Calculation of the energy levels of Ge, Sn, Pb and their ions in the VN−4V^{N-4} approximation

Energy levels of germanium, tin and lead together with their single, double and triple ionized positive ions have been calculated using the $V^{N-M}$ approximation suggested in the previous work (Dzuba, physics/0501032) (M=4 - number of valence electrons). Initial Hartree-Fock calculations are done for the quadruply ionized ions with all valence electrons removed. The core-valence correlations are included beyond the second-order of the many-body perturbation theory. Interaction between valence electrons is treated by means of the configuration interaction technique. It is demonstrated that accurate treatment of the core-valence correlations lead to systematic improvement of the accuracy of calculations for all ions and neutral atoms.Comment: 7 pages, 3 figures, 3 tables; submitted to Phys. Rev.

Frequency shift of hyperfine transitions due to blackbody radiation

We have performed calculations of the size of the frequency shift induced by a static electric field on the clock transition frequencies of the hyperfine splitting in Yb+, Rb, Cs, Ba+, and Hg+. The calculations are used to find the frequency shifts due to blackbody radiation which are needed for accurate frequency measurements and improvements of the limits on variation of the fine structure constant, alpha. Our result for Cs (delta nu E^2=-2.26 times 10^{-10}Hz/(V/m)^2) is in good agreement with early measurements and ab initio calculations. We present arguments against recent claims that the actual value might be smaller. The difference (approx 10%) is due to the contribution of the continuum spectrum in the sum over intermediate states.Comment: Added discussion of Cs results and reference

Frequency shift of cesium clock transition due to blackbody radiation

We have performed ab initio calculations of the frequency shift induced by a static electric field on the cesium clock hyperfine transition. The calculations are used to find the frequency shifts due to blackbody radiation. Our result ($\delta \nu/E^2=-2.26(2)\times 10^{-10}$Hz/(V/m)$^2$) is in good agreement with early measurements and ab initio calculations performed in other groups. We present arguments against recent claims that the actual value of the effect might be smaller. The difference ($\sim$ 10%) between ab initio and semiempirical calculations is due to the contribution of the continuum spectrum to the sum over intermediate states.Comment: Accepted for publication in Phys. Rev. Let

Limits on a Dynamically Varying Fine Structure Constant

We show that using the modified form of the Dirac Hamiltonian as suggested by Bekenstein, does not affect the analysis in [1-4] of QSO data pertaining to a measurement of alpha variation. We obtain the present time limit on Bekenstein's parameter, tan^{2}chi =(0.2 \pm 0.7)\times10^{-6}, from the measurement of the hydrogen 2p fine structure using value of alpha obtained from different experiments.Comment: references added, typos correcte

Parity nonconservation in Atomic Zeeman Transitions

We discuss the possibility of measuring nuclear anapole moments in atomic Zeeman transitions and perform the necessary calculations. Advantages of using Zeeman transitions include variable transition frequencies and the possibility of enhancement of parity nonconservation effects

A New Option for a Search for Alpha Variation: Narrow Transitions with Enhanced Sensitivity

We consider several transitions between narrow lines that have an enhanced sensitivity to a possible variation of the fine structure constant, alpha. This enhancement may allow a search to be performed with an effective suppression of the systematic sources of uncertainty that are unavoidable in conventional high-resolution spectroscopic measurements. In the future this may provide the strongest laboratory constraints on alpha variation

Coulomb energy contribution to the excitation energy in 229^{229}Th and enhanced effect of α\alpha variation

We calculated the contribution of Coulomb energy to the spacing between the ground and first excited state of $^{229}$Th nucleus as a function of the deformation parameter $\delta$. We show that despite the fact that the odd particle is a neutron, the change in Coulomb energy between these two states can reach several hundreds KeV.This means that the effect of the variation of the fine structure constant $\alpha=e^2/\hbar c$ may be enhanced $\Delta U_C/E \sim 10^4$ times in the $E=$7.6 eV "nuclear clock" transition between the ground and first excited states in the $^{229}$Th nucleus.Comment: 6 pages,2 figure

Cold atom Clocks and Applications

This paper describes advances in microwave frequency standards using laser-cooled atoms at BNM-SYRTE. First, recent improvements of the $^{133}$Cs and $^{87}$Rb atomic fountains are described. Thanks to the routine use of a cryogenic sapphire oscillator as an ultra-stable local frequency reference, a fountain frequency instability of $1.6\times 10^{-14}\tau^{-1/2}$ where $\tau$ is the measurement time in seconds is measured. The second advance is a powerful method to control the frequency shift due to cold collisions. These two advances lead to a frequency stability of $2\times 10^{-16}$ at $50,000s for the first time for primary standards. In addition, these clocks realize the SI second with an accuracy of$7\times 10^{-16}$, one order of magnitude below that of uncooled devices. In a second part, we describe tests of possible variations of fundamental constants using$^{87}$Rb and$^{133}$Cs fountains. Finally we give an update on the cold atom space clock PHARAO developed in collaboration with CNES. This clock is one of the main instruments of the ACES/ESA mission which is scheduled to fly on board the International Space Station in 2008, enabling a new generation of relativity tests.Comment: 30 pages, 11 figure

Varying constants, Gravitation and Cosmology

Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to matter. This will induce a violation of the universality of free fall. It is thus of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy. We thus detail the relations between the constants, the tests of the local position invariance and of the universality of free fall. We then review the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, Solar system observations, meteorites dating, quasar absorption spectra, stellar physics, pulsar timing, the cosmic microwave background and big bang nucleosynthesis. At each step we describe the basics of each system, its dependence with respect to the constants, the known systematic effects and the most recent constraints that have been obtained. We then describe the main theoretical frameworks in which the low-energy constants may actually be varying and we focus on the unification mechanisms and the relations between the variation of different constants. To finish, we discuss the more speculative possibility of understanding their numerical values and the apparent fine-tuning that they confront us with.Comment: 145 pages, 10 figures, Review for Living Reviews in Relativit