arXiv subjects

David M. Wardlaw

Publications and source records attributed to David M. Wardlaw.

At least 19 recordsLinked to original sources

arXiv2016

On accurate computations of slowly convergent atomic properties in few-electron ions and electron-electron correlations

We discuss an approach to accurate numerical computations of slowly convergent properties in two-electron atoms/ions which include the negatively charged Ps$^{-}$ ($e^{-} e^{+} e^{-}$) and H$^{-}$ ions, He atom and positively charged, helium-like ions from Li$^{+}$ to Ni$^{26+}$. All these ions are considered in their ground $1^{1}S-$state(s). The slowly convergent properties selected in this study include the electron-nulceus $\langle r^{2 k}_{eN} \rangle$ and electron-electron $\langle r^{2 k}_{ee} \rangle$ expectation values for $k$ = 2, 3, 4 and 5.

physics.atom-ph↗

arXiv2016

Accurate computations of bound state properties in three- and four-electron atomic systems in the basis of multi-dimensional gaussoids

Results of accurate computations of bound states in three- and four-electron atomic systems are discussed. Bound state properties of the four-electron lithium ion Li$^{-}$ in its ground $2^{2}S-$state are determined from the results of accurate, variational computations. We also consider a closely related problem of accurate numerical evaluation of the half-life of the beryllium-7 isotope. This problem is of paramount importance for modern radiochemistry.

physics.atm-clus↗

arXiv2016

Secondary electrons emitted during nuclear $β^{-}$ decay in few-electron atoms

`Additional' ionization of light atoms and ions during nuclear $β^{-}$ decay is investigated. The procedure which can be used to determine the corresponding transition probabilities and the velocity/energy spectrum of secondary electrons is developed. Emission of very fast secondary electrons ($δ-$electrons) from $β^{-}$-decaying atoms is also briefly discussed.

physics.atom-ph↗

arXiv2016

On contribution of the electron-electron correlations into bremsstrahlung from few-electron ions

A new approach is developed to evaluate contribution of the electron-electron correlations into bremsstrahlung from few-electron ions and atoms. Our approach is based on the explicit formula for the electron density distribution in such systems. We derive the closed analytical formula for the matrix elements which are needed for highly accurate computations of atomic form-factors of two-electron atoms and ions. We also discuss the energy loss due to bremsstrahlung in a plasma which contains multi-charged ions and free electrons. Bremsstrahlung from a high-temperature plasma is considered as well as its role in the high-temperature burn-up of deuterium plasma.

physics.atom-ph↗

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

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↗

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↗

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 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

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

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

Vacuum polarization in light two-electron atoms and ions

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).

nucl-th↗

arXiv2011

Bound state properties of four-body muonic quasi-atoms

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.

physics.atom-ph↗

arXiv2011

Atomic fragments from the nuclear reaction of the ${}^{6}$Li atom with slow neutrons

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.

physics.atom-ph↗

arXiv2011

Atomic analysis of the $(n;t)-$reaction of the helium-3 atoms with slow neutrons

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.

nucl-th↗

arXiv2011

On highly accurate calculations of the excited $n^1S(L = 0)-$states in helium atoms

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.

physics.atom-ph↗

arXiv2011

Compact variational wave functions for bound states in three-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.

physics.atom-ph↗