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Alexei M. Frolov

Publications and source records attributed to Alexei M. Frolov.

At least 37 records · Page 2Linked to original sources
arXiv2020

On highly accurate computations of the Coulomb two-center systems with unit charges

Results of our recent highly accurate computations of the Coulomb two-center systems with the unit electrical charges $X^{+} X^{+} e^{-}$ and $X^{+} Y^{+} e^{-}$ are discussed. In particular, we have determined (to very high accuracy) the total energies of the ground $1 s σ-$states in the two-center adiabatic (or molecular) H$_{2}^{+}$, D$_2^{+}$, HD$^{+}$, HT$^{+}$, T$^{+}_{2}$ and DT$^{+}$ ions. In these computations we applied the new masses of hydrogen isotopes, which have been measured in the recent high-energy experiments. We also derived (and tested) our accurate mass-interpolation formula for the total energies of the model two-center $X^{+} X^{+} e^{-}$ ions with very heavy masses of the point $X^{+}$ particles ($M_X \ge$ 100,000 $m_e$). By using this formula we analyze the overall accuracy and validity of the adiabatic two-center approximation in application to the three-body atomic (or Coulomb) systems.

physics.atom-ph↗
arXiv2020

Reduction of the canonical Hamiltonian of the metric GR to its natural form

The canonical Hamiltonian $H_C$ of the metric General Relativity is reduced to its natural form. The natural form of canonical Hamiltonian provides numerous advantages in actual applications to the metric GR, since the general theory of dynamical systems with such Hamiltonians is well developed. Furthermore, many analytical and numerically exact solutions for dynamical systems with natural Hamiltonians have been found and described in detail. In particular, based on this theory we can discuss an obvious analogy between gravitational field(s) and few-particle systems where particles are connected to each other by the Coulomb, or harmonic potentials. We also developed an effective method which is used to determine various Poisson brackets between analytical functions of the dynamical variables. Furthermore, such variables can be chosen either from the straight, or dual sets of symplectic dynamical variables which always arise in any Hamiltonian formulation developed for the metric gravity. PACS number(s): 04.20.Fy and 11.10.Ef

gr-qc↗
arXiv2019

Free gravitational field in the metric gravity as a Hamilton system

The closed system of Hamilton equations is derived for all tensor components of the free gravitational field $g_{αβ}$ and corresponding momenta $π^{γδ}$ in the metric General Relativity. The Hamilton-Jacobi equation for the free gravitational field $g_{αβ}$ is also derived and discussed. In general, all methods and procedures based on the Hamilton and Hamilton-Jacobi approaches are very effective in actual applications to many problems known in the metric GR.

gr-qc↗
arXiv2019

On the weakly-bound (1,1)-states in the three-body $d d μ$ and $d t μ$ muonic ions

The both total and binding energies of the (1,1)-states in the weakly-bound three-body muonic $d d μ$ and $d t μ$ ions are determined to high numerical accuracy. The binding energy of the (1,1)-state in the muonic $d t μ$ ion is evaluated as $\varepsilon(d t μ)$ = -0.66033003831(30) $eV$, while for the same state in the muonic $d d μ$ ion we have found that $\varepsilon(d d μ)$ = -1.9749806166970(30) $eV$. These energies are the most accurate numerical values obtained for these systems and they are sufficient for all current and future experimental needs.

physics.atom-ph↗
arXiv2018

Internal clusterization in the Coulomb few-body systems and stability of the five- and six-body systems with unit charges

Stability of the bound ground states in the six five-body muonic $a b μe_2$ ions (or $(a b μe_2)^{-}$) and ten six-body $a b c μe_2$ quasi-molecules is investigated. The notations $a, b, c$ stand for the bare nuclei of three hydrogen isotopes - protium ($p$), deuterium ($d$) and tritium ($t$). All these systems are the Coulomb five- and six-body systems with unit charges. It is found that the ground bound $S(L = 0)-$states are stable in all six five-body $a b μe_2$ ions and in ten six-body $a b c μe_2$ quasi-molecules. As follows from accurate variational computations of the five-body $a b μe_2$ ions their internal structure is similar to the internal structure of the negatively charged hydrogen ion H$^{-}$. Analogously, we show that the internal structures of the six-body neutral $a b c μe_2$ quasi-molecules are similar to the structure of the two-center H$_{2}$ molecule which contains two heavy hydrogen nuclei and two bound electrons.

physics.atom-ph↗
arXiv2018

On the general theory of bound state spectra in the Coulomb few- and many-body systems

Based on the fact that the Hamiltonians of the Coulomb many-particle systems are always factorized we develop the two different approaches for analytical solution of the Schrödinger equation written for arbitrary few- and many-particle Coulomb systems. The first approach is the matrix factorization method. Another method is based on the $D^{+}-$series of representations of the hyper-radial O(2,1)-algebra. The both these methods allow us to obtain the closed analytical formulas for the bound state energies in an arbitrary many-particle Coulomb system.

physics.atom-ph↗
arXiv2017

On the matrix factorization of many-particle Coulomb Hamiltonians

It is shown that the Coulomb many-particle Hamiltonians are always factorized. This fact can be used to obtain the closed analytical formula(s) for the bound state spectra of an arbitrary many-particle Coulomb system. For few- and many-electron atoms and ions these formulas are similar in some sense to the Bohr's formula which describes the bound state spectra of the hydrogen atom.

physics.atom-ph↗
arXiv2017

Bound state spectra and properties of the five- and six-body muonic ions and quasi-molecules

The ground bound states in the five-body muonic ions $a b μe_2$ (or $(a b μe_2)^{-}$), where $(a, b) = (p, d, t)$, are considered for the first time. As follows from accurate numerical computations of these five-body ions they are similar to the negatively charged hydrogen ion H$^{-}$ with a three-particle central quasi-nucleus $a b μ$ (or $(a b μ)^{+}$). These five-body ions play some role in the muon-catalyzed fusion of nuclear reaction in liquid deuterium and/or deuterium-tritium mixtures. We also discuss the bound states in the six-body $a b c μe_2$ quasi-molecules, where $(a, b, c) = (p, d, t)$. These six-body, two-electron quasi-molecules are of great interest for muon-catalyzed nuclear fusion, since in liquid deuterium and/or deuterium-tritium mixture more than 99 \% of all muon-catalyzed reactions of the $(dd)-$ and $(dt)-$fusion occur in such six-body quasi-molecules: $d d t μe_2, d d d μe_2$ and $d t t μe_2$.

physics.atom-ph↗
arXiv2016

On accurate computations of slowly convergent atomic properties in few-electron ions and electron-electron correlations

We discuss an approach to accurate numerical computations of slowly convergent properties in two-electron atoms/ions which include the negatively charged Ps$^{-}$ ($e^{-} e^{+} e^{-}$) and H$^{-}$ ions, He atom and positively charged, helium-like ions from Li$^{+}$ to Ni$^{26+}$. All these ions are considered in their ground $1^{1}S-$state(s). The slowly convergent properties selected in this study include the electron-nulceus $\langle r^{2 k}_{eN} \rangle$ and electron-electron $\langle r^{2 k}_{ee} \rangle$ expectation values for $k$ = 2, 3, 4 and 5.

physics.atom-ph↗
arXiv2016

Accurate computations of bound state properties in three- and four-electron atomic systems in the basis of multi-dimensional gaussoids

Results of accurate computations of bound states in three- and four-electron atomic systems are discussed. Bound state properties of the four-electron lithium ion Li$^{-}$ in its ground $2^{2}S-$state are determined from the results of accurate, variational computations. We also consider a closely related problem of accurate numerical evaluation of the half-life of the beryllium-7 isotope. This problem is of paramount importance for modern radiochemistry.

physics.atm-clus↗
arXiv2016

Secondary electrons emitted during nuclear $β^{-}$ decay in few-electron atoms

`Additional' ionization of light atoms and ions during nuclear $β^{-}$ decay is investigated. The procedure which can be used to determine the corresponding transition probabilities and the velocity/energy spectrum of secondary electrons is developed. Emission of very fast secondary electrons ($δ-$electrons) from $β^{-}$-decaying atoms is also briefly discussed.

physics.atom-ph↗
arXiv2016

On the hyperfine structures of the ground state(s) in the ${}^{6}$Li and ${}^{7}$Li atoms

Hyperfine structure of the ground $2^{2}S-$states of the three-electron atoms and ions is investigated. By using our recent numerical values for the doublet electron density at the atomic nucleus we determine the hyperfine structure of the ground (doublet) $2^{2}S-$state(s) in the ${}^{6}$Li and ${}^{7}$Li atoms. Our predicted values (228.2058 $MHz$ and 803.5581 $MHz$, respectivly) agree well with the experimental values 228.20528(8) $MHz$ (${}^{6}$Li) and 803.50404(48) $MHz$ (${}^{7}$Li (R.G. Schlecht and D.W. McColm, Phys. Rev. \textbf{142}, 11 (1966))). The hyperfine structures of a number of lithium isotopes with short life-times, including ${}^{8}$Li, ${}^{9}$Li and ${}^{11}$Li atoms are also predicted. The same method is used to obtain the hyperfine structures of the three-electron ${}^{7}$Be$^{+}$ and ${}^{9}$Be$^{+}$ ions in their ground $2^{2}S-$states. Finally, we conclude that our approach can be generalized to describe the hyperfine structure in the triplet $n{}^{3}S-$states of the four-electron atoms and ions.

physics.atm-clus↗
arXiv2016

On contribution of the electron-electron correlations into bremsstrahlung from few-electron ions

A new approach is developed to evaluate contribution of the electron-electron correlations into bremsstrahlung from few-electron ions and atoms. Our approach is based on the explicit formula for the electron density distribution in such systems. We derive the closed analytical formula for the matrix elements which are needed for highly accurate computations of atomic form-factors of two-electron atoms and ions. We also discuss the energy loss due to bremsstrahlung in a plasma which contains multi-charged ions and free electrons. Bremsstrahlung from a high-temperature plasma is considered as well as its role in the high-temperature burn-up of deuterium plasma.

physics.atom-ph↗
arXiv2016

On the Hamilton approach for the metric GR

Basic principles of the Hamilton approach developed for the metric General Relativity (Einstein`s GR) are discussed. In particular, we derive the Hamiltonian of the metric GR in the explicit form. This Hamiltonian is a quadratic function of the momenta $π^{mn}$ conjugate to the spatial components $g_{mn}$ of the metric tensor $g_{αβ}$. The Hamilton approach is used to analyze some problems of metric GR, including the internal structure of propagating gravitational waves and quantization of the metric GR. We also derive the Schrödinger equation for the free Gravitational field and show that actual gravitational field cannot propagate as pure harmonic oscillations, or harmonic gravitational waves. A number of inequalities useful in applications to the metric GR are derived.

physics.gen-ph↗
arXiv2015

Spectrum of secondary electrons emitted during the nuclear $β^{-}$-decay of the tritium atom

Ionization of the final ${}^{3}$He$^{+}$ ion during the nuclear $β^{-}$-decay of the tritium atom is discussed. The velocity spectrum of the emitted secondary electrons is derived in the explicit form. Our method allows to determine the relative and absolute probabilities of formation of the final states in few-electron atoms which include `free' secondary electrons moving with different velocities. \noindent PACS number(s): 23.40.-s, 12.20.Ds and 14.60.Cd

nucl-th↗
arXiv2015

Photodetachment cross-section of the negatively charged hydrogen ion

Photodetachment cross-section $σ_{ph}(p_e)$ of the negatively charged hydrogen ion H$^{-}$ is determined with the use of highly accurate variational wave functions constructed for this ion. Photodetachment cross-sections of the H$^{-}$ ion are also studied for very small and very large values of the photo-electron momentum $p_e$. Maximum of this cross-section and its location have been evaluated to high accuracy. In particular, we have found that $[σ_{ph}(p_e)]_{\max} \approx$ 3.8627035742 $\cdot 10^{-17}$ $cm^2$ at $p_e \approx$ 0.113206(1) $a.u.$ Our method is based upon the Rayleigh's formula for spherical Bessel functions.

astro-ph.SR↗
arXiv2015

On the $Q$-dependence of the lowest-order QED corrections and other properties of the ground $1^1S-$states in the two-electron ions

Formulas and expectation values which are need to determine the lowest-order QED corrections ($\sim α^3$) and corresponding recoil (or finite mass) corrections in the two-electron helium-like ions are presented. Other important properties of the two-electron ions are also determined to high accuracy, including the expectation values of the qausi-singular Vinti operator and $\langle r^{-2}_{eN} \rangle$ and $\langle r^{-2}_{ee} \rangle$ expectation values. Elastic scattering of fast electrons by the two-electron ions in the Born approximation is considered. Interpolation formulas are derived for the bound state properties of the two-electron ions as the function of the nuclear electric charge $Q$.

physics.atom-ph↗