Alexei M. Frolov

Hylleraas-configuration-interaction analysis of the low-lying states in the three-electron Li atom and Be + ion

The total energies of 28 bound S, P , D, F , G, H ,a ndI states in the three-electron Li atom and Be + ion, respectively, are determined with the use of the configuration interaction (CI) with Slater orbitals and LS eigenfunctions and the Hylleraas-configuration-interaction (Hy-CI) methods. We discuss the construction and selection of the configurations in the wave functions, optimization of the orbital exponents, and advanced computational techniques. Finally, we have developed an effective procedure which allows one to determine the energies of the excited states in three-electron atoms and ions to high accuracy by using compact wave functions. For the ground and low-lying excited states our best accuracy was ≈1 × 10 −6 a.u. with the Hy-CI method and 1 × 10 −4 a.u. for other excited states. Analogous accuracy of the CI method is substantially lower, ≈1 × 10 −3 a.u. Rotationally excited (bound) states in the three-electron Li atom and Be + ion are evaluated here to high accuracy.

Bound state spectra of three-body muonic molecular ions

AbstractThe 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.

Field shifts and lowest order QED corrections for the ground 1S1 and 2S3 states of the helium atoms

The bound state properties of the ground 1 1S(L=0) state and the lowest triplet 2 3S(L=0) state of the 3He, 4He, and infinityHe helium atoms are determined to very high accuracy from the results of direct numerical computations. To compute the bound state properties of these atoms the author applied his exponential variational expansion in relative/perimetric three-body coordinates. For the ground 1 1S(L=0) state and the lowest triplet 2 3S(L=0) state of the 3He, 4He, and infinityHe atoms the author also determined the lowest order QED corrections and the field component of isotopic shift (=field shift). For the 2 3S(L=0) state of the 3He atom the hyperfine structure splitting is evaluated. The considered properties of the ground 1 1S state and the lowest 2 3S state in the 3He and 4He atoms are of great interest in a number of applications.

Analytical formula for the Uehling potential

AbstractThe 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.

Bound state spectrum of the triplet states in the Be atom

Abstract 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 3 S , 3 3 S and 4 3 S states in the Be atom we also determine a number of bound states properties.

Highly accurate evaluation of the singular properties for the positronium and hydrogen negative ions

A large number of regular and some singular bound state properties of the ground 11S(L = 0)-states of the positronium Ps? and hydrogen ?H? negative ions are determined to a very high numerical accuracy. The highly accurate variational wavefunctions are constructed with the use of exponential basis functions written in the three-body perimetric coordinates. In particular, the total energy of the ground state of the Ps? ion determined in our calculations is E = ?0.262?005?070?232?980?107?770?3745 au, while the analogous ground state energy for the ?H? ion is E = ?0.527?751?016?544?377?196?589?733 au. These values are the best-to-date variational energies obtained for these systems.

Highly accurate three-body wavefunctions for the 23S(L = 0) states in two-electron ions

The exponential representation is used to construct highly accurate wavefunctions for the triplet states in various two-electron helium-like ions. It is shown that the exponential variational expansion in relative coordinates (r32, r31 and r21) provides a very high accuracy for the triplet 23S(L = 0) states in light two-electron ions. The developed methods are used to determine the highly accurate non-relativistic energies and other bound state properties for the 23S(L = 0) state in a number of He-like two-electron ions Li+, Be2+, B3+, C4+, N5+, O6+, F7+ and Ne8+. To represent the computed energies of these ions the Q−1 expansion is applied. The asymptotic form of the 23S(L = 0) state wavefunctions at large electron–nuclear distances for the He-like ions is briefly discussed. We also consider the hyperfine structure splitting in the 23S(L = 0) state of the helium-like ions with non-zero nuclear spin. For each of the considered two-electron ions one can determine the isotopic shifts by using our approach based on the derived interpolation formula. The lowest order QED corrections are also determined for the triplet states in all mentioned two-electron ions.

Three-particle integrals with Bessel functions

Analytical formulas for some useful three-particle integrals are derived. Many of these integrals include Bessel and/or trigonometric functions of one and two interparticle (relative) coordinates r32, r31, and r21. 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.

Isotopic effects for the ground 1S1(L=0) states in the light two-electron ions

The total energies and various bound state properties are determined to very high accuracy for the ground 1 (1)S(L=0) states in some light two-electron ions, including the Li(+), Be(2+), B(3+), and C(4+) ions. The corrections due to the finite nuclear masses and lowest order QED corrections ( approximately alpha(3)) are considered/computed for each of these ions. In particular, the specific mass shift is determined for each of the Li(+), Be(2+), B(3+), and C(4+) ions. We also discuss the field shift related to the extended nuclear charge distribution.

Four-body perimetric coordinates

The new approach to the analysis of four-body systems and computation of various four-body integrals is proposed. The approach is based on the use of six perimetric coordinates which can be introduced for an arbitrary four-body system. The proper (i.e. non-conflicting) definition of the four-body perimetric coordinates is given for an arbitrary four-body system. It is shown that these six internal perimetric coordinates describe all possible configurations in an arbitrary four-body system and can be used to simplify computations of many four-body integrals written in the relative coordinates r12, r13, r23, r14, r24 and r34. In addition to this, a number of new, very effective procedures for variational computation of different four-body systems can now be developed.