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Recent advances in optical atomic clocks and optical time transfer have enabled new possibilities in precision metrology for both tests of fundamental physics and timing applications. Here we describe a space mission concept that would place a state-of-the-art optical atomic clock in an eccentric orbit around Earth. A high stability laser link would connect the relative time, range, and velocity of the orbiting spacecraft to earthbound stations. The primary goal for this mission would be to test the gravitational redshift, a classical test of general relativity, with a sensitivity 30 000 times beyond current limits. Additional science objectives include other tests of relativity, enhanced searches for dark matter and drifts in fundamental constants, and establishing a high accuracy international time/geodesic reference.

Reduced matrix elements, oscillator strengths, and transition rates are calculated for 2l12l2[LSJ]-2l33l4[L´S´J´] electric-dipole transitions in beryllium-like ions with nuclear charges Z from 6 to 100. Many-body perturbation theory (MBPT), including the Breit interaction, is used to evaluate retarded dipole matrix elements in length and velocity forms. The calculations start with a 1s2 Dirac-Fock potential and include all possible n = 2 and n = 3 configurations. We use first-order perturbation theory to obtain intermediate coupling coefficients and second-order MBPT to determine matrix elements. The transition energies used to evaluate transition probabilities are also obtained from second-order MBPT. The importance of negative-energy contributions to the transition amplitudes in maintaining gauge independence is discussed. Our results for 2s3p 1,3P1-2s2 1S0 transitions are compared with available theoretical and experimental data throughout the isoelectronic sequence. Rates for 2l3l´ [J = 1]-2s2 1S0, 2l3l´ [J = 1]-2p2 1S2, 2l3l´ [J = 1]-2s2p 1P1, and 2l3l´ [J = 2]-2s2p 1P1 transitions are given graphically for all Z.

Reduced matrix elements and transition rates are calculated for all magnetic dipole (M1) transitions within 2l2l' configurations and for some 2l3l' - 2l2l' transitions in Be-like ions with nuclear charges ranging from Z = 4 to 100. Many-body perturbation theory (MBPT), including the Breit interaction, is used to evaluate retarded M1 matrix elements. The calculations start with a (1s)2 Dirac-Fock potential and include all possible n = 2 configurations, leading to 4 odd-parity and 6 even-parity states, and some n = 3 configurations. First-order perturbation theory is used to obtain intermediate coupling coefficients. Second-order MBPT is used to determine the matrix elements, which are evaluated for all 11 M1 transitions within 2l2l' configurations and for 35 M1 transitions between 2l3l' and 2l2l' states. The transition energies used in the calculation of oscillator strengths and transition rates are obtained from second-order MBPT. The importance of negative-energy contributions to M1 transition amplitudes is discussed.

Reduced matrix elements, oscillator strengths, and transition rates are calculated for all allowed and forbidden 2s–2p electric dipole transitions in berylliumlike ions with nuclear charges ranging from Z = 4 to 100. Many-body perturbation theory (MBPT), including the Breit interaction, is used to evaluate retarded E1 matrix elements in length and velocity forms. The calculations start with a 1s2 Dirac–Fock potential and include all possible n = 2 configurations, leading to 4 odd-parity and 6 even-parity states. First-order perturbation theory is used to obtain intermediate coupling coefficents. Second-order MBPT is used to determine the matrix elements, which are evaluated for the 16 possible E1 transitions. The transition energies used in the calculation of oscillator strengths and transition rates are evaluated using second-order MBPT. The importance of virtual electron–positron pair (negative energy) contributions to the transition amplitudes is discussed.

Recent developments in searches for dark-matter candidates with atomic clocks are reviewed. The intended audience is the atomic clock community., Comment: To appear in Journal of Physics: Conference Series (JPCS); 6 pages, 4 figures

Using the relativistic Hartree-Fock approximation, we calculate the rates of atomic ionization by absorption of axions and other Dark matter candidates. We also calculate atomic ionization by scattering of heavy Dark matter particles on electrons. The results are used to interpret possible detection of Dark matter by DAMA collaboration.