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Alexei M. Frolov

Publications and source records attributed to Alexei M. Frolov.

At least 73 records · Page 4Linked to original sources
arXiv2013

Triplet states in the Be atom: bound state spectrum and hyperfine structure

The bound state spectrum of low-lying triplet states in the Be atom is investigated. In particular, we perform accurate computations of various bound triplet S, P, D, F, and G states in the four-electron Be atom. For the 23S(L=0) state in the Be atom we determine the hyperfine structure and a number of bound states properties by using results of highly accurate computations. The energies of the hyperfine structure levels for this state are ε(F=12) = -13725.927(7) MHz, ε(F=32) = -5490.371(7) MHz and ε(F=52) = 8235.556(7) MHz, respectively. The observed hyperfine structure splittings for the the 23S(L=0) state in the 9Be atom must be Δ12 = 8235.556(7) MHz and Δ23 = 13725.927(7) MHz, respectively.

physics.atom-ph↗
arXiv2013

Three-particle integrals with the Bessel functions

Analytical formulas for some useful three-particles integrals are derived. Many of these integrals include Bessel and/or trigonometric functions of one and two interparticle (relative) coordinates $r_{32}, r_{31}$ and $r_{21}$. The formulas obtained in such an analysis allow us to consider three-particle integrals of more complicated functions of relative/perimetric coordinates. In many actual problems such three-particle integrals can be found in matrix elements of the Hamiltonian and other operators.

math-ph↗
arXiv2013

On the interaction between two point electric charges

The general formula for the interaction potential between two point electric charges which contains the lowest order corrections to the vacuum polarization is derived and investigated. Analytical derivation of this formula is based on the closed analytical expression for the Uehling potential obtained earlier. Our analytical formula has the correct asymtotic behaviour at small and large distances between two interacting electric charges. We also discuss a number of problems which are of great interest in applications, e.g., vacuum polarization corrections to the Coulomb scattering and cusp value between two electrically charged particles. An original algebraic procedure developed in this study allows one to determine consequtive corrections for vacuum polarization for Coulomb systems.

math-ph↗
arXiv2013

On the Schrödinger equation for the free gravitational field

The Hamiltonian of the metric General Relativity derived in our earlier study (Gravitation, {\bf 17}, 314 - 323 (2011)) is analyzed by the methods of Matrix Quantum Mechanics. 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 Hamiltonian is reduced to the new form which is more convenient to derive the Schrödinger equation for the free gravitational field. In turn, this Schrödinger equation is used to study possible motions of the free gravitational field(s). In particular, it is shown that harmonic oscillations of the free gravitational field, or harmonic gravitational waves, cannot be observed as an actual motion of this field. We also investigate the internal structure of the solitary gravitational wave.

math-ph↗
arXiv2013

On the ß- decay in the Li-8 and Li-9 atoms

The nuclear ß- decay from the ground and some excited states of the three-electron Li-8 and Li-9 atoms is considered. The final state probabilities for the arising Be+ ion are determined numerically with the use of highly accurate bound state wave functions of the Li atom and Be+ ion. The probability of electron ionization during the nuclear ß- decay of the Li atom is evaluated numerically. We also discuss a possibility to observe the double ß- decay by using the known values of the final state probabilities for the regular nuclear ß- decay.

physics.atom-ph↗
arXiv2013

Hylleraas-configuration-interaction analysis of the low-lying states in the three-electron Li atom and Be+ ion

The total energies of twenty eight bound S-, P-, D-, F-, G-, H-, and I-states in the three-electron systems Li atom and Be+ ion, respectively, are determined with the use of the Configuration Interaction (CI) with Slater orbitals and L-S eigenfunctions, and the Hylleraas-configuration-interaction (Hy-CI) methods. We discuss the construction and selection of the configurations in the wave functions, optimization of the orbital exponents and advanced computational techniques. Finally, we have developed a very effective procedure which allows one to determine the energies of the excited states in three-electron atoms and ions to high accuracy by using compact wave functions. For the ground and low lying excited states our best accuracy with the Hy-CI method was approximately 1.10-6 a.u. and 1.10-4 a.u. for other excited states. Analogous accuracy of the CI method is substantially lower approximately 1.10-3 a.u. Many of the rotationally excited (bound) states in the three-electron Li atom and Be+ ion have never been evaluated to such an accuracy.

physics.atom-ph↗
arXiv2013

On the bound state of the antiproton-deuterium-tritium ion

The properties of the weakly-bound $S(L = 0)-$state in the $\bar{p}dt$ ion are investigated with the use of the results of highly accurate computations. The hyperfine structure splitting of this ion is investigated. We also evaluate the life-time of the $\bar{p}dt$ ion against the nuclear $(d,t)-$fusion and discuss a possibility to evaluate the corresponding annihilation rate(s).

physics.atom-ph↗
arXiv2013

On the Galilean transformation of the few-electron wave functions

The Galilean transformations of the few-electron atomic wave functions are considered. We discuss the few-electron wave functions constructed in the model of independent electrons as well as the truly correlated (or highly accurate) wave functions. Results of our analysis are applied to determine the probability of formation of the negatively charged tritium/protium ions during the nuclear $(n,{}^{3}$He$;t,p)-$reaction of the helium-3 atoms with thermal/slow neutrons.

physics.atom-ph↗
arXiv2013

On the properties of the Uehling potential

A number of properties of the Uehling potential are investigated. In particular, we determine the Fourier spatial resolution of the Uehling potential. The lowest-order correction on vacuum polarisation is re-written in terms of the electron density distribution function. We also discuss the consecutive approximations of the perturbation theory developed for the short-range Uehling potential in the Coulomb few-body systems (atoms). The cusp problem is formulated for few-body systems in which particles interact with each other by the mixed (Coulomb + Uehling) potential.

physics.atom-ph↗
arXiv2013

On the nuclear $(n;t)-$reaction in the three-electron ${}^{6}$Li atom

The nuclear $(n;t)-$reaction of the three-electron ${}^{6}$Li atom with thermal/slow neutrons is considered. An effective method has been developed for determining the probabilities of formation of various atoms and ions in different bound states. We discuss a number of fundamental questions directly related to numerical computations of the final state atomic probabilities. A few appropriate variational expansions for atomic wave functions of the incident lithium atom and final helium atom and/or tritium negatively charged ion are discussed. It appears that the final ${}^4$He atom arising during the nuclear $(n,{}^{6}$Li; ${}^4$He$,t)$-reaction in the three-electron Li atom can also be created in its triplet states. The formation of the quasi-stable three-electron $e^{-}_3$ during the nuclear $(n; t)-$reaction at the Li atom is briefly discussed. Bremsstrahlung emitted by atomic electrons accelerated by the rapidly moving nuclear fragments from this reaction is analyzed. The frequency spectrum of the emitted radiation is investigated.

physics.atom-ph↗
arXiv2012

Hyperfine structure splitting of the positron-helium ions $e^{+}[^3$He$(2^3S)]$ and $e^{+}[^4$He$(2^3S)]$

The hyperfine structure splittings are determined for the lowest bound state in the positron-helium ion $e^{+}[^3$He$(2^3S)]$ and $e^{+}[^4$He$(2^3S)]$. In particular, we have fond that for the $e^{+}[{}^3$He$(2^3S)]$ ion one can observe the three following hyperfine structure splittinings: 5824.3986 $MHz$, 76466.5308 $MHz$ and 5824.4019 $MHz$. In the $e^{+}[{}^4$He$(2^3S)]$ ion only one hyperfine structure splitting 82963.0427 $MHz$ can be observed. All these values can be measured in modern experiments.

physics.atom-ph↗
arXiv2012

Analytical formula for the Uehling potential

The closed analytical expression for the Uehling potential is derived. The Uehling potential describes the lowest-order correction on vacuum polarisation in atomic and muon-atomic systems. We also derive the analytical formula for the interaction potential between two electrically charged point particles which includes correction to the vacuum polarisation, but has correct asymptotic behaviour at larger $r$. Our three-term analytical formula for the Uehling potential opens a new avenue in the study of the vacuum polarisation in light atomic systems.

nucl-th↗
arXiv2012

Mass corrections for the bound states in the muonic molecular ions

The mass corrections to the bound state energies of the three-body muonic molecular ions $ppμ, pdμ, ptμ, ddμ, dtμ$ and $ttμ$ are determined numerically from the results of highly accurate computations. The total energies and some other bound state properties of these ions are evaluated to very high accuracy for the bound $S(L = 0)-, P(L = 1)-$ and $D(L = 2)-$states. In these highly accurate calculations we used the most recent and accurate masses of particles $m_p, m_d, m_t$ and $m_μ$ known from high energy experiments.

physics.atom-ph↗
arXiv2012

Positron annihilation in the MuPs system

The life-time of the four-body atomic system MuPs ($μ^{+} e^{-}_2 e^{+}$ or muonium-positronium) against positron annihilation has been evaluated as $τ= \frac{1}Γ \approx 4.076453 \cdot 10^{-10}$ $sec$. Various annihilation rates for MuPs are determined to a good numerical accuracy, e.g., $Γ_{2 γ} \approx$ 2.446485$\cdot 10^{9}$ $sec^{-1}$, $Γ_{3 γ} \approx$ 6.62798$\cdot 10^{6}$ $sec^{-1}$, $Γ_{4 γ} \approx$ 3.61680$\cdot 10^{3}$ $sec^{-1}$, $Γ_{5 γ} \approx$ 6.32973 $sec^{-1}$. The hyperfine structure splitting for the ground state in the MuPs system has also been evaluated as $Δ$ = 23.078 $MHz$.

hep-ph↗
arXiv2012

Stability and hyperfine structure of the four- and five-body muon-atomic clusters $a^{+} b^{+} μ^{-} e^{-}$ and $a^{+} b^{+} μ^{-} e^{-} e^{-}$

Based on the results of accurate variational calculations we demonstrate stability of the five-body negatively charged ions $a^{+} b^{+} μ^{-} e^{-} e^{-}$. Each of these five-body ions contains two electrons $e^{-}$, one negatively charged muon $μ^{-}$ and two nuclei of the hydrogen isotopes $a, b = (p, d, t)$. The bound state properties of these five-body ions, including their hyperfine structure, are briefly discussed. We also investigate the hyperfine structure of the ground states of the four-body muonic quasi-atoms $a^{+} b^{+} μ^{-} e^{-}$. In particular, we determine the hyperfine structure splittings for the ground state of the four-body muonic quasi-atoms: $p^{+} d^{+} μ^{-} e^{-}$ and $p^{+} t^{+} μ^{-} e^{-}$.

physics.atom-ph↗
arXiv2012

The hyperfine structure of the ground states in the helium muonic atoms

The hyperfine structures of the ground states in the ${}^{3}$He$^{2+} μ^{-} e^{-}$ and ${}^{4}$He$^{2+} μ^{-} e^{-}$ helium-muonic atoms are investigated with the use of highly accurate variational wave functions. The differences between corresponding levels of hyperfine structure (i.e. hyperfine splittings) are determined to very high numerical accuracy. In particular, we have found that the hyperfine structure splitting in the ground state of the ${}^{4}$He$^{2+} μ^{-} e^{-}$ atom is $Δν\approx 4464.55454(3)$ $MHz$, while analogous splitting for the ${}^{3}$He$^{2+}μ^{-}e^{-}$ atom is $Δν\approx 4166.43547(3)$.

quant-ph↗