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 method is performed. The obtained results are employed to improve the theoretical predictions for the PNC transition amplitude in Cs and Fr. Using an average value from two most accurate measurements of the vector transition polarizability, the weak charge of $^{133}$Cs is derived to amount to $ Q_W=-72.65(29)_{\rm exp}(36)_{\rm theor}$. This value deviates by $1.1σ$ from the prediction of the standard model. The values of the $7s$-$8s$ PNC amplitude in $^{223}$Fr and $^{210}$Fr are obtained to be $-$15.49(15) and $-$14.16(14), respectively, in units of i$\times 10^{-11}(-Q_W)/N$ a.u.
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.
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…
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…
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 have reported the results of ab initio calculations of parity- and time- reversal -odd interaction constants for the ground state of alkaline-earth monofluorides. The Kramers-restricted configuration interaction method limited to single and double excitations in conjunction with the quadruple zeta quality basis sets have been employed to perform these 4-component relativistic calculations. The results are compared with the existing semi-empirical and other theoretical results, wherever available.
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.
We present a general approach within the relativistic coupled-cluster theory framework to calculate exactly the first order wave functions due to any rank perturbation operators. Using this method, we calculate the static dipole and quadrupole polarizabilities in some alkali atoms and alkaline earth-metal ions. This may be a good test of the present theory for different rank and parity interaction operators. This shows a wide range of applications including precise calculations of both parity and CP violating amplitudes due to rank zero and rank one weak interaction Hamiltonians. We also give …
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…
Heavy-atom alkaline earth monofluoride molecules are considered as prospective systems to study spatial parity or spatial parity and time-reversal symmetry violating effects such as the nuclear anapole moment or the electron electric dipole moment. Comprehensive and highly accurate theoretical study of the electronic structure properties and transition energies in such systems can simplify the preparation and interpretation of the experiments. However, almost no attempts to calculate quantum electrodynamics (QED) effects contribution into characteristics of neutral heavy-atom molecules have be…
The present status of quantum electrodynamics (QED) theory of heavy few-electron ions is reviewed. The theoretical results are compared with available experimental data. A special attention is focused on tests of QED at strong fields and on determination of the fundamental constants. A recent progress on calculations of the QED corrections to the parity nonconserving 6s-7s transition amplitude in neutral Cs is also discussed.
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 estimate the effect of the tensor parity nonconserving (PNC) interaction in the $^{181}$TaO$^+$ molecular cation. It can be used to probe the unknown quadrupole distribution of the neutrons inside the Ta nucleus. To this end, we evaluate the constant which characterizes this interaction using the relativistic Fock space coupled cluster theory for electronic structure modelling. The $^3Δ_1$ state of the TaO$^+$ cation which can be used to measure the PNC effect is found to be the ground one in agreement with the previous theoretical study.
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…
