arXiv subjects

J. Mitroy

Publications and source records attributed to J. Mitroy.

At least 19 recordsLinked to original sources

arXiv2016

Relativistic calculations of quasi-one-electron atoms and ions using Laguerre and Slater spinors

A relativistic description of the structure of heavy alkali atoms and alkali-like ions using S-spinors and L-spinors has been developed. The core wavefunction is defined by a Dirac-Fock calculation using an S-spinors basis. The S-spinor basis is then supplemented by a large set of L-spinors for the calculation of the valence wavefunction in a frozen-core model. The numerical stability of the L-spinor approach is demonstrated by computing the energies and decay rates of several low-lying hydrogen eigenstates, along with the polarizabilities of a $Z=60$ hydrogenic ion. The approach is then applied to calculate the dynamic polarizabilities of the $5s$, $4d$ and $5p$ states of Sr$^+$. The magic wavelengths at which the Stark shifts between different pairs of transitions are zero are computed. Determination of the magic wavelengths for the $5s \to 4d_{\frac32}$ and $5s \to 4d_{\frac52}$ transitions near $417$~nm (near the wavelength for the $5s \to 5p_j$ transitions) would allow a determination of the oscillator strength ratio for the $5s \to 5p_{\frac12}$ and $5s \to 5p_{\frac32}$ transitions.

physics.atom-ph↗

arXiv2015

Measurement of magic wavelengths for the 40Ca+ clock transition

We demonstrate experimentally the existence of magic wavelengths and determine the ratio of the oscillator strengths for a single trapped ion. For the first time, two magic wavelengths for the 40Ca+ clock-transition are measured simultaneously with high precision, giving Lamda|mj|=1/2 = 395.7992(7) nm and Lamda|mj|=3/2 = 395.7990(7) nm. By tuning a laser to an intermediate wavelength between two transitions (4s1/2-4p1/2 and 4s1/2-4p3/2) of 40Ca+, the sensitivity of the clock transition Stark shift to the oscillator strengths for the resonance transition has been greatly enhanced. With the measured magic wavelengths, we determine the ratio of the oscillator strengths to sub-0.5% accuracy. Our experimental method may be applied to measure magic wavelengths for other ion clock-transitions, and, promisingly, the measurement of these magic wavelengths paves the way to building lattice ion clocks.

physics.atom-ph↗

arXiv2014

Effective oscillator strength distributions of spherically symmetric atoms for calculating polarizabilities and long-range atom-atom interactions

Effective oscillator strength distributions are systematically generated and tabulated for the alkali atoms, the alkaline-earth atoms, the alkaline-earth ions, the rare gases and some miscellaneous atoms. These effective distributions are used to compute the dipole, quadrupole and octupole static polarizabilities, and are then applied to the calculation of the dynamic polarizabilities at imaginary frequencies. These polarizabilities can be used to determine the long-range $C_6$, $C_8$ and $C_{10}$ atom-atom interactions for the dimers formed from any of these atoms and ions, and we present tables covering all of these combinations.

physics.atom-ph↗

arXiv2013

Hyperfine effects on potassium tune-out wavelengths and polarizabilities

The influence of hyperfine interactions on the tune-out wavelengths of the $^{39,40,41}$K isotopes of the potassium atom was investigated. The hyperfine interaction of the $4s_{1/2}$ state result in a shift and splitting of the primary tune-out wavelength near 769 nm. The $4s_{1/2}$ ground state hyperfine splittings of the primary tune-out were almost equal to the hyperfine splittings of the ground states. The splittings in the wavelengths were 0.0008, 0.0027 and 0.0005 nm for $^{39}$K, $^{40}$K and $^{41}$K respectively. The hyperfine splitting of the $np_{J}$ levels leads to the creation of additional tune-out wavelengths. The additional tune-out wavelengths could be difficult to detect due to very small differences from the transition wavelengths to the $4p_{J,F}$ states. The hyperfine Stark shift for the ground states of all three isotopes were also computed and the value for $^{30}$K was found to be compatible with the previous experiments and the most recent calculation using relativistic many body perturbation theory.

physics.atom-ph↗

arXiv2013

Black-body radiation shift of the Ga$^{+}$ clock transition

The blackbody radiation shift of the Ga$^+$ $4s^2 \ ^1S^e_0 \to 4s4p \ ^3P^o_0$ clock transition is computed to be $-$$0.0140 \pm 0.0048$ Hz at 300 K. The small shift is consistent with the blackbody shifts of the clock transitions of other group III ions which are of a similar size. The polarizabilities of the Ga$^+$ $4s^2 \ ^1S^e_0$, $4s4p \ ^3P^o_0$, and $4s4p \ ^1P^o_1$ states were computed using the configuration interaction method with an underlying semi-empirical core potential. A byproduct of the analysis involved large scale calculations of the low lying spectrum and oscillator strengths of the Ga$^{2+}$ ion.

physics.atom-ph↗

arXiv2013

Long range interactions between alkali and alkaline-earth atoms

Dispersion coefficients between the alkali metal atoms (Li-Rb) and alkaline-earth metal atoms (Be-Sr) are evaluated using matrix elements computed from frozen core configuration interaction calculations. Besides dispersion coefficients with both atoms in their respective ground states, dispersion coefficients are also given for the case where one atom is in its ground state and the other atom is in a low lying excited state.

physics.atom-ph↗

arXiv2013

Dynamic polarizabilities for the low lying states of Ca+

The dynamic polarizabilities of the 4s, 3d and 4p states of Ca$^+$, are calculated using a relativistic structure model. The wavelengths at which the Stark shifts between different pairs of transitions are zero are computed. Experimental determination of the magic wavelengths can be used to estimate the ratio of the $f_{3d_{J}\to 4p_{J'}}$ and $f_{4s_{1/2} \to 4p_{J'}}$ oscillator strengths. This could prove valuable in developing better atomic structure models and in particular lead to improved values of the polarizabilities needed in the evaluation of the blackbody radiation shift of the Ca$^+$ ion.

physics.atm-clus↗

arXiv2013

Tune-out wavelengths for potassium

The five longest tune-out wavelengths for the potassium atom are determined using a relativistic structure model which treats the atom as consisting of a single valence electron moving outside a closed shell core. The importance of various terms in the dynamic polarizability in the vicinity of the $4p_J$, $5p_J$ and $6p_J$ transitions are discussed.

physics.atom-ph↗

arXiv2012

Blackbody radiation shift of B$^+$ clock transition

A calculation of the blackbody radiation shift of the B$^+$ clock transition is performed. The polarizabilities of the B$^+$ $2s^2$ $^1$S$^e$, $2s2p$ $^1$P$^o$, and $2s2p$ $^3$P$^o$ states are computed using the configuration interaction method with an underlying semi-empirical core potential. The recommended dipole polarizabilities are 9.64(3) $a_0^3$, 7.78(3) $a_0^3$ and 16.55(5) $a_0^3$ respectively. The derived frequency shift for the $2s^2$ $^1$S$^e$ $\to$ $2s2p$ $^3$P$^o_0$ transition at 300 K is 0.0160(5) Hz. The dipole polarizabilities agree with an earlier relativistic calculation (Safronova {\em et al.} Phys. Rev. Lett. {\bf 107} 143006 (2011)) to better than 0.2%. Quadrupole and octupole polarizabilities and non-adiabatic multipole polarizabilities are also reported.

physics.atom-ph↗

arXiv2012

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 1Se), e^+He(3s^2 1Se), and the e^+He(2s2p 3Po) states have binding energies of 0.447eV, 0.256eV and 0.486eV 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 1Se) state could be detectable in the e^+ + He collision spectrum. A resonance width of 0.068eV was computed for the e^+He(2s^2 1Se), state by using the complex rotation method. The existence of a series of e^+He(ns^2 1Se) 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 1Se) state is reported.

physics.atom-ph↗

arXiv2012

Computational investigation of static multipole polarizabilities and sum rules for ground-state hydrogen-like ions

High precision multipole polarizabilities, $α_{\ell}$ for $\ell \le 4$ of the $1s$ ground state of the hydrogen isoelectronic series are obtained from the Dirac equation using the B-spline method with Notre Dame boundary conditions. Compact analytic expressions for the polarizabilities as a function of $Z$ with a relative accuracy of 10$^{-6}$ up to $Z = 100$ are determined by fitting to the calculated polarizabilities. The oscillator strengths satisfy the sum rules $\sum_i f^{(\ell)}_{0i} = 0$ for all multipoles from $\ell = 1$ to $\ell = 4$. The dispersion coefficients for the long-range H-H and H-He$^+$ interactions are given.

physics.atom-ph↗

arXiv2012

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 DDQ, DDO, and DQQ 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, Li atoms. An exhaustive compilation of all coefficients between all possible atomic combinations is presented as supplementary data.

physics.atom-ph↗

arXiv2011

Convergence of the multipole expansion of the polarization interaction

The multipole expansion of the polarization interaction between a charged particle and an electrically charged particle has long been known to be asymptotic in nature, i.e. the multiple expansion diverges at any finite distance from the atom. However, it is shown that the multipole expansion of the polarization potential of a confined hydrogen atom is absolutely convergent at a distance outside the atoms confinement radius. It is likely that the multipole expansion of the dispersion interaction of two confined atoms will also be absolutely convergent provided the internuclear separation of the two atoms is sufficiency large to exclude any overlap between the electron charge clouds of the two atoms.

physics.atom-ph↗

arXiv2010

Theory and applications of atomic and ionic polarizabilities

Atomic polarization phenomena impinge upon a number of areas and processes in physics. The dielectric constant and refractive index of any gas are examples of macroscopic properties that are largely determined by the dipole polarizability. When it comes to microscopic phenomena, the existence of alkaline-earth anions and the recently discovered ability of positrons to bind to many atoms are predominantly due to the polarization interaction. An imperfect knowledge of atomic polarizabilities is presently looming as the largest source of uncertainty in the new generation of optical frequency standards. Accurate polarizabilities for the group I and II atoms and ions of the periodic table have recently become available by a variety of techniques. These include refined many-body perturbation theory and coupled-cluster calculations sometimes combined with precise experimental data for selected transitions, microwave spectroscopy of Rydberg atoms and ions, refractive index measurements in microwave cavities, ab initio calculations of atomic structures using explicitly correlated wave functions, interferometry with atom beams, and velocity changes of laser cooled atoms induced by an electric field. This review examines existing theoretical methods of determining atomic and ionic polarizabilities, and discusses their relevance to various applications with particular emphasis on cold-atom physics and the metrology of atomic frequency standards.

physics.atom-ph↗

arXiv2010

The dynamic dipole polarizabilities of the Li atom and the Be+ ion

The dynamic dipole polarizabilities for the Li atom and the Be+ ion in the 2s and 2p states are calculated using the variational method with a Hylleraas basis. The present polarizabilities represent the definitive values in the non-relativistic limit. Corrections due to relativistic effects are also estimated. Analytic representations of the polarizabilities for frequency ranges encompassing the n=3 excitations are presented. The recommended polarizabilities for ^7Li and ^9Be+ were 164.11 \pm 0.03 a.u. and 24.489 \pm 0.004 a.u..

physics.atom-ph↗

arXiv2009

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 H$_2$ molecule. The scattering length was $\approx -2.7$ $a_0$ while the zero energy $Z_{\rm eff}$ of 15.7 is compatible with experimental values. The variation of the scattering length and $Z_{\rm eff}$ with inter-nuclear distance was surprisingly rapid due to virtual state formation at $R \approx 3.4$ $a_0$.

physics.comp-ph↗

arXiv2009

Calculations of polarizabilities and hyperpolarizabilities for the Be$^+$ ion

The polarizabilities and hyperpolarizabilities of the Be$^+$ ion in the $2^2S$ state and the $2^2P$ state are determined. Calculations are performed using two independent methods: i) variationally determined wave functions using Hylleraas basis set expansions and ii) single electron calculations utilizing a frozen-core Hamiltonian. The first few parameters in the long-range interaction potential between a Be$^+$ ion and a H, He, or Li atom, and the leading parameters of the effective potential for the high-$L$ Rydberg states of beryllium were also computed. All the values reported are the results of calculations close to convergence. Comparisons are made with published results where available.

physics.atom-ph↗

arXiv2008

Polarizabilities of the Mg$^+$ and Si$^{3+}$ ions

A polarization analysis of the fine-structure intervals for the $n = 17$ Rydberg states of Mg and the $n = 29$ states of Si$^{2+}$ is performed. The coefficients of all terms in the polarization expansion up to $r^{-8}$ were computed using a semi-empirical single electron analysis combined with the relativistic all-order single-double method (MBPT-SD) which includes all single-double excitations from the Dirac-Fock wave functions to all orders of perturbation theory. The revised analysis yields dipole polarizabilities of $α_1 = 35.04(3)$ a.u. for Mg$^+$ and $α_1 = 7.433(25)$ a.u. for Si$^{3+}$, values only marginally larger than those obtained in a previous analysis (E. L. Snow and S. R. Lundeen (2007) Phys. Rev. A {\bf 75} 062512, {\em ibid} (2008) {\bf 77} 052501). The polarizabilities are used to make estimates of the multiplet strength for the resonant transition for both ions. The revised analysis did see significant changes in the slopes of the polarization plots. The dipole polarizabilities from the MBPT-SD calculation, namely 35.05(12) a.u. and 7.419(16) a.u., are within 0.3% of the revised experimental values.

physics.atom-ph↗