Parity-nonconserving Amplitude Research Articles

Nuclear neutron radius and weak mixing angle measurements from latest COHERENT CsI and atomic parity violation Cs data

The COHERENT collaboration observed coherent elastic neutrino nucleus scattering using a 14.6 kg cesium-iodide (CsI) detector in 2017 and recently published the updated results before decommissioning the detector. Here, we present the legacy determination of the weak mixing angle and of the average neutron rms radius of ^{133}{textrm{Cs}} and ^{127}{textrm{I}} obtained with the full CsI dataset, also exploiting the combination with the atomic parity violation (APV) experimental result, that allows us to achieve a precision as low as sim 4.5% and to disentangle the contributions of the ^{133}{textrm{Cs}} and ^{127}{textrm{I}} nuclei. Interestingly, we show that the COHERENT CsI data show a 6sigma evidence of the nuclear structure suppression of the full coherence. Moreover, we derive a data-driven APV+COHERENT measurement of the low-energy weak mixing angle with a percent uncertainty, independent of the value of the average neutron rms radius of ^{133}{textrm{Cs}} and ^{127}{textrm{I}}, that is allowed to vary freely in the fit. Additionally, we extensively discuss the impact of using two different determinations of the theoretical parity non-conserving amplitude in the APV fit. Our findings show that the particular choice can make a significant difference, up to 6.5% on R_n(Cs) and 11% on the weak mixing angle. Finally, in light of the recent announcement of a future deployment of a 10 kg and a sim 700 kg cryogenic CsI detectors, we provide future prospects for these measurements, comparing them with other competitive experiments that are foreseen in the near future.

Calculation of atomic integrals between relativistic functions by means of algebraic methods

We propose the use of Sturmian basis set for relativistic atomic structure calculations. We describe a numerically stable algebraic calculation of one- and two-particle radial integrals. The method is illustrated on the basis set independent calculation of energies, electric dipole moments, hyperfine integrals and parity non-conserving (PNC) amplitude for Cs in Dirac-Hartree-Fock approximation with frozen core orbitals. The previously reported results for electric dipole moments and PNC amplitude are found to be strongly basis dependent. Program summaryProgram title: PASCCPC Library link to program files:https://doi.org/10.17632/xycmhhcr5h.1Licensing provisions: MITProgramming language: Fortran 2008Nature of problem: Precise atomic measurements require reliable and highly accurate atomic structure calculations. Here we deal with the problem of numerical stability of the atomic integrals and basis set independence of the calculations.Solution method: The radial parts of the electronic orbitals are expanded in a discrete Sturmian functions that are eigenfunctions of one of the generators of the so(2,1) Lie algebra. This algebraic structure is used to deduce algebraic relations between the radial parts of the atomic integrals. This leads to numerically stable calculation, which in turn allows to achieve basis set independence.Additional comments including restrictions and unusual features: The method is currently restricted to the Dirac-Hartree-Fock method. However, this limitation will be lifted in future versions, which will be extended with the coupled clusters method.

Parity-mixed coupled-cluster formalism for computing parity-violating amplitudes

We formulate a parity-mixed coupled-cluster (PM-CC) approach for high-precision calculations of parity non-conserving amplitudes in mono-valent atoms. Compared to the conventional formalism which uses parity-proper (PP) one-electron orbitals, the PM-CC method is built using parity-mixed (PM) orbitals. The PM orbitals are obtained by solving the Dirac-Hartree-Fock equation with the electron-nucleus electroweak interaction included (PM-DHF). There are several advantages to such a PM-CC formulation: (i) reduced role of correlations, as for the most experimentally-accurate to date ${}^{133}{\rm Cs}\,$ $6S_{1/2}-7S_{1/2}$ transition, the PM-DHF result is only 3% away from the accurate many-body value, while the conventional DHF result is off by 18%; (ii) avoidance of directly summing over intermediate states in expressions for parity non-conserving amplitudes which reduces theoretical uncertainties associated with highly-excited and core-excited intermediate states, and (iii) relatively straightforward upgrade of existing and well-tested large-scale PP-CC codes. We reformulate the CC method in terms of the PM-DHF basis and demonstrate that the cluster amplitudes are complex numbers with opposite parity real and imaginary parts. We then use this fact to map out a strategy through which the new PM-CC scheme may be implemented.

Probing Low-Mass Vector Bosons with Parity Nonconservation and Nuclear Anapole Moment Measurements in Atoms and Molecules.

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 simple nuclear model. From measured and predicted (within the standard model) values for the PNC amplitudes in Cs, Yb, and Tl, as well as the nuclear anapole moment of ^{133}Cs, we constrain the P-violating vector-pseudovector nucleon-electron and nucleon-proton interactions mediated by a generic vector boson of arbitrary mass. Our limits improve on existing bounds from other experiments by many orders of magnitude over a very large range of vector-boson masses.

Relativistic coupled-cluster analysis of parity nonconserving amplitudes and related properties of the 6s2 S1/2 − 5d2 D3/2; 5/2 transitions in 133Cs

ABSTRACTWe present the results of our calculations of the parity nonconserving electric dipole amplitudes(E1PNC) for the 6s2S1/2 − 5d2D3/2; 5/2 transitions of 133Cs employing a relativistic coupled-cluster (RCC) method. E1PNC values for the nuclear spin-independent and nuclear spin-dependent (NSD) parity non-conservation (PNC) effects for different hyperfine levels of the 6s2S1/2 − 5d2D3/2 transition and only due to the NSD PNC interaction Hamiltonian for all possible hyperfine levels of the 6s2S1/2 − 5d2D5/2 transition are given. We have also performed calculations of several properties that are relevant for assessing the reliability of the calculations of the amplitudes of the above-mentioned transitions. We highlight the importance of correlation effects by giving the results of both the Dirac–Fock and RCC contributions. Approximate contributions to these properties from the Breit and quantum electrodynamic interactions have also been evaluated. Plausible experimental schemes to measure these transition amplitudes by light shift techniques and interference involving induced Stark shifts are outlined.

Development of the configuration-interaction + all-order method and application to the parity-nonconserving amplitude and other properties of Pb

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., Europhys. Lett. 7, 413 (1988)]. Our value for the weak charge Q_W=-117(5) is in agreement with the standard model prediction.

Limiting P-odd interactions of cosmic fields with electrons, protons, and neutrons.

We propose methods for extracting limits on the strength of P-odd interactions of pseudoscalar and pseudovector cosmic fields with electrons, protons, and neutrons, by exploiting the static and dynamic parity-nonconserving amplitudes and electric dipole moments they induce in atoms. Candidates for such fields are dark matter (including axions) and dark energy, as well as several more exotic sources described by Lorentz-violating standard model extensions. Atomic calculations are performed for H, Li, Na, K, Rb, Cs, Ba(+), Tl, Dy, Fr, and Ra(+). From these calculations and existing measurements in Dy, Cs, and Tl, we constrain the interaction strengths of the parity-violating static pseudovector cosmic field to be 7 × 10(-15) GeV with an electron, and 3 × 10(-8) GeV with a proton.

Measurement of weak optical transition moments through two-pathway coherent control

We present a full description of the (ω, 2ω) two-pathway coherent control interference technique for measurement of weak, highly forbidden optical transitions. We have recently applied this technique to the measurement of the magnetic dipole transition moment M1 of the 6s 2S1/2 → 7s 2S1/2 transition in atomic cesium. We also demonstrate detailed methods by which this technique may be used for measurement of the electroweak-induced parity nonconserving amplitude in atomic cesium. The principal benefits of this technique include reduced systematic errors related to field reversals often encountered in related measurements, reduced interference from adjacent, noninterfering transitions, and the absence of electric quadrupole transitions. We present a critical evaluation of the effects induced by stray fields and other systematic effects.

Correlation effects in Yb+and implications for parity violation

Calculation of the energies, magnetic dipole hyperfine structure constants, $E$1 transition amplitudes between the low-lying states, and nuclear spin-dependent parity-nonconserving amplitudes for the ${}^{2}{S}_{1/2}\ensuremath{-}{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2,5/2}$ 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 results obtained by two methods. The accuracy of different methods is evaluated. We find that the monovalent description is inadequate for evaluation of some atomic properties due to significant mixing of the one-particle and the hole-two-particle configurations. Performing the calculation by such different approaches allowed us to establish the importance of various correlation effects for Yb${}^{+}$ atomic properties for future improvement of theoretical precision in this complicated system.

Parity nonconservation in hyperfine transitions

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.

Calculation of nuclear-spin-dependent parity nonconservation ins–dtransitions of Ba+, Yb+, and Ra+ions

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.

Calculation of parity nonconservation in neutral ytterbium

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 $6{s}^{2} {}^{1}{S}_{0}$ ground state and the $6s5d {}^{3}{D}_{1}$ excited state of $^{171}\mathrm{Yb}$ and $^{173}\mathrm{Yb}$. The results are presented in a form convenient for extracting spin-dependent interaction constants (such as anapole moment) from the measurements.

Atomic calculations for tests of fundamental physics1This review is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas.

An overview of applications of atomic calculations for atomic physics tests of fundamental physics is presented. The current status of atomic parity violation studies is discussed in detail. The progress on the development of a novel method for precision calculation of properties of atomic systems with a few valence electrons is reported. This method combines the all-order approach currently used for monovalent atoms with the configuration interaction approach that is applicable for many-electron systems. Development of this method is aimed at significant improvement in the theoretical accuracy of the parity nonconserving amplitude calculations in systems with more than one valence electron. Tests of fundamental symmetries and other applications not only require precise calculations of the atomic properties but also evaluation of the accuracy of the results. Possible approaches to evaluating the uncertainties of the theoretical values and an example of such an evaluation are considered.

Relativistic multireference Fock-space coupled-cluster calculation of the forbidden6s2S01→6s5dD13magnetic-dipole transition in ytterbium

We report the forbidden 6s{sup 2} {sup 1}S{sub 0}{yields}6s5d {sup 3}D{sub 1} magnetic-dipole transition amplitude computed using multireference Fock-space coupled-cluster theory. Our computed transition matrix element (1.34x10{sup -4}){mu}{sub B} is in excellent agreement with the experimental value (1.33x10{sup -4}){mu}{sub B}. This value in combination with other known quantities will be helpful in determining the parity-nonconserving amplitude for the 6s{sup 2} {sup 1}S{sub 0}{yields}6s5d {sup 3}D{sub 1} transition in atomic Yb. To our knowledge, this calculation is the most accurate to date, and can be very important in the search for physics beyond the standard model. We further report the 6s6p {sup 3}P{sub 0}{yields}6s6p {sup 1}P{sub 1} and 6s5d {sup 3}D{sub 1}{yields}6s6p {sup 3}P{sub 0} transition matrix elements, which are also in good agreement with the earlier theoretical estimates.

Breit interaction and parity nonconservation in many-electron atoms

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 corrections to the Breit interaction are especially important for the $s-d$ PNC amplitudes. We confirm good agreement of the PNC measurements for cesium and thallium with the standard model .

Electric dipole transition amplitudes for 207Pb+

Electric dipole transition amplitudes of certain low-lying states of Pb+ have been calculated using the relativistic coupled-cluster theory and compared with previous calculations. The role of electron correlation is found to be important. Some of the results we have obtained would be useful in estimating the size of the parity non-conserving amplitude for the 6p2P1/2 → 6p2P3/2 transition.

Radiative and correlation effects on the parity-nonconserving transition amplitude in heavy alkali-metal atoms

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 $\ensuremath{\alpha}Z$ 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 $\ensuremath{-}0.27(3)%$ for Cs and $\ensuremath{-}0.28(5)%$ for Fr. Moreover, a high-precision calculation of the electron-correlation and Breit-interaction effects on the $7s\text{\ensuremath{-}}8s$ 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 $^{133}\mathrm{Cs}$ is derived to amount to ${Q}_{W}=\ensuremath{-}72.65{(29)}_{\mathrm{exp}}{(36)}_{\mathrm{theor}}$. This value deviates by $1.1\ensuremath{\sigma}$ from the prediction of the standard model. The values of the $7s\text{\ensuremath{-}}8s$ PNC amplitude in $^{223}\mathrm{Fr}$ and $^{210}\mathrm{Fr}$ are obtained to be $\ensuremath{-}15.49(15)$ and $\ensuremath{-}14.16(14)$, respectively, in units of $i\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}(\ensuremath{-}{Q}_{W})∕N\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$

Accurate spline solutions for the Dirac equation with a parity-nonconserving potential

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 $10^{-7}$.

Vacuum-Polarization Corrections to Parity-Nonconserving Effects in Atomic Systems

The dominant one-loop vacuum-polarization correction to atomic wave functions are evaluated for the 6s–7s parity nonconserving (PNC) E1 transition amplitude in cesium. This correction increases the size of the PNC amplitude by 0.4% and thus increases the difference between the experimental value of the weak charge Q W and the one predicted by the standard model.

QED radiative corrections to parity nonconservation in heavy atoms.

The self-energy and vertex QED radiative corrections [approximately Zalpha2f(Zalpha)] are shown to give a large negative contribution to the parity nonconserving (PNC) amplitude in heavy atoms. The correction -0.73(20)% found for the 6s-7s PNC amplitude in 133Cs brings the experimental result for this transition into agreement with the standard model. The calculations are based on a new relation that expresses the radiative corrections to the PNC matrix element via corrections to the energy shifts induced by the finite nuclear size.