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 term which deviates from the sum by less than 20%. This term corresponds to an s-p_{1/2} weak matrix element, which can be calculated to better than 1%, and a p_{1/2}-d_{3/2} E1 transition amplitude, which can be measured. Also, the s-d amplitudes are about four times larger than the corresponding s-s transitions. We have shown that by using a hybrid mixed-states/sum-over-states approach the accuracy of the calculations of PNC s-d amplitudes could compete with that of Cs 6s-7s if p_{1/2}-d_{3/2} E1 amplitudes are measured to high accuracy.
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 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…
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 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 present the theoretical basis of a cavity-enhanced polarimetric scheme for the measurement of parity-nonconserving (PNC) optical rotation. We discuss the possibility of detecting PNC optical rotation in accessible transitions in metastable Xe and Hg, and ground state I. In particular, the physics of the PNC optical rotation is presented, and we explore the lineshape effects on the expected PNC optical rotation signals. Furthermore, we present an analysis of the eigenpolarizations of the cavity-enhanced polarimeter, which is necessary for understanding the measurement procedure and the abili…
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 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…
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…
The complete gauge-invariant set of the one-loop QED corrections to the parity-nonconserving 6s-7s amplitude in $^{133}$Cs is evaluated to all orders in $αZ$ using a local version of the Dirac-Hartree-Fock potential. The calculations are peformed in both length and velocity gauges for the absorbed photon. The total binding QED correction is found to be -0.27(3)%, which differs from previous evaluations of this effect. The weak charge of $^{133}$Cs, derived using two most accurate values of the vector transition polarizability $β$, is $Q_W=-72.57(46)$ for $β= 26.957(51) a_{\rm B}^3$ and $Q_W=-7…
The weak interaction does not conserve parity, which is apparent in many nuclear and atomic phenomena. However, thus far, parity nonconservation has not been observed in molecules. Here we consider nuclear-spin-dependent parity nonconserving contributions to the molecular Hamiltonian. These contributions give rise to a parity nonconserving indirect nuclear spin-spin coupling which can be distinguished from parity conserving interactions in molecules of appropriate symmetry, including diatomic molecules. We estimate the magnitude of the coupling, taking into account relativistic corrections. Fi…
We present the results of our calculations of the parity nonconserving electric dipole amplitudes ($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 use configuration interaction and many-body perturbation theory techniques to calculate spin-independent and spin-dependent parts of the parity nonconserving amplitudes of the transitions between the $6s^2 \ ^1$S$_0$ ground state and the $6s5d \ ^3$D$_1$ excited state of $^{171}$Yb and $^{173}$Yb. The results are presented in a form convenient for extracting spin-dependent interaction constants (such as, e.g., anapole moment) from the measurements.
Pseudoscalar or pseudovector cosmic fields, that serve as a source of parity ($\mathcal{P}$) violation, are invoked in different models for cold dark matter or in the standard model extension that allows for Lorentz invariance violation. A direct detection of the timelike-component of such fields requires a direct measurement of $\mathcal{P}$-odd potentials or their evolution over time. Herein, advantageous properties of chiral molecules, in which $\mathcal{P}$-odd potentials lead to resonance frequency differences between enantiomers, for direct detection of such $\mathcal{P}$-odd cosmic fiel…
We discuss a parity nonconserving (PNC) asymmetry in the cross section of dielectronic recombination of polarized electrons on multiply charged ions with Z>40. This effect is strongly enhanced for close doubly-excited states of opposite parity in the intermediate compound ion. Such states are known for He-like ions. However, these levels have large energy and large radiative widths which hampers observation of the PNC asymmetry. We argue that accidentally degenerate states of the more complex ions may be more suitable for the corresponding experiment.
We use correlation potential and many-body perturbation theory techniques to calculate spin-independent and nuclear spin-dependent parts of the parity nonconserving amplitudes of the transitions between the $6s_{1/2}$ ground state and the $5d_{3/2}$ excited state of Ba$^+$ and Yb$^+$ and between the $7s_{1/2}$ ground state and the $6d_{3/2}$ excited state of Ra$^+$. The results are presented in a form convenient for extracting of the constants of nuclear-spin-dependent interaction (such as, e.g., anapole moment) from the measurements.
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.
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 report the result of our {\it ab initio} calculation of the $6s ^2S_{1/2} \to 5d ^2D_{3/2}$ parity nonconserving electric dipole transition amplitude in $^{137}\text{Ba}^+$ based on relativistic coupled-cluster theory. Considering single, double and partial triple excitations, we have achieved an accuracy of less than one percent. If the accuracy of our calculation can be matched by the proposed parity nonconservation experiment in Ba$^+$ for the above transition,then the combination of the two results would provide an independent non accelerator test of the Standard Model of particle physi…
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…
Calculation of the energies, magnetic dipole hyperfine structure constants, E1 transition amplitudes between the low-lying states, and nuclear spin-dependent parity-nonconserving amplitudes for the ^2S_{1/2} - ^2D_{3/2,5/2} transitions in ^{171}Yb^+ ion is performed using two different approaches. First, we carried out many-body perturbation theory calculation considering Yb^+ as a monovalent system. Additional all-order calculations are carried out for selected properties. Second, we carried out configuration interaction calculation considering Yb as a 15-electron system and compared the resu…
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 discuss a parity nonconserving asymmetry in the cross section of KLL dielectronic recombination of polarized electrons on the hydrogen-like ions with $Z \lesssim 60$. This effect is strongly enhanced because of the near-degeneracy of doubly-excited $2l2l'$ states of opposite parity in He-like ions. For ions with $Z \sim 30$ the asymmetry is of the order of $10^{-9}$. For $Z \approx 48$ a level crossing takes place, leading to the PNC asymmetry of $\pm 5\times 10^{-9}$, which is $10^8$ times greater than the basic strength of the weak interaction in atoms.
We report on a theoretical analysis of the suitability of the 7s 2S1/2 <-> 6d 2D3/2 transition in singly ionized radium to measure parity nonconservation, in the light of an experiment planned at the KVI of the University of Groningen. Relativistic coupled-cluster theory has been employed to perform an ab initio calculation of the parity nonconserving electric dipole amplitude of this transition, including single, double, and leading triple excitations. We discuss the prospects for a sub-1% precision test of the electroweak theory of particle physics.
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.
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 present a new technique based on two-pathway optical coherent control for the sensitive detection and precise measurement of highly-forbidden transitions in atomic systems. Specifically, we show that ($ω$, 2$ω$) coherent control can be applied to the measurement of the magnetic dipole and electroweak parity nonconserving amplitudes in atomic cesium, with the principal advantage of reduced systematic errors related to field reversals often encountered in previous measurements of these effects. We present a complete analysis in one specific geometry, and discuss prospects for improved laborat…
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…
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.
Parity (P) and time (T) invariance violating effects in the Ra atom are strongly enhanced due to close states of opposite parity, the large nuclear charge Z and the collective nature of P,T-odd nuclear moments. We have performed calculations of the atomic electric dipole moments (EDM) produced by the electron EDM and the nuclear magnetic quadrupole and Schiff moments. We have also calculated the effects of parity non-conservation produced by the nuclear anapole moment and the weak charge. Our results show that as a rule the values of these effects are much larger than those considered so far i…
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.
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…
The relations between matrix elements of different P- and T-odd weak interactions are derived. We demonstrate that similar relations hold for parity nonconserving (PNC) transition amplitudes and electron electric dipole moments (EDM) of atoms and molecules. This allows to express P- and T-odd effects in many-electron systems caused by different symmetry-breaking mechanisms via each other using simple analytical formulas. We use these relations for the interpretation of the anapole moment measurements in cesium and thallium and for the analysis of the relative contributions of the scalar-pseudo…
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.
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…
Fock-space perturbed relativistic coupled-cluster calculations of electric dipole polarizability and nuclear spin-dependent parity non-conservation in Cs
The parity nonconservation effect on the radiative recombination of electrons with heavy hydrogenlike ions is studied. Calculations are performed for the recombination into the $2^1S_0$ state of helium-like thorium and gadolinium, where, due to the near-degeneracy of the opposite-parity $2^1S_0$ and $2^3P_0$ states, the effect is strongly enhanced. Two scenarios for possible experiments are studied. In the first scenario, the electron beam is assumed to be fully polarized while the H-like ions are unpolarized and the polarization of the emitted photons is not detected. In the second scenario, …
We perform calculations of s-d_5/2 nuclear-spin-dependent parity nonconservation amplitudes for Rb, Cs, Ba+, Yb+, Fr, Ra+ and Ac++. These systems prove to be good candidates for the use in atomic experiments to extract the so-called anapole moment, a P-odd T-even nuclear moment important for the study of parity violating nuclear forces. We also extend our previous works by calculating the missed spin-dependent amplitudes for the s-d_3/2 transitions in the above systems.
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.,…
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 present calculations of nuclear-spin-dependent and nuclear-spin-independent parity violating amplitudes in Ba, Ra, Ac+, Th and Pa. Parity nonconservation in these systems is greatly enhanced due to the presence of very close electronic energy levels of opposite parity, large nuclear charge, and strong nuclear enhancement of parity-violating effects. The presented amplitudes constitute several of the largest atomic parity-violating signals predicted so far. Experiments using these systems may be performed to determine values for the nuclear anapole moment, a P-odd T-even nuclear moment given…
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…
With their rich electronic, vibrational, rotational and hyperfine structure, molecular systems have the potential to play a decisive role in precision tests of fundamental physics. For example, electroweak nuclear interactions should cause small energy differences between the two enantiomers of chiral molecules, a signature of parity symmetry breaking. Enantioenriched oxorhenium(VII) complexes S-(-)- and R-(+)-3 bearing a chiral 2-methyl-1-thio-propanol ligand have been prepared as potential candidates for probing molecular parity violation effects via high resolution laser spectroscopy of the…
The 10-electron generalized relativistic effective core potential and the corresponding correlation spin-orbital basis sets are generated for the Ra atom and the relativistic coupled cluster calculations for the RaO molecule are performed. The main goal of the study is to evaluate the P,T-odd parameter X characterized by the molecular electronic structure and corresponding to a "volume effect" in the interaction of the ^{225}Ra nucleus Schiff moment with electronic shells of RaO. Our final result for X(^{225}RaO) is -7532 which is surprisingly close to that in ^{205}TlF but has different sign.…
Our improved calculation of the nuclear spin-independent parity violating electric dipole transition amplitude ($E1_{PV}$) for $6s ~ ^2S_{1/2} - 7s ~ ^2S_{1/2}$ in $^{133}$Cs in combination with the most accurate (0.3\%) measurement of this quantity yields a new value for the nuclear weak charge $Q_W=-73.71(26)_{ex} (23)_{th}$ against the Standard Model (SM) prediction $Q_W^{\text{SM}}=-73.23(1)$. The advances in our calculation of $E1_{PV}$ have been achieved by using a variant of the perturbed relativistic coupled-cluster theory which treats the contributions of the core, valence and excited…
Contributions from the Breit interaction in atomic-structure calculations account for 1.3sigma of the previously reported 2.5sigma deviation from the Standard Model in the 133Cs weak charge [S.C. Bennett and C.E. Wieman, Phys. Rev. Lett. 82, 2484 (1999)]. The updated corrections for the neutron distribution reduce the discrepancy further to 1.0sigma. The updated value of the weak charge is Q_W(133Cs) = -72.65(28)_{expt}(34)_{theor}. The present analysis is a higher-order extension of previous calculation [A. Derevianko, E-print physics/0001046].
We report the result of our calculation of the nuclear spin-independent parity violating electric dipole transition amplitude ($E1_{PV}$) for the $6s ~ ^2S_{1/2} - 7s ~ ^2S_{1/2}$ transition in $^{133}$Cs to an accuracy of 0.3\% using a variant of the perturbed relativistic coupled-cluster theory. In the present work, we treat the contributions of both the low-lying and high-lying excited states to the above mentioned amplitude on the same footing, thereby overcoming the limitations of previous high accuracy relativistic coupled cluster calculations. We obtain an accurate value for the vector …
In Phys. Rev. D 103, L111303 (2021), we had reported an improved calculation of the nuclear spin-independent parity violating electric dipole transition amplitude ($E1_{PV}$) for the $6s ~ ^2S_{1/2} - 7s ~ ^2S_{1/2}$ transition in $^{133}$Cs by employing a relativistic coupled-cluster (RCC) theory. In a recent Comment, B. M. Roberts and J. S. M. Ginges have raised questions about our calculation of the so-called Core contribution to $E1_{PV}$. Our result for this contribution does not agree with theirs, but is in agreement with results from previous calculations where this contribution is give…
Recent progress in calculations of QED radiative corrections to parity nonconservation in atoms is reviewed. The QED vacuum polarization, the self-energy corrections and the vertex corrections are shown to be described very reliably by different methods used by different groups. All new calculations have recently converged to very close final values. Each separate radiative correction is very large, above 1 % for heavy atoms, but having different signs they partly compensate each other. Our results for the radiative corrections for all atoms are presented. The corrections are -0.54 % for 133 C…
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…
A semi-empirical calculation of the 6s - 7s Stark amplitude $α$ in Cs has been performed using the most accurate measurements and calculations of the electromagnetic amplitudes available. This is then used to extract the parameters of the electroweak theory from experimental data. The results are: $α= 269.0 (1.3) a_0^3$, weak charge of Cs $Q_W = -72.41(25)_{exp} (80)_{theor}$, deviation from the Standard model $S = -1.0(.3)_{exp} (1.0)_{theor}$ and limit on the mass of the extra Z-boson in SO(10) model $M_{Z_x} > 550 GeV$.
We calculate the self-energy and the vertex radiative corrections to the effect of parity nonconservation in heavy atoms. The sum of the corrections is of the form ${\cal A}\ln(λ_C/r_0)+{\calB}$, where ${\cal A}$ and ${\cal B}$ are functions of $Zα$, and $λ_C$ and $r_0$ are the Compton wavelength and the nuclear radius, respectively. The function ${\cal A}$ is calculated exactly in $Zα$ and the function ${\cal B}$ is calculated in the leading order. In the leading order ${\cal A}\propto α(Zα)^2$ and ${\cal B}\propto α(Zα)$. The sum of the corrections is -0.85% for Cs and -1.48% for Tl. Using t…
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 …
We carry out high-precision calculation of parity violation in cesium atom, reducing theoretical uncertainty by a factor of two compared to previous evaluations. We combine previous measurements with our calculations and extract the weak charge of the 133Cs nucleus, Q_W = -73.16(29)_exp(20)_th. The result is in agreement with the Standard Model (SM) of elementary particles. This is the most accurate to-date test of the low-energy electroweak sector of the SM. In combination with the results of high-energy collider experiments, we confirm the energy-dependence (or "running") of the electroweak …
We propose methods and present calculations that can be used to search for evidence of cosmic fields by investigating the parity-violating effects, including parity nonconservation amplitudes and electric dipole moments, that they induce in atoms. The results are used to constrain important fundamental parameters describing the strength of the interaction of various cosmic fields with electrons, protons, and neutrons. Candidates for such fields are dark matter (including axions) and dark energy, as well as several more exotic sources described by standard-model extensions. Existing parity nonc…
