arXiv subjects

Alexei M. Frolov

Publications and source records attributed to Alexei M. Frolov.

At least 19 recordsLinked to original sources

arXiv2026

On bound state spectra of the one-electron diatomic ions

The total energies of a large number of diatomic (or two-center) one-electron $A^{+} B^{+} e^{-}$ ions with unit electrical charges are determined numerically to high accuracy. Based on these results we derive some accurate mass-interpolation formulas for the total energies of such three-body systems (ions). These formulas can be applied to the both symmetric $A^{+} A^{+} e^{-}$ and non-symmetric $A^{+} B^{+} e^{-}$ diatomic ions. Based on the results obtained in this study we also consider a few actual and currently unsolved problems, which are known for the two-center (or diatomic) one-electron ions.

physics.atom-ph↗

arXiv2025

Properties of the weakly-bound (1,1)-states and rotationally excited (2,0)-states in the muonic molecular $d d μ, d t μ$ and $t t μ$ ions

Total energies and other bound state properties of the weakly-bound (1,1)-states and rotationally excited (2,0)-states in the three-body muonic molecular $d d μ, d t μ$ and $t t μ$ ions are determined to high numerical accuracy and investigated. Our current numerical accuracy achieved for the total and binding energies of the weakly-bound (1,1)-states in the both $d d μ$ and $d t μ$ ions significantly exceeds similar accuracy obtained in earlier computations of these weakly-bound states in these two ions. The bound state properties of the weakly-bound (1,1)-states and (2,0)-states in the $d d μ, d t μ$ and $t t μ$ muonic ions have never been determined to high accuracy in earlier studies. We also briefly discuss the current status of muon-catalyzed nuclear fusion and develop the new universal variational expansion which can be used for extremely accurate bound state calculations of arbitrary three-body systems, including the truly adiabatic ${}^{\infty}$H$^{+}_{2}$ ion and close systems.

physics.atom-ph↗

arXiv2024

General Principles of Hamiltonian Formulations of the Metric Gravity

Principles of successful Hamiltonian approaches, which were developed to describe free gravitational field(s) in the metric gravity, are formulated and discussed. By using the standard $Γ-Γ$ Lagrangian ${\cal L}_{Γ-Γ}$ of the metric GR we properly introduce all momenta of the metric gravitational field and derive the both canonical $H_C$ and total $H_t$ Hamiltonians of the metric GR. We also developed an effective method which is used to determine various Poisson brackets between analytical functions of the basic dynamical variables, i.e., generalized coordinates $g_{αβ}$ and momenta $π^{μν}$. In general, such variables can be chosen either from the straight $\{ g_{αβ}, π^{μν} \}$, or dual $\{ g^{αβ}, π_{μν} \}$ sets of symplectic dynamical variables which always arise (and complete each other) in any Hamiltonian formulation developed for the coupled system of tensor fields. By applying canonical transformation(s) of dynamical variables we reduce the canonical Hamiltonian $H_C$ 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 have been found and described in detail for dynamical systems with the Hamiltonians already reduced to their natural forms. In particular, reduction of the canonical Hamiltonian $H_C$ to its natural form allows one to derive the Jacobi equation for the free gravitational field(s), which takes a particularly simple form.

gr-qc↗

arXiv2024

On matrix elements of the vector physical quantities

Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical quantities. These formulas are applied to a large number of quantum systems which have an explicit spherical symmetry. Multiple commutators of different powers of the angular momenta $\hat{\bf J}^{2}$ and vector-operator $\hat{\bf A}$ are determined in the general form. Calculations of the expectation values averaged over orbital angular momenta are also described in detail. This effective and elegant old technique, which was successfully used by E. Fermi and A. Bohr, is almost forgotten in modern times. We also discuss quantum systems with additional relations (or constraints) between some vector-operators and orbital angular momentum. For similar systems such relations allow one to obtain some valuable additional information about their properties, including the bound state spectra, correct asymptotics of actual wave functions, etc. As an example of unsolved problems we consider applications of the algebras of angular momenta to investigation of the one-electron, two-center (Coulomb) problem $(Q_1, Q_2)$. For this problem it is possible to obtain the closed analytical solutions which are written as the `correct' linear combinations of products of the two one-electron wave functions of the hydrogen-like ions with the nuclear charges $Q_1 + Q_2$ and $Q_1 - Q_2$, respectively. However, in contrast with the usual hydrogen-like ions such hydrogenic wave functions must be constructed in three-dimensional pseudo-Euclidean space with the metric (-1,-1,1).

physics.atom-ph↗

arXiv2024

One-photon annihilation of the electron-positron pair at heavy atomic nuclei

We investigate one-photon annihilation of the electron-positron pair in the field of a central, very heavy and positively charged atomic nucleus. The explicit formula for the annihilation rate of this process $Γ^{(b)}_{1 γ}$ is derived. Our formula for this rate can directly be used to describe the actual one-photon annihilation in the ground (bound) states of all positronium hydrides HPs, quasi-stable triplet states of the positron-helium atoms $e^{+}[$ He($2^{3}S_e$)] ions and other systems.

hep-ph↗

arXiv2024

Bound state properties, positron annihilation and hyperfine structure of the four-body positronium hydrides

Bound state properties of the ground (bound) ${}^{1}S(L = 0)-$state(s) in the four-body positronium hydrides ${}^{1}$HPs, ${}^{2}$HPs (DPs), ${}^{3}$HPs (TPs) and MuPs are determined and investigated. By using numerical data from our computations of these four-body systems we have determined a number of different annihilation rates for each of these positronium hydrides and evaluated the hyperfine structure splitting. The properties of the ground (bound) states in the four-body exitonic ${}^{M}h^{+} e^{-}_{2} e^{+}$ complexes, where $M \ge 1$ and $M \le 1$, have also been evaluated numerically. The neutral four-body systems ${}^{M}h^{+} e^{-}_{2} e^{+}$ with $M \gg 1$ are similar to the HPs hydrides. In particular, each of these states has only one bound state. We also discuss applications of the exponential and semi-exponential variational expansions for accurate, bound state computations of the four-body positronium hydrides.

physics.atom-ph↗

arXiv2024

Differential equation for the Uehling potential

The second-order differential equation for the Uehling potential is derived explicitly. The right side of this differential equation is a linear combination of the two Macdonald's functions $K_{0}(b r)$ and $K_{1}(b r)$. This central potential is of great interest in many QED problems, since it describes the lowest-order correction for vacuum polarization in few- and many-electron atoms, ions, muonic and bi-muonic atoms/ions as well as in other similar systems.

quant-ph↗

arXiv2023

Bound state properties and positron annihilation in the negatively charged Ps$^{-}$ ion. On thermal sources of fast positrons and annihilation $γ$-quanta in our Galaxy

The total energy and other bound state properties of the ground (bound) $1^{1}S$-state in the Ps$^{-}$ (or $e^{-}e^{+}e^{-}$) ion are determined to very high accuracy. Our best variational energy for the ground state in this ion equals $E$ = -0.26200507023298010777040211998 $a.u.$, which is the lowest variational energy ever obtained for this ion. By using our highly wave functions we evaluated (to very high accuracy) a number of different expectation values (or properties) of the Ps$^{-}$ ion which have never been determined in earlier studies. This includes a number of $\langle r^{k}_{ij} \rangle$ expectation values (where $5 \le k \le 11$), all independent quasi-singular Vinty-type expectation values $\langle \frac{{\bf r}_{ij} {\bf r}_{jk}}{r^{3}_{ij}} \rangle$, the two truly singular $\langle \frac{1}{r^{3}_{ij}} \rangle$ expectation values, etc. Our highly accurate expectation values of the electron-positron delta-function of the Ps$^{-}$ ion we have evaluated (to very high accuracy) the rates of two-, three-, four- and five-photon annihilation. We also discuss thermal sources of the fast positrons and annihilation $γ$-quanta located in our Galaxy.

physics.atom-ph↗

arXiv2023

Thermodynamics of the electron-positron plasma at very high temperatures

Thermodynamic properties of the electron-positron plasma (or gas) at high and very high temperatures are investigated. To achieve this goal we have derived a number of analytical formulas for the Fermi-Dirac distribution functions (or spectral functions) which can be applied to various Fermi gases in different cases. Almost all these formulas are represented in the form of series expansions. The coefficients in these expansions are the explicit and relatively simple functions of the $\fracμ{T}$ ratio, where $T$ is the temperature and $μ$ is the chemical potential of this Fermi system. Our new approach works very well for high temperature electron-positron plasma, which is in thermal equilibrium with the photon gas of annihilation $γ-$quanta, and for the model ultra-relativistic gas of fermions, where there is no radiation at all.

physics.plasm-ph↗

arXiv2022

Density functional theory and non-relativistic photoelectric effects in the few-electron atomic systems

Closed analytical formulas are derived for the differential and total cross sections of the non-relativistic photoelectric effect in the three main classes of few-electron atomic systems: (1) neutral atoms and positively charged atomic ions which contain more than one bound electron, (2) negatively charged atomic ions, and (3) one-electron atoms and ions. Our procedure developed in this study is a combination of QED methods and results of the density functional theory obtained for atoms and ions. In all these systems the photoelectric effect is considered as photodetachment of the outer-most electron and our analysis is based on the results of density functional theory obtained for the electron density (radial) distribution in these atomic systems. Analytical formulas (similar to ours) for the differential and total cross sections of photoelectric effect for atomic systems from classes (1) and (2) have never been produced in earlier studies.

physics.atom-ph↗

arXiv2022

Metric gravity in the Hamiltonian form. Canonical transformations. Dirac's modifications of the Hamilton method and integral invariants of the metric gravity

Two different Hamiltonian formulations of the metric gravity are discussed and applied to describe a free gravitational field in the $d$ dimensional Riemann space-time. Theory of canonical transformations, which relate equivalent Hamiltonian formulations of the metric gravity, is investigated in details. In particular, we have formulated the conditions of canonicity for transformation between the two sets of dynamical variables used in our Hamiltonian formulations of the metric gravity. Such conditions include the ordinary condition of canonicity known in classical Hamilton mechanics, i.e., the exact coincidence of the Poisson (or Laplace) brackets which are determined for the both new and old dynamical Hamiltonian variables. However, in addition to this any true canonical transformations defined in the metric gravity, which is a constrained dynamical system, must also guarantee the exact conservation of the total Hamiltonians $H_t$ (in the both formulations) and preservation of the algebra of first-class constraints. We show that Dirac's modifications of the classical Hamilton method contain a number of crucial advantages, which provide an obvious superiority of this method in order to develop various non-contradictory Hamiltonian theories of many physical fields, when a number of gauge conditions are also important. Theory of integral invariants and its applications to the Hamiltonian metric gravity are also discussed. For Hamiltonian dynamical systems with first-class constraints this theory leads to a number of peculiarities some of which have been investigated.

gr-qc↗

arXiv2022

On Maxwell electrodynamics in multi-dimensional spaces

The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the electromagnetic field in multi-dimensional pseudo-Euclidean (flat) spaces has also been developed and investigated. Based on the two arising first-class constraints we have generalized to multi-dimensional spaces a number of different gauges known for the three-dimensional electromagnetic field. For multi-dimensional spaces of non-zero curvature the governing equations for the multi-dimensional electromagnetic field are written in manifestly covariant form. Multi-dimensional Einstein's equations of metric gravity in the presence of electromagnetic field have been re-written in the true tensor form. Methods of scalar electrodynamics are applied to analyze Maxwell equations in the two- and one-dimensional spaces.

physics.gen-ph↗

arXiv2021

Uehling potential and lowest-order corrections on vacuum polarization to the cross sections of some QED processes

Properties and different representations of the Uehling potential are investigated. Based on these properties and by using our formulas for the Fourier transform of the Uehling potential we have developed the new analytical, logically closed and physically transparent procedure which can be used to evaluate the lowest-order vacuum polarization correction to the cross sections of a number of QED processes, including the Mott electron scattering, bremsstrahlung, creation and/or annihilation of the $(e^{-}, e^{+})-$pair in the field of a heavy Coulomb center, e.g., atomic nucleus.

hep-ph↗

arXiv2021

Photodetachment of the outer-most electrons in a few- and many-electron atomic systems

Photodetachment of the outer-most electrons in few- and many-electron atomic systems is studied in the non-relativistic dipole approximation. Such a photodetachment is analyzed for the neutral atoms and positively charged atomic ions. We also investigate photodetachment of the outer-most electrons in the negatively charged atomic ions, including the negatively charged hydrogen ion. In all these cases we have derived the closed analytical formulas for the photodetachemnt cross-section(s) of the outer-most electrons.

physics.atom-ph↗

arXiv2020

Mass-dependencies of the bound state properties for three-body positronium-like exitonic complexes

Mass-dependencies of a number of bound state properties are investigated in some light two-electron exitonic complexes (or clusters) $Z^{+} e^{-} e^{-}$, where $m_e \le m_Z \le 2 m_e$. These exitonic complexes (or model ions) play a great role in modern solid state physics, since such complexes describe optical absorption in a number of semiconductors. We also derived and tested a number of accurate mass-interpolation formulas for these properties. In general, our mass-interpolation formulas allow one to predict (fast and accurately) numerical values of these bound state properties in the `new' exitonic complexes, i.e., in three-body exitonic complexes with new mass ratios.

physics.atom-ph↗

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↗