The solution of one time-optimal problem on the basis of the Markov moment min-problem with even gaps

The time-optimal problem for a linear system considered. This problem is reduced to the power Markov moment min-problem with even gaps. The new generating function is suggested for finding the optimal timeyesBelgorod State Universit

Mass-symmetry breaking in three-body ions

The ground-state energy of three-body ions $(M^+,M^+,m^-)$ evolves when the like-charge constituents are given different masses. The comparison of $(m_1^+,m_2^+,m^-)$ with the average of $(m_1^+,m_1^+,m^-)$ and $(m_2^+,m_2^+,m^-)$ reveals a competition between the symmetric term and the antisymmetric one. The former dominates in the Born--Oppenheimer regime such as the (p,t,e) case, while the latter wins for H$^-$-like systems with two negative light particles surrounding a heavy nucleus. A comparison is also made with the case of baryons in simple quark models with flavour independence.Comment: 4 pages, 3 figure

Nonrelativistic ionization energy for the helium ground state

The helium ground state nonrelativistic energy with 24 significant digits is presented. The calculations are based on variational expansion with randomly chosen exponents. This data can be used as a benchmark for other approaches for many electron and/or three-body systems.Comment: 3 pages, 0 figure

Corrections to the Nonrelativistic Ground Energy of a Helium Atom

Considering the nuclear motion, the authors give out the nonrelativistic ground energy of a helium atom by using a simple but effective variational wave function with a flexible parameter $k$. Based on this result, the relativistic and radiative corrections to the nonrelativistic Hamiltonian are discussed. The high precision value of the helium ground energy is evaluated to be -2.90338 a.u., and the relative error is 0.00034%.Comment: 8 pages, no figures, 2 table

Contribution of hadronic light-by-light scattering to the hyperfine structure of muonium

The contribution of hadronic scattering of light-by-light to the hyperfine structure of muonium is calculated using experimental data on the transition form factors of two photons into a hadron. The amplitudes of interaction between a muon and an electron with horizontal and vertical exchange are constructed. The contributions due to the exchange of pseudoscalar, axial vector, scalar and tensor mesons are taken into account.Comment: 13 pages, 1 figur

Ionization Potential of the Helium Atom

Ground state ionization potential of the He^4 atom is evaluated to be 5 945 204 221 (42) MHz. Along with lower order contributions, this result includes all effects of the relative orders alpha^4, alpha^3*m_e/m_alpha and alpha^5*ln^2(alpha).Comment: 4 page

Energy levels of mesonic helium in quantum electrodynamics

On the basis of variational method we study energy levels of pionic helium $(\pi-e-He)$ and kaonic helium $(K-e-He)$ with an electron in ground state and a meson in excited state with principal and orbital quantum numbers $n\sim l+1\sim 20$. Variational wave functions are taken in the Gaussian form. Matrix elements of the basic Hamiltonian and corrections to vacuum polarization and relativism are calculated analytically in a closed form. We calculate some bound state energies and transition frequencies which can be studied in the experiment.Comment: 12 pages, 6 figure