem for systems with multidimensional control and unknown bounded perturbations. Using V.I. Korobov's controllability function method, a bounded control which steers an arbitrary initial point to the origin at some finite time is constructed; an estimate from above for the time of motion is given. The range of a segment where the perturbations can vary is found. As an example, the problem of stopping the oscillations of the system of two coupled pendulums is considered

Energy levels in muonic helium

The energy spectrum of bound states and hyperfine structure of muonic helium is calculated on the basis of stochastic variational method. The basis wave functions of the muonic molecule are taken in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. For numerical calculation, a computer code is written in the MATLAB system. As a result, the numerical values of bound state energies and hyperfine structure for muonic helium are obtained.The work is supported by the RSF (Grant 18-12-00128)

Forbidden transitions in the helium atom

Nonrelativistically forbidden, single-photon transition rates between low lying states of the helium atom are rigorously derived within quantum electrodynamics theory. Equivalence of velocity and length gauges, including relativistic corrections is explicitly demonstrated. Numerical calculations of matrix elements are performed with the use of high precision variational wave functions and compared to former results.Comment: 11 pages, 1 figure, submitted to Phys. Rev.

Hyperfine structure of the ground state muonic He-3 atom

On the basis of the perturbation theory in the fine structure constant $\alpha$ and the ratio of the electron to muon masses we calculate one-loop vacuum polarization and electron vertex corrections and the nuclear structure corrections to the hyperfine splitting of the ground state of muonic helium atom $(\mu\ e \ ^3_2He)$. We obtain total result for the ground state hyperfine splitting $\Delta \nu^{hfs}=4166.471$ MHz which improves the previous calculation of Lakdawala and Mohr due to the account of new corrections of orders $\alpha^5$ and $\alpha^6$. The remaining difference between our theoretical result and experimental value of the hyperfine splitting lies in the range of theoretical and experimental errors and requires the subsequent investigation of higher order corrections.Comment: Talk on poster section of XXIV spectroscopy congress, 28 February-5 March 2010, Moscow-Troitsk, Russia, 21 pages, LaTeX, 8 figure

On Pole Assignment and Stabilizability of Neutral Type Systems

In this note we present a systematic approach to the stabilizability problem of linear infinite-dimensional dynamical systems whose infinitesimal generator has an infinite number of instable eigenvalues. We are interested in strong non-exponential stabilizability by a linear feed-back control. The study is based on our recent results on the Riesz basis property and a careful selection of the control laws which preserve this property. The investigation may be applied to wave equations and neutral type delay equations

Production of Slow Protonium in Vacuum

We describe how protonium, the quasi-stable antiproton-proton bound system, has been synthesized following the interaction of antiprotons with the molecular ion H$_2^+$ in a nested Penning trap environment. From a careful analysis of the spatial distributions of antiproton annihilation events in the ATHENA experiment, evidence is presented for protonium production with sub-eV kinetic energies in states around $n$ = 70, with low angular momenta. This work provides a new 2-body system for study using laser spectroscopic techniques.Comment: 9 pages with 5 figures and 1 table. Proceedings of the 4th International Conference on Trapped Charged Particles and Fundamental Physics (TCP 06), published in Hyperfine Interaction