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.
Very brief summary of the most recent developments in an area of QED corrections to the parity nonconservation in atoms is presented. Main conclusion - experimental results of Wood et al do not contradict the standard model
The self-energy and the vertex radiative corrections to the effect of parity nonconservation in heavy atoms are calculated analytically in orders Z alpha^2 and Z^2 alpha^3 ln(lambda_C/r_0), where lambda_C and r_0 being the Compton wavelength and the nuclear radius, respectively. The value of the radiative correction is -0.85% for Cs and -1.41% for Tl. Using these results we have performed analysis of the experimental data on atomic parity nonconservation. The obtained values of the nuclear weak charge, Q_W=-72.90(28)_{exp}(35)_{theor} for Cs, and Q_W=-116.7(1.2)_{exp}(3.4)_{theor} for Tl, agre…
Anapole moments are parity-odd, time-reversal-even moments of the E1 projection of the electromagnetic current. Although it was recognized, soon after the discovery of parity violation in the weak interaction, that elementary particles and composite systems like nuclei must have anapole moments, it proved difficult to isolate this weak radiative correction. The first successful measurement, an extraction of the nuclear anapole moment of 133Cs from the hyperfine dependence of the atomic parity violation, was obtained only recently. An important anapole moment bound in Tl also exists. We discuss…
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.
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…
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.
Parity nonconservation due to the nuclear weak charge is considered. We demonstrate that the radiative corrections to this effect due to the vacuum fluctuations of the characteristic size larger than the nuclear radius $r_0$ and smaller than the electron Compton wave-length $λ_C$ are enhanced because of the strong electric field of the nucleus. The parameter that allows one to classify the corrections is the large logarithm $\ln(λ_C/r_0)$. The vacuum polarization contribution is enhanced by the second power of the logarithm. Although the self-energy and the vertex corrections do not vanish, th…
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.
The parity nonconservation (PNC) effect on the laser-induced 2^3S_1 - 2^1S_0 transition in heavy heliumlike ions is considered. A simple analytical formula for the PNC correction to the cross section is derived for the case, when the opposite-parity 2^1S_0 and 2^3P_0 states are almost degenerate and, therefore, the PNC effect is strongly enhanced. Numerical results are presented for heliumlike gadolinium and thorium, which seem most promising candidates for such kind of experiments. In both Gd and Th cases the photon energy required will be anticipated with a high-energy laser built at GSI. Al…
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.
The contribution of the axial triangle anomalous graph to the parity non-conservation effect in atoms is evaluated. The final answer looks like the emission of the electric photon by the magnetic dipole. The relative contribution to the parity non-conservation effect in neutral atoms appears to be negligible but is essentially larger in case of multicharged ions.
Nuclei with spin $I \ge 1$ have a weak quadrupole moment which leads to tensor contribution to the parity non-conserving interaction between nuclei and electrons. We calculate this contribution for Yb$^+$, Fr and Ra$^+$ and found it to be small. In contrast, in many lanthanides (e.g., Nd, Gd, Dy, Ho, Er, Pr, Sm) and Ra close levels of opposite parity lead to strong enhancement of the effect making it sufficiently large to be measured. Another possibility is to measure the PNC transitions between the hyperfine components of the ground state of Bi. Since nuclear weak charge is dominated by neutr…
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 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.
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 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.
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 investigate the parity nonconservation effect in the elastic scattering of polarized electrons on heavy He-like ions, being initially in the ground state. The enhancement of the parity violation is achieved by tuning the energy of the incident electron in resonance with quasidegenerate doubly-excited states of the corresponding Li-like ion. We consider two possible scenarios. In the first one we assume that the polarization of the scattered electron is measured, while in the second one it is not detected.
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 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 investigate the parity nonconservation (PNC) effect in the dielectronic recombination (DR) of a polarized electron with a heavy He-like ion into doubly-excited $((1s 2p_{1/2})_{0} nκ)_{1/2}$ and $\left(\left(1s 2s\right)_{0} nκ\right)_{1/2}$ states of Li-like ion. We determine the nuclear charge number $Z$ for which these opposite-parity levels are near to cross and, therefore, the PNC effect will be significantly enhanced. Calculations are performed for quantum numbers $n \geq 4$ and $κ= \pm 1$.
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.
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 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…
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…
The lifetimes of the $6d \ ^2D_{3/2}$ and $6d \ ^2D_{5/2}$ states in Fr are estimated to be 540(10) ns and 1704(32) ns respectively. They are determined by calculating the radiative transition amplitudes of the allowed electric dipole (E1) and the forbidden electric quadrupole (E2) and magnetic dipole (M1) channels using the second order many-body perturbation theory (MBPT(2)) and the coupled-cluster (CC) method at different levels of approximation in the relativistic framework. These long lifetimes and the large electric dipole parity non conserving amplitudes of $7s \ ^2S_{1/2} \rightarrow 6…
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.
Parity nonconservation (PNC) effect in recombination of a polarized electron with a heavy H-like ion in case of resonance with a doubly excited state of the corresponding He-like ion is studied. It is assumed that photons of the energy corresponding to the one-photon decay of the doubly excited state into the $2^1S_0$ or the $2^3P_0$ state are detected at a given angle with respect to the incident electron momentum. Calculations are performed for heliumlike thorium ($Z = 90$) and gadolinium ($Z = 64$), where the $2^1S_0$ and $2^3P_0$ levels are near to cross and, therefore, the PNC effect is s…
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 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 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…
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 show that the interaction of an axion field, or in general a pseudoscalar field, with the axial-vector current generated by an electron through a derivative-type coupling can give rise to a time-dependent mixing of opposite-parity states in atomic and molecular systems. Likewise, the analogous interaction of an axion field with the axial-vector current generated by a nucleon can give rise to time-dependent mixing of opposite-parity states in nuclear systems. This mixing can induce oscillating electric dipole moments, oscillating parity non-conservation effects and oscillating anapole moment…
We propose a method for measuring the magnetic dipole (M1) transition moment of the $6S_{1/2} \big(\mathrm{m}=-1/2\big)\leftrightarrow 5D_{3/2}\big(\mathrm{m}=-1/2\big)$ transition in single trapped Ba$^{+}$ by exploiting different symmetries in the electric quadrupole (E2) and M1 couplings between the states. The technique is adapted from a previously proposed method for measuring atomic parity nonconservation in a single trapped ion [Norval Fortson, Phys. Rev. Lett. \textbf{70}, 17 (1993)]. Knowledge of M1 is crucial for any parity nonconservation measurement in Ba$^{+}$, as laser coupling t…
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…
We report on a measurement of the highly forbidden $6s^2 ^1S_0 \to 5d6s ^3 D_1$ magnetic-dipole transition in atomic ytterbium using the Stark-interference technique. This amplitude is important in interpreting a future parity nonconservation experiment that exploits the same transition. We find $| < 5d6s ^3 D_1 | M1 | 6s^2 ^1S_0 > | ~ = ~ 1.33(6)_{Stat}(20)_β \times 10^{-4} μ_0$, where the larger uncertainty comes from the previously measured vector transition polarizability $β$. The $M1$ amplitude is small and should not limit the precision of the parity nonconservation experiment.
Parity violating electron nucleus scattering is a clean and powerful tool for measuring the spatial distributions of neutrons in nuclei with unprecedented accuracy. Parity violation arises from the interference of electromagnetic and weak neutral amplitudes, and the $Z^0$ of the Standard Model couples primarily to neutrons at low $Q^2$. The data can be interpreted with as much confidence as electromagnetic scattering. After briefly reviewing the present theoretical and experimental knowledge of neutron densities, we discuss possible parity violation measurements, their theoretical interpretati…
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.
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…
Employing the relativistic coupled-cluster method, comparative studies of the parity non-conserving electric dipole amplitudes for the $7s \ ^2S_{1/2} \rightarrow 6d \ ^2D_{5/2}$ transitions in $^{210}$Fr and $^{211}$Fr isotopes have been carried out. It is found that these transition amplitudes, sensitive only to the nuclear spin dependent effects, are enhanced by more than 3 orders compared to the low-lying $S-D_{5/2}$ transitions in Ba$^+$ and Ra$^+$ owing to the very large contributions from the electron core-polarization effects in Fr. This translates to a relatively large and, in princip…
Single trapped and laser cooled Radium ion as a possible candidate for measuring the parity violation induced frequency shift has been discussed here. Even though the technique to be used is similar to that proposed by Fortson [1], Radium has its own advantages and disadvantages. The most attractive part of Radium ion as compared to that of Barium ion is its mass which comes along with added complexity of instability as well as other issues which are discussed here
Atomic Parity Violation provides the rare opportunity of a low energy window into possible new fundamental processes at very high mass scales normally investigated at large high energy accelerators. Precise measurements on atomic systems are currently the most sensitive probes of many kinds of new physics, and complement high energy experiments. Present atomic experiments are beginning to reach their limits of precision due to either sensitivity, systematics or atomic structure uncertainties. An experiment in a single trapped Barium ion can improve on all of these difficulties. This experiment…
We report measurements of the Stark shift of the cesium $6s \: ^2S_{3/2} \rightarrow 7p \: ^2P_{3/2} $ and the $6s \: ^2S_{1/2} \rightarrow 7p \: ^2P_{1/2} $ transitions at $λ= 456$ nm and 459 nm, respectively, in an atomic beam. From these, we determine the static scalar polarizability for both 7P states, and the tensor polarizability for the 7P$_{3/2}$ state. The fractional uncertainty of the scalar polarizabilites is $\sim$0.18\%, while that of the tensor term is 0.66\%. These measurements provide sensitive tests of theoretical models of the Cs atom, which has played a central role in parit…
In this paper we present some concepts in heavy ion atomic physics for the extraction of parity violating effects. We investigate the effects of the so-called Stark-quenching, i.e., the fast decay of a meta stable state induced by a Stark field, and the superposition of one- and two-photon transitions in beryllium-like heavy ions. It turns out that the discussed theoretical phenomena for heavy ions with few electrons are beyond the scope of present day experimental possibilities because one has to require beam energies of up to 1 TeV/A, laser intensities of up to $10^{17} {\rm W/cm^2}$ and ion…
Single trapped ions are ideal systems in which to test atomic physics at high precision: they are effectively isolated atoms held at rest and largely free from perturbing interactions. This thesis describes several projects developed to study the structure of singly-ionized barium and more fundamental physics. First, we describe a spin-dependent "electron-shelving" scheme that allows us to perform single ion electron spin resonance experiments in both the ground 6S_{1/2} and metastable 5D_{3/2} states at precision levels of 10^{-5}. We employ this technique to measure the ratio of off-resonant…
We report the results from our first-generation experiment to measure the magnetic-dipole transition moment (M1) between the $6S_{1/2}$ and $5D_{3/2}$ manifolds in Ba$^{+}$. Knowledge of M1 is crucial for the proposed parity-nonconservation experiment in the ion \cite{Fortson93}, where M1 will be a leading source of systematic error. To date, no measurement of M1 has been made in Ba$^{+}$, and moreover, the sensitivity of the moment to electron-electron correlations has confounded accurate theoretical predictions. A precise measurement may help to resolve the theoretical discrepancies while pr…
We report measurements of the lifetimes of the 3d $^2$D$_{5/2}$ and 3d $^2$D$_{3/2}$ metastable states of a single laser-cooled $^{40}$Ca$^+$ ion in a linear Paul trap. We introduce a new measurement technique based on high-efficiency quantum state detection after coherent excitation to the D$_{5/2}$ state or incoherent shelving in the D$_{3/2}$ state, and subsequent free, unperturbed spontaneous decay. The result for the natural lifetime of the D$_{5/2}$ state of 1168(9) ms agrees excellently with the most precise published value. The lifetime of the D$_{3/2}$ state is measured with a single …
Precision measurements of parity non-conserving (PNC) interactions in atoms, molecules and ions can lead to the discovery of new physics beyond the standard model and understanding of weak-force induced interactions in the nucleus. In this paper, we propose and analyze a novel atomic parity violation measurement scheme for a forbidden transition where we combine a two-pathway coherent control mechanism with probe gain techniques. We detail a feasible experimental geometry for $6S_{1/2}\rightarrow 7S_{1/2}$ transitions in a cesium vapor cell, and consider the statistical noise of such a measure…
An accurate study of the lowest $1σ_g$ and the low-lying excited $1σ_u$, $1π_{u,g}$, $1δ_{g,u}$ electronic states of the exotic molecular ion $H_3^{2+}$ in linear configuration parallel to a magnetic field is carried out. The magnetic field ranges from $10^{10}$ G up to $4.414 \times 10^{13}$ G where non-relativistic considerations are justified. The variational method is exploited and the {\it same} trial function is used for different magnetic fields. It is shown that the states of positive $z$-parity $1σ_g, 1π_u, 1δ_{g}$ are bound states of the $H_3^{2+}$ exotic ion for all magnetic fields …
