Measurement of Magic Wavelengths for the

We demonstrate experimentally the existence of magic wavelengths and determine the ratio of oscillator strengths for a single trapped ion. For the first time, two magic wavelengths near 396 nm for the ^{40}Ca^{+} clock transition are measured simultaneously with high precision. By tuning the applied laser to an intermediate wavelength between transitions 4s_{1/2}→4p_{1/2} and 4s_{1/2}→4p_{3/2}, the sensitivity of the clock transition Stark shift to the oscillator strengths is greatly enhanced. Furthermore, with the measured magic wavelengths, we determine the ratio of the oscillator strengths with a deviation of less than 0.5%. Our experimental method may be applied to measure magic wavelengths for other ion clock transitions. Promisingly, the measurement of these magic wavelengths paves the way to building all-optical trapped ion clocks.

Solution of the Dirac Coulomb equation for helium-like ions in the Poet-Temkin model.

The Dirac-Coulomb equation for the helium atom is studied under the restrictions of the Poet-Temkin model which replaces the 1/r12 interaction by the simplified 1/r> form. The effective reduction in the dimensionality made it possible to obtain binding energies for the singlet and triplet states in this model problem with a relative precision from 10(-8) to 10(-10). The energies for the singlet state were consistent with a previous configuration interaction calculation [H. Tatewaki and Y. Watanabe, Chem. Phys. 389, 58 (2011)]. Manifestations of Brown-Ravenhall disease were noted at higher values of nuclear charge and ultimately limited the accuracy of the Poet-Temkin model energy. The energies from a no-pair configuration interaction (CI) calculation (the negative-energy states for the appropriate hydrogen-like ion were excluded from the CI expansion) were found to be different from the unrestricted B-spline calculation.

Long-range interactions of excited He atoms with the alkaline earth atoms Mg, Ca, and Sr.

Dispersion coefficients for the long-range interactions of the first four excited states of He, i.e., He(2 (1, 3)S) and He(2 (1, 3)P), with the low-lying states of the alkaline earth atoms Mg, Ca, and Sr are calculated by summing over the reduced matrix elements of multipole transition operators.

Positron attachment to the He doubly excited states.

The projection method is used to demonstrate the existence of positron attachment to three doubly excited states of helium. The e(+)He(2s(2) (1)S(e))deg, e(+)He(3s(2) (1)S(e)), and the e(+)He(2s2p (3)P(o)) states have binding energies of 0.447, 0.256, and 0.486 eV, respectively. These energies were computed with the stochastic variational method and the configuration interaction method. These states will exist as resonances in the e(+)-He continuum, and the e(+)He(2s(2) (1)S(e)) state could be detectable in the e(+)+He collision spectrum. A resonance width of 0.068 eV was computed for the e(+)He(2s(2) (1)S(e)) state by using the complex rotation method. The existence of a series of e(+)He(ns(2) (1)S(e)) resonances associated with the He(ns(2)) double Rydberg series is also predicted, and an explicit calculation demonstrating the existence of the e(+)He(3s(2) (1)S(e)) state is reported.

Convergence of the multipole expansions of the polarization and dispersion interactions for atoms under confinement.

The multipole expansion of the polarization interaction between a charged particle and an electrically neutral object has long been known to be asymptotic in nature, i.e., the multiple expansion diverges at any finite distance from the atom. However, the multipole expansion of the polarization potential of a confined hydrogen atom is shown to be absolutely convergent at a distance outside the confinement radius, R(0), of the atom. The multipole expansion of the dispersion potential between two confined hydrogen atoms is also shown to be absolutely convergent provided the two atoms satisfy R > 2R(0), where R is the inter-nuclear separation. These results were established analytically using oscillator strength sum rules and verified numerically using a B-spline description of the hydrogen ground state and its excitation spectrum.

The long-range non-additive three-body dispersion interactions for the rare gases, alkali, and alkaline-earth atoms.

The long-range non-additive three-body dispersion interaction coefficients Z(111), Z(112), Z(113), and Z(122) are computed for many atomic combinations using standard expressions. The atoms considered include hydrogen, the rare gases, the alkali atoms (up to Rb), and the alkaline-earth atoms (up to Sr). The term Z(111) arising from three mutual dipole interactions is known as the Axilrod-Teller-Muto coefficient or the DDD (dipole-dipole-dipole) coefficient. Similarly, the terms Z(112), Z(113), and Z(122) arise from the mutual combinations of dipole (1), quadrupole (2), and octupole (3) interactions between atoms and they are sometimes known, respectively, as dipole-dipole-quadrupole, dipole-dipole-octupole, and dipole-quadrupole-quadrupole coefficients. Results for the four Z coefficients are given for the homonuclear trimers, for the trimers involving two like-rare-gas atoms, and for the trimers with all combinations of the H, He, and Li atoms. An exhaustive compilation of all coefficients between all possible atomic combinations is presented as supplementary data.

Long-range dispersion coefficients for Li, Li(+), and Be(+) interacting with the rare gases.

The long-range dispersion coefficients for the ground and excited states of Li, Li(+), and Be(+) interacting with the He, Ne, Ar, Kr, and Xe atoms in their ground states are determined. The variational Hylleraas method is used to determine the necessary lists of multipole matrix elements for He, Li, Li(+), and Be(+), while pseudo-oscillator strength distributions are used for the heavier rare gases. Some single electron calculations using a semiempirical Hamiltonian are also performed for Li and Be(+) and found to give dispersion coefficients in good agreement with the Hylleraas calculations. Polarizabilities are given for some of the Li and Li(+) states and the recommended (7)Li(+) polarizability including both finite-mass and relativistic effects was 0.192 486 a.u. The impact of finite-mass effects upon the dispersion coefficients has been given for some selected interatomic interactions.

Multipole polarizabilities and long-range interactions of the fluorine atom.

The polarizabilities of the ground state of fluorine are determined by the box-based B-spline configuration-interaction method. The ground-state static and tensor polarizabilities are calculated as alpha(d) = 3.49a(0)(3) and alpha(2) = 0.303a(0)(3), respectively. The resulting excitation matrix elements are employed to compute the interatomic dispersion interactions for the HF and F(2) molecules.

Positron scattering and annihilation from the hydrogen molecule at zero energy.

The confined variational method is used to generate a basis of correlated Gaussians to describe the interaction region wave function for positron scattering from the H2 molecule. The scattering length was approximately = -2.7a(0) while the zero energy Z(eff) of 15.7 is compatible with experimental values. The variation of the scattering length and Z(eff) with internuclear distance was surprisingly rapid due to virtual state formation at R approximately = 3.4a(0).

Elastic scattering using an artificial confining potential.

The discrete energies of a scattering Hamiltonian calculated under the influence of an artificial confining potential of almost arbitrary functional form can be used to determine its phase shifts. The method exploits the result that two short-range Hamiltonians having the same energy will have the same phase shifts upon removal of the confining potential. An initial verification is performed on a simple model problem. Then the stochastic variational method is used to determine the energies of the confined e(-)-He(2)S(e) system and thus determine the low energy phase shifts.

Properties and long range interactions of the calcium atom.

The properties of a number of states of calcium are determined from a large basis configuration interaction calculation. The main focus is on the polarizabilities of the low lying states (the 4s2 1Se, 4s3d 1,3De, 4s4p 1,3Po, and 4s5s 1,3Se states) and the dispersion interactions of those states with the calcium ground state, the hydrogen atom, and the rare gases.

Second bound state of PsH.

The existence of a second bound state of PsH that is electronically stable and also stable against positron annihilation by the normal 2gamma and 3gamma processes is demonstrated by explicit calculation. The state can be found in the ;{2,4}S;{o} symmetries with the two electrons in a spin-triplet state. The binding energy against dissociation into the H(2p)+Ps(2p) channel was 7.03 x 10;(-4) hartree. The dominant decay mode of the states will be radiative decay into a configuration that autoionizes or undergoes positron annihilation. The NaPs system of the same symmetry is also electronically stable with a binding energy of 1.514 x 10;(-3) hartree with respect to the Na(3p)+Ps(2p) channel.

Existence of a 2P(o) excited state for the e+ Ca system.

The configuration interaction method is used to demonstrate that there is an electronically stable state of positronic calcium with an orbital angular momentum of L=1. This prediction relies on the use of an asymptotic series to estimate the variational limit of the energy. The best estimate of the binding energy is 37 meV. A discussion of the structure of the system is also presented.

Positron-atom complexes as quantum halo states.

The wave functions of a number of positron-atom complexes are analyzed and three of the systems, namely, e(+)Be, e(+)Na, and e(+)He((3)S(e)), are seen to exhibit quantum halo structures with 45%-50% of their probability distribution lying in the large r classically forbidden region. The mean square distance between the large r fragments (e(+) + Be, Ps + Na+, Ps + He+) for these systems range from 1.8 to 2.2 times larger than the square of the classical turning point, another indication of their halolike nature.

Spin-orbit quenching of positronium during atomic collisions.

When positrons are injected into a gas, 75% of the positronium (Ps) is likely to be formed as long-lived ortho-Ps. The main decay mechanisms for the ortho-Ps have been assumed to be natural decay of ortho-Ps and pickoff annihilation of the positron during Ps-atom collisions. A third possibility for annihilation is ortho-Ps-->para-Ps conversion due to the spin-orbit interaction between the atom and colliding Ps. This extra quenching mechanism may explain a number of phenomena observed in the annihilation spectrum of Kr and Xe, including the very small Ps fraction of 3% seen for Xe.

Elastic positronium-atom scattering using the stochastic variational method.

The stochastic variational method is used in conjunction with stabilization ideas to compute the low energy phase shifts and scattering lengths for positronium-atom scattering. Results are obtained for the Ps-H, Ps- Li+, Ps-He, and Ps-Ps systems. The Ps-H scattering lengths are probably accurate to better than 5% and are the most accurate so far computed. The results for Ps- Li+ and Ps-Ps scattering represent the first published scattering lengths for these systems. The positive scattering length for completely spin-aligned 3Ps-3Ps scattering, namely 2.95a(0), is particularly significant since it demonstrates the feasibility of forming a stable Bose-Einstein condensate of 3Ps atoms.