arXiv subjects
Publications and source records attributed to Alexei M. Frolov.
The original text has been changed substantially since the first version of this paper. Finally, we have decided to split that submission in two parts. Each of them includes a large number of updates and corrections. They were placed on ArXiv with new numbers (see: ArXiv:1110.3433 and 1111.2303).
Total energies and various bound state properties are determined for the ground states in all six four-body muonic $a^{+} b^{+} μ^{-} e^{-}$ quasi-atoms. These quasi-atoms contain two nuclei of the hydrogen isotopes $p^{+}, d^{+}, t^{+}$, one negatively charged muon $μ^{-}$ and one electron $e^{-}$. In general, each of the four-body muonic $a^{+} b^{+} μ^{-} e^{-}$ quasi-atoms, where $(a, b) = (p, d, t)$, can be considered as the regular one-electron (hydrogen) atom with the complex nucleus $a^{+} b^{+} μ^{-}$ which has a finite number of bound states. Furthermore, all properties of such quasi-nuclei $a^{+} b^{+} μ^{-}$ are determined from highly accurate computations performed for the three-body muonic ions $a^{+} b^{+} μ^{-}$ with the use of pure Coulomb interaction potentials between particles. It is shown that the bound state spectra of such quasi-atoms are similar to the spectrum of the regular hydrogen atoms, but there are a few important differences. Such differences can be used in future experiments to improve the overall accuracy of current evaluations of various properties of hydrogen-like systems, including the lowest-order relativistic and QED corrections.
Approximate probabilities of formation of various atoms and ions in different bound states are determined for the exothermic nuclear $(n,{}^{6}$Li$;t,{}^{4}$He)-reaction of atomic lithium-6 with slow neutrons. In our calculations of the final state probabilities we have assumed that the incident lithium atom is in its ground (doublet) atomic ${}^2S(L = 0)-$state. It is straightforward to generalize our analysis to other bound states of the three-electron Li atom.
Probabilties of formation of various hydrogenic species during the exothermic nuclear $(n,{}^3$He$;t,p)-$reaction of atomic helium-3 with slow neutrons are determined. In particular, we have found that the probability to form the tritium atom ${}^3$H in its ground state is $\approx$ 55.19287 %, while analogous probability to form the protium atom ${}^1$H is $\approx$ 1.02363 %. Analogous probabilities of formation of the negatively charged hydrogen ions, i.e. the ${}^3$H$^{-}$ and ${}^1$H$^{-}$ ions, in the nuclear $(n,{}^3$He$; t,p)-$reaction with slow neutrons, are $\approx$ 7.8680 % and $\approx$ 0.06583 %, respectively. We also consider bremsstrahlung from fast fission-type reactions in atomic systems. The spectrum of emitted radiation is analyzed.
The total energies and various bound state properties of the excited $2^1S(L = 0)-$states in two-electron helium atoms, including the ${}^{\infty}$He, ${}^4$He and ${}^3$He atoms, are determined to very high numerical accuracy. The convergence of the results obtained for some electron-nuclear and electron-electron expectation values and, in particular, for the electron-nuclear and electron-electron cusp values, is discussed. The field component of the isotope shift and lowest order QED correction are estimated for the $2^1S(L = 0)-$states in the ${}^4$He and ${}^3$He atoms. We also apply our highly accurate methods to numerical computations of the excited $n^1S-$states (for $n$ = 3 and 4) in two-electron atomic systems.
The variational procedure to construct compact and accurate wave functions for three-electron atoms and ions is developed. The procedure is based on the use of six-dimensional gaussoids written in the relative four-body coordinates $r_{12}, r_{13}, r_{23}, r_{14}, r_{24}$ and $r_{34}$. The non-linear parameters in each basis function have been optimized carefully. By using these variational wave functions we have determined the energies and other bound state properties are determined for the ground $1^2S$-states in a number of three-electron atoms and ions. The three-electron atomic systems considered in this work include the neutral Li atom and nine positively charged lithium-like ions: Be$^+$, B$^{2+}$, C$^{3+}, ...$Na$^{8+}$ and Mg$^{9+}$. Our variational wave functions are used to determine the hyperfine structure splitting and field shifts for some lithium-like ions. The explicit formulas of the $Q^{-1}$ expansion are derived for the total energies of these three-electron systems.
The results of highly accurate calculations are presented for all twenty-two known bound $S(L = 0)-, P(L = 1)-, D(L = 2)-$ and $F(L = 3)-$states in the six three-body muonic molecular ions $ppμ, pdμ, ptμ, ddμ, dtμ$ and $ttμ$. A number of bound state properties of these muonic molecular ions have been determined numerically to high accuracy. The dependence of the total energies of these muonic molecules upon particle masses is considered. We also discuss the current status of muon-catalysis of nuclear fusion reactions.
The basic principles of classical and semi-classical theories of molecular optical activity are discussed. These theories are valid for dilute solutions of optically active organic molecules. It is shown that all phenomena known in the classical theory of molecular optical activity can be described with the use of one pseudo-scalar which is a uniform function of the incident light frequency $ω$. The relation between optical rotation and circular dichroism is derived from the basic Kramers-Kronig relations. In our discussion of the general theory of molecular optical activity we introduce the tensor of molecular optical activity. It is shown that to evaluate the optical rotation and circular dichroism at arbitrary frequencies one needs to know only nine (3 + 6) molecular tensors. The quantum (or semi-classical) theory of molecular optical activity is also briefly discussed. We also raise the possibility of measuring the optical rotation and circular dichroism at wavelengths which correspond to the vacuum ultraviolet region, i.e. for $λ\le 150$ $nm$.
The optical activity tensor (OAT) is explicitly derived. It is shown that to evaluate a large number of effects related to optical activity of some atomic/molecular system at arbitrary frequency $ω$ of the incident light, one needs to know only four optical activity tensors which have twelve irreducible (tensor) components. An additional amplification factor contains one $3 \times 3$ tensor of light scattering with three irreducible components. The explicit dependence of all irreducible components of OAT upon $ω$ and some molecular parameters is derived and discussed. We apply OAT to explain the dispersion of optical rotation in dilute solutions of organic molecules. This study opens a new avenue in application of methods of modern Quantum Electrodynamics to the optical activity.
The thermonuclear burn-up of highly compressed deuterated methane CD$_4$ is considered in the spherical geometry. The minimal required values of the burn-up parameter $x = ρ_0 \cdot r_f$ are determined for various temperatures $T$ and densities $ρ_0$. It is shown that thermonuclear burn-up in $CD_4$ becomes possible in practice if its initial density $ρ_0$ exceeds $\approx 5 \cdot 10^3$ $g \cdot cm^{-3}$. Burn-up in CD$_2$T$_2$ methane requires significantly ($\approx$ 100 times) lower compressions. The developed approach can be used in order to compute the critical burn-up parameters in an arbitrary deuterium containing fuel.
An effective optimization strategy has been developed to construct highly accurate bound state wave functions in various three-body systems. Our procedure appears to be very effective for computations of weakly bound states and various excited states, including rotationally excited states, i.e. states with $L \ge 1$. The efficiency of our procedure is illustrated by computations of the excited $P^{*}(L = 1)-$states in the $ddμ, dtμ$ and $ttμ$ muonic molecular ions, $P(L = 1)-$states in the non-symmetric $pdμ, ptμ$ and $dtμ$ ions and $2^{1}P(L = 1)-$ and $2^{3}P(L = 1)-$states in He atom(s).
Probabilities of various final states are determined numerically for a number of ß- decaying light atoms. In our evaluations of the final state probabilities we have used the highly accurate atomic wave functions constructed for each few-electron atom/ion. We also discuss an experimental possibility to observe negatively charged ions which form during the nuclear ß+ decays. High order corrections to the results obtained for ß+/- decays in few-electron atoms with the use of sudden approximation are considered.
The internal conversion of nuclear transition in the ${}^{235}U$ atom is considered. The low-energy $γ-$quanta ($E_γ \approx$ 76.8 $eV$) are emitted during the $E3-$transition from the excited state ($I = (\frac12)^+$) of the ${}^{235}U$ nucleus to its ground state ($I = (\frac72)^-$). The decay rate of this ${}^{235m}U$ isomer ($E \approx 76.8$ $eV$) noticeably depends upon the chemical composition and actual physical conditions (i.e. temperature $T$ and pressure $p$). By varying such a composition and physical conditions one can change the life-time of the ${}^{235m}U$ isomer to relatively large/small values. A specific attention is given to the fullerene molecules containing the central ${}^{235}U$ atom. It is shown that the decay rate $λ$ of the ${}^{235m}U$ isomer in the ${}^{235m}U@C_{60-n}X_n$ molecules and related compounds can differ significantly from the values obtained for isolated ${}^{235}U$ atoms. Some applications of this effect are considered.
The hyperfine structure of the ground states in a number of positronium hydrides (TPs, DPs, ${}^{1}$HPs) and MuPs ($μ^{+} e^{-}_2 e^{+}$) is determined with the use of highly accurate variational wave functions. We also evaluate the probabilities of various processes in the MuPs system, including the $(e^{-}, e^{+})$-pair annihilation and its conversion into the charge conjugate system $μ^{+} e^{-}_2 e^{+} \to μ^{-} e^{-} e^{+}_2$.
Annihilation of the electron-positron pairs in macroscopic polyelectrons is considered. It is shown that very fast collapse of the spatial area occupied by macroscopic polyelectron (or dense electron-positron plasma) produces an instant annihilation of a very large number of electron-positron pairs. This phenomenon corresponds to the so-called annihilation explosion. Annihilation of each electron-positron pair is a highly exothermic process. Therefore, in dense electron-positron plasma one can observe a very interesting phenomenon of photon detonation, i.e. a self-organized formation and propagation of the detonation wave which coincides with the annihilation wave. The photon detonation can be used in many applications, including many military and astrophysical problems.
Rates of the two-, three-, four- and five-photon annihilations of the electron-positron pairs are determined numerically for the three-body positronium ion Ps$^-$ ($e^- e^+ e^-$) and four-body bi-positronium `molecule' Ps$_2$ ($e^- e^+ e^- e^+$). The values obtained in our computations are $Γ_{2 γ}($Ps$^-) \approx$ 2.08048530525$\cdot 10^{9}$ $sec^{-1}$, $Γ_{3 γ}($Ps$^-) \approx$ 5.6364151550$\cdot 10^{6}$ $sec^{-1}$, $Γ_{4 γ}($Ps$^-) \approx$ 3.075$\cdot 10^{3}$ $sec^{-1}$, $Γ_{5 γ}($Ps$^-) \approx 5.383$ $sec^{-1}$ and $Γ_{2 γ}($Ps$_2) \approx$ 4.4385952$\cdot 10^{9}$ $sec^{-1}$, $Γ_{3 γ}($Ps$_2) \approx$ 1.202497$ \cdot 10^7$ $sec^{-1}$, $Γ_{4 γ}($Ps$_2) \approx$ 6.562$\cdot 10^3$ $sec^{-1}$, $Γ_{5 γ}($Ps$_2) \approx$ 11.484 $sec^{-1}$. The four- and five-photon annihilation rates are significantly smaller than the corresponding two- and three-photon annihilation rates known for these systems. We also determine the rates of one- and zero-photon annihilation for the Ps$^{-}$ ion and Ps$_2$ system. The corresponding numerical values are $Γ_{1 γ}($Ps$^-) \approx$ 3.82491$\cdot 10^{-2}$ $sec^{-1}$, $Γ_{1 γ}($Ps$_2) \approx$ 1.94188$\cdot 10^{-1}$ $sec^{-1}$ and $Γ_{0 γ}($Ps$_2) \approx$ 2.32197$\cdot 10^{-9}$ $sec^{-1}$. Pusblished almost `as is' in Phys. Rev. A {\bf 80}, 014502 (2009).
This paper has been withdrawn due to disagreement of suggested results and methods between authors.