In this paper, we have calculated parity nonconserving electric dipole transition amplitudes of the hyperfine components for the transitions between the ground and first excited states of $^{137}$Ba$^{+}$ and $^{87}$Sr$^{+}$ using sum-over-states technique. The results are presented to extract the constants associated with the nuclear spin dependent amplitudes from experimental measurements. The wavefunctions to calculate the most dominant part of the sums are constructed using highly correlated coupled-cluster theory based on the Dirac-Coulomb-Gaunt Hamiltonian.
The atomic parity non-conservation(PNC) experiments has reached accuracies which have important implications for physics beyond the standard model. An optical rotation experiment to measure the atomic PNC of the 3P1(6s6p)--1P1(6s6p) in Yb was proposed recently. Our screened electron-electron coulomb potential multi-configuration Dirac-Fock calculation of th PNC induced E1 transition amplitude of this transition E1_PNC = -96.0 x 10^{-11}iea_0(-Q_W/N) of 171Yb is more than two orders of magnitude larger than E1_PNC(6s-7s) = -0.8991 x 10^{-11}iea_0(-Q_W/N) of 133Cs.
We discuss experiments aimed at measurements of atomic parity nonconservation (PNC) effects in the 1S0-3D1 transition (408 nm) in atomic Ytterbium (Z=70). According to theoretical predictions, the PNC-induced E1 amplitude of this transition is ~100 times larger than the analogous amplitude in Cs. Such an experiment will determine differences in PNC effects between different hyperfine components for odd-neutron-number Yb isotopes and, thereby, will allow measurements of the nuclear anapole moments in nuclei with unpaired neutrons. In addition, measurements of PNC in different isotopes would giv…
We present nuclear spin-independent and dependent parity non-conservation amplitudes for the $[4f^{14}]6s\;^2S_{1/2}-[4f^{14}]5d\;^2D_{3/2}$ transition of $^{171}$Yb$^+$, calculated using perturbed relativistic coupled-cluster theory. As a proxy to estimate theoretical uncertainty of these results we calculate the excitation energies, hyperfine structure constants and E1 transition amplitudes for the important low lying states. The PNC results presented in paper shall be useful in the propose PNC experiments.
Currently the theoretical uncertainty limits the interpretation of the atomic parity non-conservation (PNC) measurements. We calculate the PNC $5s$ - $6s$ electric dipole transition amplitude in rubidium and demonstrate that rubidium is a good candidate to search for new physics beyond the standard model since accuracy of the atomic calculations in rubidium can be higher than in cesium. PNC in cesium is currently the best low-energy test of the standard model, therefore, similar measurements for rubidium present a good option for further progress in the field. We also calculate nuclear spin-de…
Removal energies and hyperfine constants of the lowest four $ns, np_{1/2}$ and $np_{3/2}$ states in Na, K, Rb and Cs are calculated; removal energies of the n=7--10 states and hyperfine constants of the n=7 and 8 states in Fr are also calculated. The calculations are based on the relativistic single-double (SD) approximation in which single and double excitations of Dirac-Hartree-Fock (DHF) wave functions are included to all-orders in perturbation theory. Using SD wave functions, accurate values of removal energies, electric-dipole matrix elements and static polarizabilities are obtained, howe…
The complete gauge-invariant set of the one-loop QED corrections to the parity-nonconserving (PNC) amplitude in cesium and francium is evaluated to all orders in $αZ$ using a local form of the Dirac-Fock potential. The calculations are performed in both length and velocity gauges for the absorbed photon and the total binding QED correction is found to be $-$0.27(3)% for Cs and $-$0.28(5)% for Fr. Moreover, a high-precision calculation of the electron-correlation and Breit-interaction effects on the 7$s-8s$ PNC amplitude in francium using a large-scale configuration-interaction Dirac-Fock metho…
Corrections from Breit interaction to basic properties of atomic 133Cs are determined in the framework of third-order relativistic many-body perturbation theory. The corrections to energies, hyperfine-structure constants, off-diagonal hyperfine 6S-7S amplitude, and electric-dipole matrix elements are tabulated. It is demonstrated that the Breit corrections to correlations are comparable to the Breit corrections at the Dirac-Hartree-Fock level. Modification of the parity-nonconserving (PNC) 6S-7S amplitude due to Breit interaction is also evaluated; the resulting weak charge of $^{133}$Cs shows…
The complete system of the B-spline solutions for the Dirac equation with the parity-nonconserving (PNC) weak interaction effective potential is obtained. This system can be used for the accurate evaluation of the radiative corrections to the PNC amplitudes in the multicharged ions and neutral atoms. The use of the scaling procedure allows for the evaluation of the PNC matrix elements with relative accuracy $10^{-7}$.
We consider parity nonconservation (PNC) in singly ionized ytterbium (Yb+) arising from the neutral current weak interaction. We calculate the PNC electric dipole transition amplitude (E1_PNC) and the properties associated with it using the relativistic coupled-cluster theory. E1_PNC for the [4f^{14}] ^2 6s --> [4f^{14}] ^2 5d_{3/2} transition in Yb+ has been evaluated to within an accuracy of 5%. The improvement of this result is possible. It therefore appears that this ion is a promising candidate for testing the standard model of particle physics.
We present the results of our calculations of the parity nonconserving electric dipole amplitudes ($E1_{PNC}$) for the $6s ~ ^2S_{1/2} - 5d ~ ^2D_{3/2;5/2}$ transitions of $^{133}$Cs employing a relativistic coupled-cluster (RCC) method. $E1_{PNC}$ values for the nuclear spin independent (NSI) and nuclear spin dependent (NSD) parity non-conservation (PNC) effects for different hyperfine levels of the $6s ~ ^2S_{1/2} - 5d ~ ^2D_{3/2}$ transition and only due to the NSD PNC interaction Hamiltonian for all possible hyperfine levels of the $6s ~ ^2S_{1/2} - 5d ~ ^2D_{5/2}$ transition are given. We…
We have calculated parity nonconserving 7s - 6d_{3/2} amplitude E_PNC in 223Ra+ using high-precision relativistic all-order method where all single and double excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Detailed study of the uncertainty of the parity nonconserving (PNC) amplitude is carried out; additional calculations are performed to estimate some of the missing correlation corrections. A systematic study of the parity conserving atomic properties, including the calculation of the energies, transition matrix elements, lifetimes, hyperfine c…
A rigorous QED theory of the spectral line profiles is applied to transition probabilities in few-electron highly charged ions. Interelectron interaction corrections are included as well as radiative corrections. Parity nonconserving (PNC) amplitudes with effective weak interactions between the electrons and nucleus are also considered. QED and interelectron interaction corrections to the PNC amplitudes are derived.
We use previously developed radiative potential method to calculate quantum electrodynamic (QED) corrections to energy levels and electric dipole transition amplitudes for atoms which are used for the study of the parity non-conservation (PNC) in atoms. The QED shift in energies and dipole amplitudes leads to noticeable change in the PNC amplitudes. This study compliments the previously considered QED corrections to the weak matrix elements. We demonstrate that the QED corrections due to the change in energies and dipole matrix elements are comparable in value to those due to change in weak ma…
Fock-space perturbed relativistic coupled-cluster calculations of electric dipole polarizability and nuclear spin-dependent parity non-conservation in Cs
We present a detailed study of the effect of the double core polarization (the polarization of the core electrons due to the simultaneous action of the electric dipole and parity-violating weak fields) for amplitudes of the s-s and s-d parity non-conserving transitions in Rb, Cs, Ba +, La 2+, Tl, Fr, Ra +, Ac 2+ and Th 3+ as well as electron EDM enhancement factors for the ground states of the above neutral atoms and Au. This effect is quite large and has the potential to resolve some disagreement between calculations in the literature. It also has significant consequences for the use of exper…
We have further developed and extended a method for calculation of atomic properties based on a combination of the configuration interaction and coupled-cluster approach. We have applied this approach to the calculation of different properties of atomic lead, including the energy levels, hyperfine structure constants, electric-dipole transition amplitudes, and E1 parity nonconserving (PNC) amplitude for the (6p^2) ^3P_0 - (6p^2) ^3P_1 transition. The uncertainty of the E1 PNC amplitude was reduced by a factor of two in comparison with the previous most accurate calculation [V.~A.~Dzuba et.al.,…
We have performed ab initio mixed-states and sum-over-states calculations of parity nonconserving (PNC) electric dipole (E1) transition amplitudes between s-d electron states of Cs, Fr, Ba II, and Ra II. For the lower states of these atoms we have also calculated energies, E1 transition amplitudes, and lifetimes. We have shown that PNC E1 transition amplitudes between s-d states can be calculated to high accuracy. Contrary to the Cs 6s-7s transition, in these transitions there are no strong cancelations between different terms in the sum-over-states approach. In fact, there is one dominating t…
The absolute frequency measurement for all of the hyperfine transitions of 6P1/2 -> 7S1/2 using a self-referencing frequency comb is reported. This transition can be used as a bench marker for the accurate atomic wave function, and then improve the calculation of the atomic parity- non-conservation (PNC). The frequency center is precisely determined by saturation spectroscopy utilizing a pair of the counter-propagating laser beams intersecting with atomic beam. Such a Doppler-free profile has been improved to 350 kHz in the absolute frequency measurement. The 7S1/2 state hyperfine splittings h…
We present accurate {\em ab initio} non-perturbative calculations of the Breit correction to the parity non-conserving (PNC) amplitudes of the $6s-7s$ and $6s-5d_{3/2}$ transitions in Cs, $7s-8s$ and $7s-6d_{3/2}$ transitions in Fr, $6s-5d_{3/2}$ transition in Ba$^+$, $7s-6d_{3/2}$ transition in Ra$^+$, and $6p_{1/2} - 6p_{3/2}$ transition in Tl. The results for the $6s-7s$ transition in Cs and $7s-8s$ transition in Fr are in good agreement with other calculations while calculations for other atoms/transitions are presented for the first time. We demonstrate that higher-orders many-body correc…
We calculated the parity nonconserving (PNC) 6s -> 7s amplitude in Cs. In the Dirac-Coulomb approximation our result is in a good agreement with other calculations. Breit corrections to the PNC amplitude and to the Stark-induced amplitude $β$ are found to be -0.4% and -1% respectively. The weak charge of $^{133}$Cs is $Q_W=-72.5 \pm 0.7$ in agreement with the standard model.
The self-energy and vertex QED radiative corrections (Z alpha^2 f(Z alpha)) are shown to give a large negative contribution to the parity nonconserving (PNC) amplitude in heavy atoms. The correction -0.7(2)% found for the 6s-7s PNC amplitude in Cs brings the experimental result for this transition into agreement with the standard model. The calculations are based on a new identity that expresses the radiative corrections to the PNC matrix element via corrections to the energy shifts induced by the finite nuclear size.
We have calculated the 6s-7s parity nonconserving (PNC) E1 transition amplitude, E_{PNC}, in cesium. We have used an improved all-order technique in the calculation of the correlations and have included all significant contributions to E_{PNC}. Our final value E_{PNC} = 0.904 (1 +/- 0.5 %) \times 10^{-11}iea_{B}(-Q_{W}/N) has half the uncertainty claimed in old calculations used for the interpretation of Cs PNC experiments. The resulting nuclear weak charge Q_{W} for Cs deviates by about 2 standard deviations from the value predicted by the standard model.
We have estimated the size of the light-shifts due to parity nonconservation (PNC) interactions in different isotopes of Ba+ and Ra+ ions based on the work of Fortson [Phys. Rev. Lett. 70, 2383 (1993)]. We have used the nuclear spin independent (NSI) amplitudes calculated earlier by us [Phys. Rev. Lett. 96, 163003 (2006); Phys. Rev. A 78, 050501(R) (2008)] and we have employed the third order many-body perturbation theory (MBPT(3)) in this work to estimate the nuclear spin dependent (NSD) amplitudes in these ions. Ra+ is found to be more favourable than Ba+ for measuring both the NSI and NSD P…
We have developed a relativistic coupled-cluster theory to incorporate nuclear spin-dependent interaction Hamiltonians perturbatively. This theory is ideal to calculate parity violating nuclear spin-dependent electric dipole transition amplitudes, $E1_{\rm PNC}^{\rm NSD}$, of heavy atoms. Experimental observation of which is a clear signature of nuclear anapole moment, the dominant source of nuclear spin-dependent parity violation in atoms and ions. We apply the theory to calculate $E1_{\rm PNC}^{\rm NSD}$ of Cs, which to date has provided the best atomic parity violation measurements. We also…
Investigation of P,T-parity nonconservation (PNC) phenomena is of fundamental importance for physics. Experiments to search for PNC effects have been performed on TlF and YbF molecules and are in progress for PbO and PbF molecules. For interpretation of molecular PNC experiments it is necessary to calculate those needed molecular properties which cannot be measured. In particular, electronic densities in heavy-atom cores are required for interpretation of the measured data in terms of the P,T-odd properties of elementary particles or P,T-odd interactions between them. Reliable calculations of …
Stark-induced electric dipole amplitudes between states of the same nominal parity can be important in experiments to observe parity nonconservation in atoms. The Stark-induced E1 amplitudes are expressed in terms of an irreducible spherical-tensor decomposition. This formalism is applied to the specific case of transitions between hyperfine sublevels of a single atomic state. It is shown that in the ground states of alkali atoms, such transitions are suppressed by many orders of magnitude relative to naive expectations.
Hyperfine constants and anomalies of ground as well as few low lying excited states of $^{113,115,117}$In III are studied with highly correlated relativistic coupled-cluster theory. The ground state hyperfine splitting of $^{115}$In III is estimated to be 106.8 GHz. A shift of almost 1.9 GHz of the above frequency has been calculated due to modified nuclear dipole moment. This splitting result shows its applicability as communication band and frequency standards at $10^{-11}$ sec. Correlations study of hyperfine constants indicates a few distinct features of many-body effects in the wave-funct…
The self-energy and vertex QED radiative corrections to the parity nonconservation (PNC) amplitude in atoms are obtained using the perturbation theory in powers of (alpha Z). The calculated linear in (alpha Z) term gives -0.6 % for the PNC amplitude in Cs. The estimated nonlinear terms make corrections larger -0.9(2) %. This result brings the experimental data for the 6s-7s transition in 133 Cs in agreement with the standard model.
Parity nonconservation amplitudes are calculated for the 7s-6d transitions of the francium isoelectronic sequence (Fr, Ra +, Ac 2+, Th 3+, Pa 4+, U 5+ and Np 6+) and for the 6s-5d transitions of the cesium isoelectronic sequence (Cs, Ba +, La 2+, Ce 3+ and Pr 4+). We show in particular that isotopes of La 2+, Ac 2+ and Th 3+ ions have strong potential in the search for new physics beyond the standard model - the PNC amplitudes are large, the calculations are accurate and the nuclei are practically stable. In addition, 232-Th 3+ ions have recently been trapped and cooled [C. J. Campbell et al.,…
Many-body calculation of nuclear spin-dependent parity-nonconserving amplitude for (7s,F=4) --> (7s,F=5) transition between hyperfine sublevels of the ground state of $^{211}$Fr is carried out. The final result is <7s,F=5 ||d_PNC|| 7s,F=4> = -0.49 10^{-10} i kappa a.u., where kappa is the dimensionless coupling constant. This is approximately an order of magnitude larger than similar amplitude in Cs. The dominant contribution to kappa is associated with the anapole moment of the nucleus.
We examine the feasibility of a parity non-conserving (PNC) optical rotation experiment for the $^2$P$_{3/2}\rightarrow ^2$P$_{1/2}$ transition of atomic iodine at 1315 nm. The calculated $E1_{\rm PNC}$ to $M1$ amplitude ratio is $R=0.80(16)\times 10^{-8}$. We show that very large PNC rotations (greater than 10 $μ$rad) are obtained for iodine-atom column densities of $\sim 10^{22}$ cm$^{-2}$, which can be produced by increasing the effective interaction pathlength by a factor of $\sim 10^4$ with a high-finesse optical cavity. The simulated signals indicate that measurement of the nuclear anapo…
We have employed the 12.6 GHz microwave transition resonance of a single trapped$^{171}$Yb+ ion to accurately measure the size and relative orientation of the magnetic and optical electric fields at the position of the ion in the trap. Accurate knowledge of these fields is required for precision experiments such as single ion PNC. As a proof of the principle we have measured the polarization dependent light-shift of the ground state hyperfine levels due to the 369 nm cooling laser to determine its electric field amplitude and polarization.
We use configuration interaction technique to calculate parity non-conservation (PNC) in metastable Xe and Hg [proposal of the experiment in L. Bougas et al, Phys. Rev. Lett. 108, 210801 (2012)]. Both, nuclear spin-independent and nuclear spin-dependent (dominated by the nuclear anapole moment) parts of the amplitude are considered. The amplitudes are strongly enhanced by proximity of the states of opposite parity.
We report a measurement of the transition amplitude ratio $χ$ of an electric quadrupole ($E2$) to a magnetic dipole ($M1$) of the $6P_{1/2}\rightarrow6P_{3/2}$ transition in atomic thallium. We utilized the electromagnetically induced transparency (EIT) mechanism and the sideband-bridging technique to resolve the isotopic transitions and their hyperfine manifold. Our measurement gave $χ_{205}~=~0.2550(20)(7)$ for $^{205}$Tl, and $χ_{203}=0.2532(73)(7)$ for $^{203}$Tl, which was measured for the first time. Our result provides a reference point for the theoretical calculation of atomic structur…
This work presents precise calculations of important electromagnetic transition amplitudes along with detail of their many-body correlations using relativistic coupled cluster method. Studies of hyperfine interaction constants, useful for plasma diagnostic, with this correlation exhaustive many-body approach are another important area of this work. The calculated oscillator strengths of allowed transitions, amplitudes of forbidden transitions and lifetimes are compared with the other theoretical results wherever available and they show a good agreement. Hyperfine constants of different isotope…
We report a new calculation of the parity non-conserving E1 amplitude for the 6p_{1/2} -> 6p_{3/2} transition in Tl. Our result for the reduced matrix element is $E1_{PNC}=-(66.7 \pm 1.7) i 10^{-11} (-Q_W/N)$ a.u. Comparison with the experiment of Vetter et al [PRL,{\bf 74},2658 (1995)] gives the following result for the weak charge of $^{205}$Tl: $Q_W/Q_W^{SM} = 0.97 (\pm 0.01)_{expt} (\pm 0.03)_{theor}$, where $Q_W^{SM}=-116.7$ is the standard model prediction. This result confirms an earlier conclusion based on the analysis of a Cs experiment that atomic PNC experiments are in agreement wit…
We report our detailed analysis of a table-top system for the measurement of the weak-force-induced electric dipole moment of a ground state hyperfine transition carried out in an atomic beam geometry. We describe an experimental configuration of conductors for application of orthogonal r.f. and static electric fields, with cavity enhancement of the r.f. field amplitude, that allows confinement of the r.f. field to a region in which the static fields are uniform and well-characterized. We carry out detailed numerical simulations of the field modes, and analyze the expected magnitude of statist…
We use relativistic Hartree-Fock and correlation potential methods to calculate nuclear spin-dependent parity non-conserving amplitudes (dominated by the nuclear anapole moment) between hyperfine structure components of the ground state of odd isotopes of K, Rb, Cs, Ba+, Yb+, Tl, Fr, and Ra+. The results are to be used for interpretation of current and future measurements.
We calculate magnetic dipole transition amplitudes in s-s and s-d transitions of Rb, Cs, Ba+, Fr, Ra+, Yb+, Ac2+ and Th3+. These transitions were used or considered to be used for the measurements of parity non-conservation (PNC). We also calculate the magnetic g-factor anomalies for a selection of states, along with electric quadrupole transition amplitudes for s-d transitions in these systems.
Parity violation experiment in Yb is made on the strongly forbidden M1 transition 6s^2 1S0 \to 5d6s 3D1. The hyperfine mixing of the 5d6s 3D1 and 5d6s 3D2 levels opens E2 channel, whose amplitude differs for F-sublevels of the 3D1 level. This effect may be important for the experimental search for the nuclear-spin-dependent parity violation effects predominantly caused by the nuclear anapole moment.
We calculate nuclear spin-dependent parity non-conserving $E1$-amplitudes for optical transition $6p_{1/2,F} -> 6p_{3/2,F'}$ and for hyperfine transition $6p_{1/2,F} -> 6p_{1/2,F'}$ in Tl. Experimental limit on the former amplitude placed by Vetter et al. [PRL, 74, 2658 (1995)] corresponds to the anapole moment constant $κ_a = -0.26 \pm 0.27$. Experiment on the hyperfine transition can give direct measurement of the spin-dependent amplitude, because spin-independent amplitude turns to zero.
In the presence of P-violating interactions, the exchange of vector bosons between electrons and nucleons induces parity-nonconserving (PNC) effects in atoms and molecules, while the exchange of vector bosons between nucleons induces anapole moments of nuclei. We perform calculations of such vector-mediated PNC effects in Cs, Ba$^+$, Yb, Tl, Fr and Ra$^+$ using the same relativistic many-body approaches as in earlier calculations of standard-model PNC effects, but with the long-range operator of the weak interaction. We calculate nuclear anapole moments due to vector boson exchange using a sim…
In the framework of the quasipotential method in quantum electrodynamics we calculate corrections to the nuclear structure proportional to $r_N^2$ from two-photon exchange amplitudes in the fine and hyperfine structure of P-states in muonic hydrogen, as well as the photon-photon interaction amplitudes, leading to the exchange of the axial vector meson. In constructing the quasipotential of the muon-nucleus interaction, we use the method of projection operators on states of two particles with a definite spin and total angular momentum. Analytical calculation of the matrix elements is performed …
We have calculated the 6s-7s parity nonconserving E1 transition amplitude (E_{PNC}) in cesium. This calculation has been performed with higher numerical accuracy than our 1989 calculation [V.A. Dzuba, V.V. Flambaum, and O.P. Sushkov, Phys. Lett. A {\bf 141}, 147]. Also the Breit interaction has been included and the radiative corrections estimated. Our final result is E_{PNC}=0.902 (1 +/- 0.7%)iea_{B}(Q_{W}/N). This represents an improvement in the accuracy of the calculation from the 1% error claimed in 1989. This result corresponds to a nuclear weak charge for Cs, Q_{W}=-72.39 (1 +/- 0.4% (e…
We have performed relativistic many-body calculations of the hyperfine interaction in the $6s$ and $7s$ states of Cs, including the off-diagonal matrix element. The calculations were used to determine the accuracy of the semi-empirical formula for the electromagnetic transition amplitude $<6s|M1|7s>$ induced by the hyperfine interaction. We have found that even though the contribution of the many-body effects into the matrix elements is very large, the square root formula $<6s|H_{hfs}|7s > = \sqrt{< 6s|H_{hfs}|6s > < 7s|H_{hfs}|7s >}$ remains valid to the accuracy of a fraction of $10^{-3}$. T…
The fluorescence spectra of a sub-micron atomic cesium vapor layer observable under resonant excitation on D2 line have been studied in the presence of an external magnetic field. Substantial changes in amplitudes and frequency positions of the individual (resolved) hyperfine transitions have been recorded in moderate magnetic fields (up to ~ 50 Gauss). These features are caused by mixing of the hyperfine states of the upper level resulting from comparable values of the hyperfine splitting of the 62^P_{3/2} manifold and Larmor frequencies of the magnetic sublevels. The results of simulation sh…
Atomic parity violation has been observed in the 6s^2 1S0 - 5d6s 3D1 408-nm forbidden transition of ytterbium. The parity-violating amplitude is found to be two orders of magnitude larger than in cesium, where the most precise experiments to date have been performed. This is in accordance with theoretical predictions and constitutes the largest atomic parity-violating amplitude yet observed. This also opens the way to future measurements of neutron skins and anapole moments by comparing parity-violating amplitudes for various isotopes and hyperfine components of the transition.
Configuration interaction method is used to calculate transition amplitudes and other properties of the low states of dysprosium which are used in cooling and in study of the time variation of the fine structure constant and violation of fundamental symmetries. The branching ratio for the cooling state to decay to states other than ground state is found to be smaller than $10^{-4}$. The matrix element of the weak interaction between degenerate states at $E=19797.96$ cm$^{-1}$ is about 2 Hz which is consistent with the experimental limit $|H_W| = |2.3 \pm 2.9({\rm statistical}) \pm 0.7({\rm sys…
We present relativistic coupled-cluster (CC) calculations of energies, magnetic-dipole hyperfine constants, and electric-dipole transition amplitudes for low-lying states of atomic boron. The trivalent boron atom is computationally treated as a monovalent system. We explore performance of the CC method at various approximations. Our most complete treatment involves singles, doubles and the leading valence triples. The calculations are done using several approximations in the coupled-cluster (CC) method. The results are within 0.2-0.4% of the energy benchmarks. The hyperfine constants are repro…
The amplitude of two-photon transitions between hyperfine states in hydrogenlike ions is derived based on relativistic Dirac equation and second order perturbation theory. We study angular and linear polarization properties of the photon pair emitted in the decay of $2s$ states, where spin-flip and non-spin-flip transitions are highlighted. We pay particular attention to hydrogenlike uranium, since it is an ideal candidate for investigating relativistic and high-multipole effects, such as spin-flip transitions. Two types of emission patterns are identified: i) non-spin-flip transitions are fou…
We report modulation transfer spectroscopy on the D2 transitions in 85Rb and 87Rb using a simple home-built electro-optic modulator (EOM). We show that both the gradient and amplitude of modulation transfer spectroscopy signals, for the 87Rb F=2 to F'=3 and the 85Rb F=3 to F'=4 transitions, can be significantly enhanced by expanding the beams, improving the signals for laser frequency stabilization. The signal gradient for these transitions is increased by a factor of 3 and the peak to peak amplitude was increased by a factor of 2. The modulation transfer signal for the 85Rb F=2 to F' transiti…
It is demonstrated that Breit and negative-energy state contributions reduce the 2.5 sigma deviation [S.C. Bennett and C.E. Wieman, Phys. Rev. Lett. 82, 2484 (1999)] in the value of the weak charge of 133Cs from the Standard Model prediction to 1.7sigma. The corrections are obtained in the relativistic many-body perturbation theory by combining all-order Coulomb and second-order Breit contributions. The corrections to parity-nonconserving amplitudes amount to 0.6% in 133Cs and 1.1% in 223Fr. The relevant magnetic-dipole hyperfine structure constants are modified at the level of 0.3% in Cs, and…
We describe a method for determining the radiative decay properties of a molecule by studying the saturation of laser-induced fluorescence and the associated power broadening of spectral lines. The fluorescence saturates because the molecules decay to states that are not resonant with the laser. The amplitudes and widths of two hyperfine components of a spectral line are measured over a range of laser intensities and the results compared to a model of the laser-molecule interaction. Using this method we measure the lifetime of the A(v'=0) state of CaF to be tau=19.2 \pm 0.7 ns, and the Franck-…
