arXiv subjects

Alexei M Frolov

Publications and source records attributed to Alexei M Frolov.

7 recordsLinked to original sources

arXiv2019

Asymptotic and interpolation series for the Coulomb three-body systems with unit charges

Accurate mass-interpolation and mass-asymptotic formulas are derived for one- and two-center three-body ions with unit charges. The derived formulas are applied to predict accurate numerical values of the total energies of the ground (bound) $1^{1}S(L = 0)-$states in one-center atomic ions $X^{+} e^{-} e^{-}$ and analogous ground (bound) $1 s σ-$states in the two-center, quasi-adiabatic (or quasi-molecular) $X^{+} X^{+} e^{-}$ ions. We also discuss a few problems which currently remain unsolved for the $Q^{-1}$ expansions constructed for the ground (bound) states in few-electron atoms and ions.

physics.atom-ph↗

arXiv2017

Highly accurate bound state calculations of the two-center molecular ions by using the universal variational expansion for three-body systems

The universal variational expansion for the non-relativistic three-body systems is explicitly constructed. Three-body universal expansion can be used to perform highly accurate numerical computations of the bound state spectra in arbitrary three-body systems, including Coulomb three-body systems with arbitrary particle masses and electric charges. Our main interest is related to the adiabatic three-body systems which contain one bound electron and two heavy nuclei of hydrogen isotopes: the protium $p$, deuterium $d$ and tritium $t$. We also consider the analogous (model) hydrogen ion ${}^{\infty}$H$^{+}_2$ with the two infinitely heavy nuclei. PACS number(s): 36.10.-k and 36.10.Dr

physics.atom-ph↗

arXiv2017

Matrix mechanics for actual atoms and molecules

Matrix mechanics is developed to describe the bound state spectra in few- and many-electron atoms, ions and molecules. Our method is based on the matrix factorization of many-electron (or many-particle) Coulomb Hamiltonians which are written in hyperspherical coordinates. As follows from the results of our study the bound state spectra of many-electron (or many-particle) Coulomb Hamiltonians always have the `ladder' structure and this fundamental fact can be used to determine and investigate the bound states in various few- and many-body Coulomb systems.

quant-ph↗

arXiv2017

Quasi-atomic three- and four-body systems with muonium

Properties of some few-body systems which include one positively charged muon $μ^{+}$ and two electrons $e^{-}$ are discussed. In particular, we consider the negatively charged muonium ion Mu$^{-}$ (or $μ^{+} e^{-}_{2}$) and four-body MuPs (or $μ^{+} e^{-}_{2} e^{+}$) systems each of which has only one stable bound (ground) state. The problem of annihilation of the electron-positron pair(s) in the MuPs system is investigated. The hyperfine structure splitting of the ground state in the MuPs system evaluated with our expectation value of the muon-positron delta-function is $Δ\approx$ 23.05758 $MHz$. Another group of interesting four-body neutral systems investigated in this study includes the $p^{+} μ^{+} e^{-}_2, d^{+} μ^{+} e^{-}_2$ and $t^{+} μ^{+} e^{-}_2$ `quasi-molecules'. These quasi-molecules are formed in large numbers when positively charged muons slow down in liquid hydrogen, or in liquid deuterium and/or tritium. The properties of these systems are unique, since they occupy an intermediate position between actual two-center molecules and one-center atoms.

physics.atom-ph↗

arXiv2016

On the hyperfine structure of the triplet $n^{3}S-$states of the four-electron atoms and ions

Hyperfine structures of the triplet $n^3S-$states in the four-electron Be-atom(s) and Be-like ions are considered. It is shown that to determine the hyperfine structure splitting in such atomic systems one needs to know the triplet electron density at the central atomic nucleus $ρ_T(0)$. We have developed the procedure which allows allows one to determine such an electron density $ρ_T(0)$ for arbitrary four-electron atoms and ions.

physics.atom-ph↗

arXiv2010

Compact and accurate variational wave functions of three-electron atomic systems constructed from semi-exponential radial basis functions

The semi-exponential basis set of radial functions (A.M. Frolov, Physics Letters A {\bf 374}, 2361 (2010)) is used for variational computations of bound states in three-electron atomic systems. It appears that semi-exponential basis set has a substantially greater potential for accurate variational computations of bound states in three-electron atomic systems than it was originally anticipated. In particular, the 40-term Larson's wave function improved with the use of semi-exponential radial basis functions now produces the total energy \linebreak -7.47805413551 $a.u.$ for the ground $1^2S-$state in the ${}^{\infty}$Li atom (only one spin function $χ_1 = αβα- βαα$ was used in these calculations). This variational energy is very close to the exact ground state energy of the ${}^{\infty}$Li atom and it substantially lower than the total energy obtained with the original Larson's 40-term wave function (-7.477944869 $a.u.$).

hep-ph↗

arXiv2010

On bound state computations in three- and four-electron atomic systems

A variational approach is developed for bound state calculations in three- and four-electron atomic systems. This approach can be applied to determine, in principle, an arbitrary bound state in three- and four-electron ions and atoms. Our variational wave functions are constructed from four- and five-body gaussoids which depend upon the six ($r_{12}, r_{13}, r_{14}, r_{23}, r_{24}, r_{34}$) and ten ($r_{12}, r_{13}, r_{14}, r_{15}, r_{23}, r_{24}, r_{25}, r_{34}, r_{35}$ and $r_{45}$) relative coordinates, respectively. The approach allows one to operate with the different number of electron spin functions. In particular, the trial wave functions for the ${}^1S$-states in four-electron atomic systems include the two independent spin functions $χ_1 = αβαβ+ βαβα- βααβ- αββα$ and $χ_2 = 2 ααββ+ 2 ββαα- βααβ- αββα- βαβα- αβαβ$. We also discuss the construction of variational wave functions for the excited $2^3S$-states in four-electron atomic systems.

physics.atom-ph↗