arXiv subjects

Alexei M. Frolov

Publications and source records attributed to Alexei M. Frolov.

At least 55 records · Page 3Linked to original sources

arXiv2015

On the interpolation formula for the bound state energies of atomic systems

By using results of highly accurate computations of the total energies of a large number of few-electron atoms we construct a few interpolation formulas which can be used to approximate the total energies of bound atomic states. In our procedure the total energies of atomic states $E$ are represented as a function of the electric charge of atomic nucleus $Q$ and the total number of bound electrons $N_e$. Some general properties of the $E(Q, N_e)$ function are investigated. The knowledge of the $E(Q, N_e)$ function allows one to determine the total (and binding) energies of these states in arbitrary atoms and ions with different $Q$ and $N_e$.

physics.atom-ph↗

arXiv2015

New method for highly accurate calculations of the photodetachment cross-sections of the negatively charged hydrogen ions

New approach to highly accurate calculations of the photodetachment cross-sections of the negatively charged hydrogen ions is developed. This effective, fast and numerically stable method is based on the use of the Rayleigh's formula for the spherical Bessel functions. Photodetachment cross-sections of the negatively charged hydrogen ion(s) ${}^{\infty}$H$^{-}$, ${}^{1}$H$^{-}$ (protium), ${}^{2}$H$^{-}$ (deuterium D$^{-}$) and ${}^{3}$H$^{-}$ (tritium T$^{-}$) are determined with the use of highly accurate, truly correlated, variational wave functions constructed for these ions. Our method allows one to investigate the problem of photodetachment of the negatively charged hydrogen ions completely, i.e. without any limitation by numerical values of the photo-electron momentum $p_e$.

astro-ph.SR↗

arXiv2015

Properties of negatively charged lithium ions and evaluation of the half-life of ${}^{7}$Be atom(s)

Bound state properties of the four-electron lithium ion Li$^{-}$ in its ground $2^{2}S-$state and isotope-subsistuted ${}^{6}$Li$^{-}$ and ${}^{7}$Li$^{-}$ ions in their ground $2^1S-$state(s) are determined from the results of accurate, variational computations. Another closely related problem discussed in this study is accurate numerical evaluation of the half-life of the beryllium-7 isotope. This problem is of paramount importance for modern radiochemistry.

physics.atom-ph↗

arXiv2015

Bound state properties and photodetachment of the negatively charged hydrogen ions

Absorption of infrared and visible radiation from stellar emission spectra by the negatively charged hydrogen ions H$^{-}$ is considered. The explicit formula for the photodetachment cross-section of the negatively charged hydrogen ion(s) is derived. Photodetachemnt cross-sections of the ${}^{\infty}$H$^{-}$, ${}^{3}$H$^{-}$ (or T$^{-}$), ${}^{2}$H$^{-}$ (or D$^{-}$) and ${}^{1}$H$^{-}$ ions are determined to high accuracy and for a large number of photo-electron momenta/energies. We introduce criteria which can be used to evaluate the overall quality of highly accurate wave functions of the hydrogen ion(s). One of these criteria is based on highly accurate calculations of the lowest order QED corrections in the negatively charged hydrogen ions, including ${}^{1}$H$^{-}$ (protium), ${}^{2}$H$^{-}$ (deuterium), ${}^{3}$H$^{-}$ (tritium) and model ion with the infinitely heavy nucleus ${}^{\infty}$H$^{-}$. An effective approach has been developed to calculate three-body integrals with the Bessel functions of different orders. Some preliminary evaluations of the phototdetachment cross-sections of the negatively charged hydrogen ions are performed. Inverse bremsstrahlung in the field of the neutral hydrogen atom is briefly discussed.

astro-ph.SR↗

arXiv2015

Singlet and triplet bound state spectra in the four-electron Be-like atomic systems

A large number of bound singlet and triplet states in the four-electron Be-atom and Be-like ions B$^+$, C$^{2+}$, F$^{5+}$ and Mg$^{8+}$ are determined to milli-Hartree numerical accuracy ($1\cdot 10^{-3}$ a.u.). These states include the bound singlet and triplet $S$-, $P$-, $D$-, $F$-, $G$-, $H$-, $I$- and $K$-states. Based on computational results we analyze the singlet and triplet series of the Be atom bound state spectrum and some four-electron ions: B$^+$, C$^{2+}$, F$^{5+}$ and Mg$^{8+}$ (Be-like ions). The analogous study of the Be atom triplet states was the topic of our earlier study (A.M. Frolov and M.B. Ruiz, CPL 595-596, 197 (2014)). The computational data allowed us to draw the spectral diagram of the bound state spectrum of the Be-atom and other four-electron ions mentioned above. The Be-atom spectrum contains the two optical series of bound states: singlets and triplets.

physics.atom-ph↗

arXiv2015

Annihilation, bound state properties and photodetachment of the positronium negatively charged ion

Bound state properties of the negatively charged Ps$^{-}$ ion (or $e^{-} e^{+} e^{-}$) are discussed. The expectation values of operators which correspond to these properties have been determined with the use of the highly accurate wave functions constructed for this ion. Our best variational energy obtained for the Ps$^{-}$ ion is $E$ = -0.2620050 7023298 0107770 40051 $a.u.$ Annihilation of the electron-positron pair(s) in the negatively charged Ps$^{-}$ ion (or $e^{-} e^{+} e^{-}$) is considered in detail. By using accurate values for a number annihilation rates $Γ_{n γ}$, where $n$ = 1, 2, 3, 4 and 5, we evaluated the half-life $τ_a$ of the Ps$^{-}$ ion against positron annihilation ($τ_a = \frac{1}Γ \approx 4.793584140 \cdot 10^{-10}$ $sec$). Photodetachment of the Ps$^{-}$ ion is considered in the long-range, asymptotic approximation. The overall accuracy of our photodetachment cross-section of the Ps$^{-}$ ion is very good for such a simple approximation.

physics.atom-ph↗

arXiv2015

On the 150th anniversary of Maxwell equations

In this lecture we discuss some interesting developments in the modern theory of electromagnetic field(s). In particular, by using the methods developed in Dirac's constraint dynamics we derive the Schrödinger equation for the free electromagnetic field. The electromagnetic field that arises only contains combinations of transverse photons and does not include any scalar and/or longitudinal photons. This approach is also used to determine and investigate the actual symmetry of the free electromagnetic field. Then we discuss the Majorana representation of the Maxwell equations, the symmetric form of Maxwell equations and an original approach to electrodynamics called the "scalar electrodynamics".

quant-ph↗

arXiv2015

Tree-particle integrals with spherical Bessel and Neumann functions

A few approaches are derived to calculate three-particle integrals which include spherical Bessel functions of the first and second kind, i.e., the $j_{\ell}(V r)$ and $n_{\ell}(V r)$ functions. Such integrals are important in applications to various problems known in atomic and nuclear physics. In particular, these integrals are needed in accurate computations of the photodetachment cross-section(s) of the negatively charged hydrogen ions.

math-ph↗

arXiv2015

Internal structure and positron annihilation in the four-body MuPs system

A large number of bound state properties of the four-body muonium-positronium system MuPs (or $μ^{+} e^{-}_2 e^{+}$) are determined to high accuracy. Based on these expectation values we predict that the weakly-bound four-body MuPs system has the `two-body' cluster structure Mu + Ps. The two neutral clusters Mu ($μ^{+} e^{-}$) and Ps ($e^{+} e^{-}$) interact with each other by the attractive van der Waals forces. By using our expectation values of the electron-positron delta-functions we evaluated the half-life $τ_a$ of the MuPs system against annihilation of the electron-positron pair: $τ_a = \frac{1}Γ \approx 4.071509 \cdot 10^{-10}$ $sec$. The hyperfine structure splitting of the ground state in the MuPs system evaluated with our expectation values is $Δ\approx$ 23.064(5) $MHz$.

quant-ph↗

arXiv2014

Ionization of light atoms and ions during the nuclear $β^{-}$-decay

Ionization of light atoms and ions during the nuclear $β^{-}$-decay is considered. To determine the final state probabilities of electron ionization we have developed a procedure based on the natural orbital expansions for the bound state wave functions of all atoms/ions involved in this process.

physics.atom-ph↗

arXiv2014

Numerical evaluations of the isotopic shifts and lowest-order QED corrections for the ground $1^1S-$states of the ${}^{3}$He and ${}^{4}$He atoms

The both mass-dependent and field shift components of the isotopic shifts and the lowest order QED corrections for the ground (singlet) $1^1S(L = 0)-$states of the ${}^{3}$He and ${}^{4}$He atoms are determined to high accuracy. For the same states we also evaluated the lowest-order QED corrections and the corresponding recoil (or finite mass) corrections. In our calculations we have used the new (corrected) formula for the recoil correction to the lowest-order QED correction which can be applied to atoms/ions with arbitrary nuclear charge $Q \ge 1$.

physics.atom-ph↗

arXiv2014

On the symmetry definitions for the constraint dynamical systems

The problem of proper symmetry definition for constraint dynamical systems with Hamiltonians is considered. Finally, we choose a definition of symmetry which agrees with the analogous definition used for the non-constraint dynamical systems with Hamiltonians. Our symmetry definition allows one to consider the whole spectrum of the Hamiltonian without splitting it into a few different parts.

quant-ph↗

arXiv2014

Accurate evaluations of the field shift and lowest-order QED correction for the ground $1^1S-$states of some light two-electron ions

Mass-dependent and field shift components of the isotopic shift are determined to high accuracy for the ground $1^1S-$states of some light two-electron Li$^{+}$, Be$^{2+}$, B$^{3+}$ and C$^{4+}$ ions. To determine the field components of these isotopic shifts we apply the Racah-Rosental-Breit formula. We also determine the lowest order QED corrections to the isotopic shifts for each of these two-electron ions.

physics.atom-ph↗

arXiv2014

On the products of bipolar harmonics

The products of the two and three bipolar harmonics ${\cal Y}^{\ell_1 \ell_2}_{LM}({\bf r}_{31}, {\bf r}_{32})$ are represented as the finite sums of powers of the three relative coordinates $r_{32}, r_{31}$ and $r_{21}$. The complete (angular+radial) integrals of the products of the two and three bipolar harmonics in the basis of exponential radial functions are expressed as finite sums of the auxiliary three-particle integrals $Γ_{n,k,l}(α, β, γ)$. The formulas derived in this study can be used to accelerate highly accurate computations of the rotationally excited (bound) states in arbitrary three-body systems. In particular, we have constructed compact (400-term) variational wave functions for the triplet and singlet $2P(L = 1)-$states in light two-electron atoms and ions. Highly accurate calculations (20 - 21 stable decimal digits in the total energy) of the triplet and singlet $2P(L = 1)-$states in the two-electron Li$^{+}$, Be$^{2+}$, B$^{3+}$ and C$^{4+}$ ions are performed for the first time

physics.atom-ph↗

arXiv2014

Bound state spectra and properties of the doublet states in three-electron atomic systems

The bound state spectra of the doublet states in three-electron atomic systems are investigated. By using different variational expansions we determine various bound state properties in these systems. Such properties include the electron-nucleus and electron-electron delta-functions and cusp values. The general structure of the bound state spectra in several three-electron atomic systems (Li, Be+, C3+ and F6+) is investigated with the use of the Hylleraas-Configuration Interaction and the Configuration Interaction wave functions. The advantage of our Configuration Interaction based procedure is that it provides high numerical accuracy for all rotationally excited states, including the bound states with L >= 7.

physics.atom-ph↗

arXiv2014

Bound state spectrum of the triplet states in the Be atom

The bound state spectrum of the low-lying triplet states in the Be atom is investigated. In particular, we perform accurate computations of the bound triplet $S$, $P$, $D$, $F$, $G$, $H$ and $I$ states in the Be atom. The results of these calculations are employed to draw the spectral diagram which contains the energy levels of the triplet states. Based on our computational results we can observe transitions from the low-lying bound states to the weakly-bound Rydberg states. For the $2^3S$, $3^3S$ and $4^3S$ states in the Be atom we also determine a number of bound states properties.

physics.atom-ph↗

arXiv2013

On the absorption of radiation by the negatively charged hydrogen ion. I. General theory and construction of the wave functions

The absorption of infrared and visible radiation from stellar emission spectra by the negatively charged hydrogen ions H$^{-}$ is considered. We derive the explicit formulas for the bound-free absorption coefficient $a_ν$ for the negatively charged hydrogen ion ${}^{\infty}$H$^{-}$ and its isotopes ${}^{1}$H$^{-}$ (protium) and ${}^{2}$H$^{-}$ (deuterium or D$^{-}$). The bound-free absorption coefficient $a_ν$ is used to evaluate the actual absorption of infrared and visible radiation by the H$^{-}$ ion in photospheres of many cold stars with surface temperatures $T_s \le$ 8,250 $K$.

astro-ph.SR↗

arXiv2013

Hyperfine structure of the $2^3S-$state in the ${}^9$Be atom

A number of bound states properties and the hyperfine structure of the 23S(L=0)-state in the Be atom are determined from the results of highly accurate computations. The energies of the hyperfine structure levels for this state are ε(F=12) = -13725.635(7) MHz, ε(F=32) = -5490.254(7) MHz and ε(F=52) = 8235.381(7) MHz, respectively. The hyperfine structure splittings are Δ12 = 8235.381(7) MHz and Δ23 = 13725.635(7) MHz, respectively. The spectrum of low-lying (bound) triplet states in the Be atom is briefly investigated.

physics.atom-ph↗