scispace - formally typeset
Search or ask a question
Author

Alexei M. Frolov

Bio: Alexei M. Frolov is an academic researcher from University of Western Ontario. The author has contributed to research in topics: Bound state & Ion. The author has an hindex of 20, co-authored 133 publications receiving 1313 citations. Previous affiliations of Alexei M. Frolov include Queen's University & Harvard University.
Topics: Bound state, Ion, Hyperfine structure, Electron, Atom


Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, the positron annihilation rates for the three-body system and the MuPs were evaluated for positronium hydrides, TPs, DPs, and the ion.
Abstract: The bound-state spectra of the positronium hydrides $^{\mathrm{\ensuremath{\infty}}}\mathrm{HPs}$, TPs, DPs, $^{1}\mathrm{HPs}$, and MuPs are considered. The properties of the bound ground S states (L=0) in these systems and the ${\mathrm{Ps}}_{2}$ molecule have been determined by extensive variational calculations. The hyperfine structure of these states is also investigated. The positron annihilation rates have been evaluated for the positronium hydrides, the ${\mathrm{Ps}}_{2}$ molecule, and the ${\mathrm{Ps}}^{\mathrm{\ensuremath{-}}}$ ion and compared. The positron annihilation rates ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{n}\ensuremath{\gamma}}$ (where n\ensuremath{\geqslant}2) in the positronium hydrides are significantly closer to those in the ${\mathrm{Ps}}^{\mathrm{\ensuremath{-}}}$ ion (the three-body system) than in the ${\mathrm{Ps}}_{2}$ molecule.

93 citations

Journal ArticleDOI
TL;DR: In this article, the problem of high-precision, variational, bound-state calculations in few-body systems is discussed and a simple and very effective variational procedure developed below makes possible numerical, bound state computations in few body systems with extremely high accuracy.
Abstract: The problem of high-precision, variational, bound-state calculations in few-body systems is discussed. The simple and very effective variational procedure developed below makes possible numerical, bound-state computations in few-body systems with extremely high accuracy. This procedure is based on the proposed two-stage strategy, which is used to construct the approximate wave function. The highly accurate numerical results, which include both energetical and geometrical properties, for various three-body systems $[{\mathrm{Ps}}^{\ensuremath{-}}{,}^{\ensuremath{\infty}}{\mathrm{H}}^{\ensuremath{-}}{,}^{\ensuremath{\infty}}\mathrm{He}$, and ${(\mathrm{ppe})}^{+}$] are presented.

91 citations

Journal ArticleDOI
TL;DR: The long-standing problem of highly accurate determination of the weakly bound (1,1) states in the ddmu and dtmu muonic molecular ions has finally been solved and is shown that the present approach can be used to solve various three-body problems with, in principle, arbitrary precision.
Abstract: Variational, multibox approach is proposed to construct extremely accurate, bound-state wave functions for arbitrary three-body systems. The high efficiency of our present approach is based on an optimal choice of nonlinear parameters in the exponential basis functions. The proposed method is very flexible, since the final wave function can also include a large number of separately optimized cluster fragments. The wave functions obtained are very compact and highly accurate. Such wave functions can be used to compute various bound state properties for different three-body systems. The proposed approach has been successfully tested on a large number of actual systems. It is shown that the present approach can be used to solve various three-body problems with, in principle, arbitrary precision. In particular, the long-standing problem of highly accurate determination of the weakly bound ~1,1! states in the ddm and dtm muonic molecular ions has finally been solved. The determined binding energies are 21.974 988 088 065310 210 eV and 20.660 338 7461 310 28 eV, respectively. In this study an advanced and variational approach is proposed and discussed. This approach can be used to determine to high accuracy, the bound-state spectra for various threebody systems. In fact, the proposed approach is found to be very effective and quite simple in solving a large number of bound-state, three-body problems. The accuracy of the bound-state determination in this approach is usually higher than in other competing methods, and more important, the accuracy can easily be increased. It should be mentioned, however, that highly accurate calculations are of great importance for many Coulomb three-body systems. For instance, to compute the hyperfine splitting in the helium-muonic atoms one needs to determine the electron-nucleus and electron-muonic delta functions with a maximal absolute error less than 1 310 28 a.u. @1#. The total bound-state energies for such systems are ’400 a.u. It can be estimated from this that the required wave function must reproduce the ground state energy with an absolute error less than ’1 310 218 a.u. Only for such highly accurate wave functions, eight significant figures as required for the two mentioned delta functions, are stable. Also, the electron-positron and nucleus-nucleus delta functions are very important for predicting the corresponding annihilation rates in the Ps 2 ion and fusion rates in the muonic molecular ions, respectively ~see, e.g. @2‐4 #!. Moreover, highly accurate nonrelativistic wave functions can be used to compute relativistic and Q.E.D. corrections for some actual atoms and ions. In fact, this is the only way to compute these corrections, since the alternative approach based on the Dirac equations cannot be used directly for three-body systems ~see, e.g., @5#!. The nonrelativistic Hamiltonian for an arbitrary Coulomb three-body system can be written in the form

79 citations

Journal ArticleDOI
TL;DR: In this paper, the positronium negative ion (Ps or eee) properties were determined by using highly accurate variational wave functions, which were constructed by applying the advanced two-stage strategy proposed by Frolov.
Abstract: Various geometrical and energetical ~bound-state! properties of the positronium negative ion (Ps or eee) are determined by using highly accurate variational wave functions. These wave functions have been constructed by applying the advanced two-stage strategy proposed by Frolov @Phys. Rev. A 57, 2436 ~1998!#. The determined total energy of the ground state E520.262 005 070 232 975 7 a.u. is the lowest and most accurate value obtained for this system to date ~the corresponding binding energy equals 20.326 674 721 317 821 eV). The computation of the second-order relativistic corrections (.a) to the total energy is discussed also. The general form of the Breit-Pauli Hamiltonian in the relative coordinates for the Ps ion is presented. @S1050-2947~99!04910-0#

62 citations

Journal ArticleDOI
TL;DR: In this paper, the exponential variational expansion in relative coordinates r32, r31 and r21 has been shown to have a number of advantages for the bound state calculations in Coulomb three-body systems.
Abstract: The exponential representation in the Coulomb three-body problem is considered. It is shown that the exponential variational expansion in relative coordinates r32, r31 and r21 has a number of advantages for the bound state calculations in Coulomb three-body systems. Moreover, it appears that the exponential (or Laplace–Fourier) representation of the Coulomb three-body problem is an optimal approach to analyse and solve various three-body problems. The optimization of nonlinear parameters in the trial wavefunctions is also considered. The developed methods are used to determine the highly accurate ground 11S(L = 0)-state energies and other bound state properties for a number of He-like two-electron ions (Li+, Be2+, B3+, C4+, N5+, O6+, F7+ and Ne8+). To represent the ground state energies of these He-like ions we apply the Z−1 expansion. The asymptotic form of the ground state wavefunctions at large electron–nuclear distances for the He-like ions is briefly discussed. Considered hypervirial theorems are of great interest for these ions, since they allow one to obtain some useful relations between different expectation values. The generalization of the exponential variational expansion in relative coordinates to the four-body non-relativistic systems is also considered.

43 citations


Cited by
More filters
Book ChapterDOI
01 Jan 1998

1,532 citations

Journal Article
TL;DR: In this paper, the subject of quantum electrodynamics is presented in a new form, which may be dealt with in two ways: using redundant variables and using a direct physical interpretation.
Abstract: THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

1,398 citations

Journal ArticleDOI
TL;DR: In this article, the authors present a review of the application of atomic physics to address important challenges in physics and to look for variations in the fundamental constants, search for interactions beyond the standard model of particle physics and test the principles of general relativity.
Abstract: Advances in atomic physics, such as cooling and trapping of atoms and molecules and developments in frequency metrology, have added orders of magnitude to the precision of atom-based clocks and sensors. Applications extend beyond atomic physics and this article reviews using these new techniques to address important challenges in physics and to look for variations in the fundamental constants, search for interactions beyond the standard model of particle physics, and test the principles of general relativity.

1,077 citations

Journal ArticleDOI
TL;DR: In this paper, the real variable is replaced by a complex variable, and the factorial and related functions of the complex variable are used to solve linear differential equations of the second order.
Abstract: 1. The real variable 2. Scalars and vectors 3. Tensors 4. Matrices 5. Multiple integrals 6. Potential theory 7. Operational methods 8. Physical applications of the operational method 9. Numerical methods 10. Calculus of variations 11. Functions of a complex variable 12. Contour integration and Bromwich's integral 13. Contour integration 14. Fourier's theorem 15. The factorial and related functions 16. Solution of linear differential equations of the second order 17. Asymptotic expansions 18. The equations of potential, waves and heat conduction 19. Waves in one dimension and waves with spherical symmetry 20. Conduction of heat in one and three dimensions 21. Bessel functions 22. Applications of Bessel functions 23. The confluent hypergeometric function 24. Legendre functions and associated functions 25. Elliptic functions Notes Appendix on notation Index.

771 citations

Journal ArticleDOI
TL;DR: Explicitly Correlated Electrons in Molecules Christof Hattig, Wim Klopper,* Andreas K€ohn, and David P. Tew Lehrstuhl.
Abstract: Explicitly Correlated Electrons in Molecules Christof H€attig, Wim Klopper,* Andreas K€ohn, and David P. Tew Lehrstuhl f€ur Theoretische Chemie, Ruhr-Universit€at Bochum, D-44780 Bochum, Germany Abteilung f€ur Theoretische Chemie, Institut f€ur Physikalische Chemie, Karlsruher Institut f€ur Technologie, KIT-Campus S€ud, Postfach 6980, D-76049 Karlsruhe, Germany Institut f€ur Physikalische Chemie, Johannes Gutenberg-Universit€at Mainz, D-55099 Mainz, Germany School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom

474 citations