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V. I. Korobov

Publications and source records attributed to V. I. Korobov.

34 records · Page 2Linked to original sources
arXiv2016

Leading order relativistic corrections to the dipole polarizability of the hydrogen molecular ions

The static dipole polarizability for the hydrogen molecular ions H$_2^+$, HD$^+$, and D$_2^+$ are calculated. These new data for polarizability takes into account the leading order relativistic corrections to the wave function of the three-body system resulted from the Breit-Pauli Hamiltonian of $mα^4$ order. Our study covers a wide range of rotational ($L=0-5$) and vibrational ($v=0-10$) states, which are of practical interest for precision spectroscopy of the hydrogen molecular ions.

physics.atom-ph↗
arXiv2015

Controllability function as time of motion. I

The admissible positional control problem for the canonical system with geometrical restrictions on the control is considered. The investigation is performed with the help of the controllability function method. We obtain controllability functions which are the time of motion from an arbitrary initial condition to the origin. We also reveal a set of controls which solves this problem.

math.OC↗
arXiv2014

One-loop vacuum polarization at $mα^7$ order for the two center problem

We present calculations of the one-loop vacuum polarization contribution (Uehling potential) for the two-center problem in the NRQED formalism. The cases of hydrogen molecular ions ($Z_1=Z_2=1$) as well as antiprotonic helium ($Z_1=2$, $Z_2=-1$) are considered. Numerical results of the vacuum polarization contribution at $mα^7$ order for the fundamental transitions $(v=0,L=0)\to(v'=1,L'=0)$ in H$_2^+$ and HD$^+$ are presented.

physics.atom-ph↗
arXiv2014

Theoretical transition frequencies beyond 0.1 ppb accuracy in H$_2^+$, HD$^+$, and antiprotonic helium

We present improved theoretical calculations of transition frequencies for the fundamental transitions $(L\!=\!0,v\!=\!1)\to(L'\!=\!0,v'\!=\!0)$ in the hydrogen molecular ions H$_2^+$ and HD$^+$ with a relative uncertainty $4\cdot10^{-11}$ and for the two-photon transitions in the antiprotonic helium atom with a relative uncertainty $10^{-10}$. To do that, the one-loop self-energy correction of order $α(Zα)^6$ is derived in the two Coulomb center approximation, and numerically evaluated in the case of the aforementioned transitions. The final results also include a complete set of other spin-independent corrections of order $mα^7$. The leading order corrections of $α^2\ln^3(Zα)^{-2}(Zα)^6$ are also considered that allows to estimate a magnitude of yet uncalculated contributions.

physics.atom-ph↗
arXiv2013

Stepwise synthesis of constrained controls for single input nonlinear systems of special form

The controllability problem for nonlinear control systems with one-dimensional control of the form $ dx/dt=a(x)+B(x)β(x,u)$ is considered, where $a(x)$ is an $n$-dimensional vector function, $B(x)$ is an $(n\times m)$-matrix, and $β(x,u)$ is an $m$-dimensional vector function. Under certain conditions we reduce such system to a system consisting of $m$ subsystems; in each subsystem all equations are linear except of the last one. We use the controllability function method to give sufficient conditions for controllability of the considered system. We propose an approach for construction of controls which transfer an arbitrary initial point to the rest point in a certain finite time. Each such control is constructed as a concatenation of a finite number of positional controls (we call it a stepwise synthesis control). On each step of our approach we choose a new synthesis control. Our approach essentially uses nonlinearity of a system with respect to a control. The obtained results are illustrated by examples. In particular, the problem of the complete stoppage of a two-link pendulum is solved. We also introduce the class of nonlinear systems which is called the class of staircase systems that provides the applicability of our approach.

math.OC↗
arXiv2013

Bounds on fifth forces at the sub-Angstrom length scale

Constraints on a possible fifth-force interaction between hadrons are derived based on an analysis of results from laser precision frequency measurements of antiprotonic helium atoms, both $\bar{p}\,^{4}$He$^{+}$ and $\bar{p}\,^{3}$He$^{+}$ species, and from experiments on resonant formation rates of $ddμ^{+}$-ions in muon-catalyzed fusion processes. A comparison is made between accurate experimental data and first-principles theoretical descriptions of the exotic systems within a quantum electrodynamical framework. The agreement between theory and experiment sets limits on a possible additional hadron-hadron interaction written in the form of a Yukawa potential $V_5(r)=α_5 \exp(-r/λ)/r$, with $λ$ representing the characteristic length scale associated with the mass of a hypothetical force-carrying particle via $λ=\hbar/(m_5c)$. The laser spectroscopic data of antiprotonic helium set a constraint of $α_5/α_{EM} < 10^{-8}$ for $λ< 1$ Å, while the binding energy of the muonic molecular deuterium ion delivers a constraint of $α_5/α_{EM} \sim 10^{-5}$ for $λ< 0.05$ Å, where $α_{EM}$ represents the strength of the electromagnetic interaction or the fine structure constant.

hep-ph↗
arXiv2012

Calculation of the nonrelativistic Bethe logarithm in the velocity gauge

We consider a general procedure to evaluate the Bethe logarithm for a general few-body atomic or molecular system. As benchmarks we use calculation for the ground states of a helium atom and H_2^+ molecular ion. The obtained values are: β_He=4.37016022306(2) for the helium atom and β_{H_2^+} = 3.012230335(1) for the H_2^+. Both results substantially improve the best known values for these quantities.

physics.atom-ph↗
arXiv2007

Relativistic corrections of mα^6 order to the ro-vibrational spectrum of H_2^+ and HD^+ molecular ions

The major goal of the high-precision studies of ro-vibrational states in the hydrogen molecular ions is to provide an alternative way for improving the electron-to-proton mass ratio, or the atomic mass of electron. By now the complete set of relativistic and radiative corrections have been obtained for a wide range of ro-vibrational states of H_2^+ and HD^+ up to order R_\inftyα^4. In this work we complete calculations of various contributions to the R_\inftyα^4 order by computing the relativistic corrections to the binding energy of electron.

physics.atom-ph↗
arXiv2007

Relativistic corrections of order mα^6 to the two-center problem

Effective potentials of the relativistic mα^6 order correction for the ground state of the Coulomb two-center problem are calculated. They can be used to evaluate the relativistic contribution of that order to the energies of hydrogen molecular ions or metastable states of the antiprotonic helium atom, where precision spectroscopic data are available. In our studies we use the variational expansion based on randomly chosen exponents that permits to achieve high numerical accuracy.

physics.atom-ph↗
arXiv2004

Relativistic and QED corrections to the $2pσ_{u}(\upsilon = 1)$ vibrational state of the $H^{+}_{2}$ molecular ion

Relativistic and QED corrections to the recently discovered first vibrational $2pσ_u$ state are presented. This state has an extremely small nonrelativistic binding energy $E_B=1.085045252(1)\times10^{-9}$ a.u. Its wave functions has a maximum at $R\approx100$ a.u. and extends up to several hundreds. It is shown that this state does not disappear if higher order relativistic and QED corrections, including the Casimir--Polder effect, are taken into account.

physics.atom-ph↗
arXiv2004

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.

physics.atom-ph↗
arXiv2000

Relativistic corrections to the dipole polarizability of the ground state of the molecular ion H_2^+

The recently reported precise experimental determination of the dipole polarizability of the H_2^+ molecular ion ground state [P.L. Jacobson, R.A. Komara, W.G. Sturrus, and S.R. Lundeen, Phys. Rev. A 62, 012509 (2000)] reveals a discrepancy between theory and experiment of about 0.0007a_0^3, which has been attributed to relativistic and QED effects. In present work we analyze an influence of the relativistic effects on the scalar dipole polarizability of an isolated H_2^+ molecular ion. Our conclusion is that it accounts for only 1/5 of the measured discrepancy.

physics.atom-ph↗
arXiv1999

Variational methods, multiprecision and nonrelativistic energies

It is known that the variational methods are the most powerful tool for studying the Coulomb three-body bound state problem. However, they often suffer from loss of stability when the number of basis functions increases. This problem can be cured by applying the multiprecision package designed by D.H. Bailey. We consider the variational basis functions of the type exp(-a_n r_1 - b_n r_2 - g_n r_12) with complex exponents. The method yields the best available energies for the ground states of the helium atom and the positive hydrogen ion as well as many other known atomic and molecular systems.

physics.atom-ph↗
arXiv1995

Resonant nuclear transition in the d-mu-Li6 muonic molecule

The reaction rate of the nuclear fusion d+Li6 ----> Be8*(2+,0) is estimated in the case where the nuclei are confined to each other by a muon. For the description of nuclear transitions, a method which is analogous to the Linear Combination of Atomic Orbitals has been used. Using the complex coordinate rotation method, we found that a molecular d-mu-Li6 state exists with energy (-20.3084-i0.0066) eV and |Ψ_{m}(0)|=0.44x10^{-7} fm^-3/2. The nuclear wave functions needed, were constructed in the form of antisymmetrized products of harmonic-oscillator functions for the three-cluster approximation, (ddα), to the five-body (NNNNα) problem. It was found that the reaction rate λis strongly dependent on the energy gap between the d-Li6 threshold and the energy of the final Be8^* resonant state. The value of λobtained by averaging over the width of this resonance, is 0.183x10^10 sec^{-1}.

nucl-th↗