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Register a new userCalculations of Time-Reversal Symmetry Violation Sensitivity Parameters Based on Analytic Relativistic Coupled-Cluster Gradient Theory
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We develop an analytic-gradient based method for relativistic coupled-cluster calculations of effective electric field, $mathcal{E}_{text{eff}}$, with improved efficiency and robustness over the previous state of the art. The enhanced capability to calculate this time-reversal symmetry violation sensitivity parameter enables efficient screening of candidate molecules for the electron electric dipole moment (eEDM) search. As examples, the |$mathcal{E}_{text{eff}}$| values of metal methoxides including BaOCH$_3$, YbOCH$_3$, and RaOCH$_3$ are shown to be as large as those of the corresponding fluorides and hydroxides, which supports the recent proposal of using these symmetric-top molecules to improve the sensitivity of eEDM measurements. The computational results also show that molecules containing late actinide elements, NoF, NoOH, LrO, and LrOH$^+$, exhibit particularly large |$mathcal{E}_{text{eff}}$| values of around 200 GV/cm.
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With increasing demand for accurate calculation of isotope shifts of atomic systems for fundamental and nuclear structure research, an analytic energy derivative approach is presented in the relativistic coupled-cluster theory framework to determine the atomic field shift and mass shift factors. This approach allows the determination of expectation values of atomic operators, overcoming fundamental problems that are present in existing atomic physics methods, i.e. it satisfies the Hellmann-Feynman theorem, does not involve any non-terminating series, and is free from choice of any perturbative parameter. As a proof of concept, the developed analytic response relativistic coupled-cluster theory has been applied to determine mass shift and field shift factors for different atomic states of indium. High-precision isotope-shift measurements of $^{104-127}$In were performed in the 246.8-nm (5p $^2$P$_{3/2}$ $rightarrow$ 9s $^2$S$_{1/2}$) and 246.0-nm (5p $^2$P$_{1/2}$ $rightarrow$ 8s $^2$S$_{1/2}$) transitions to test our theoretical results. An excellent agreement between the theoretical and measured values is found, which is known to be challenging in multi-electron atoms. The calculated atomic factors allowed an accurate determination of the nuclear charge radii of the ground and isomeric states of the $^{104-127}$In isotopes, providing an isotone-independent comparison of the absolute charge radii.
Recent measurements in paramagnetic molecules improved the limit on the electron electric dipole moment (EDM) by an order of magnitude. Time-reversal (T) and parity (P) symmetry violation in molecules may also come from their nuclei. We point out that nuclear T,P-odd effects are amplified in paramagnetic molecules containing deformed nuclei, where the primary effects arise from the T,P-odd nuclear magnetic quadrupole moment (MQM). We perform calculations of T,P-odd effects in the molecules TaN, ThO, ThF$^+$, HfF$^+$, YbF, HgF, and BaF induced by MQMs. We compare our results with those for the diamagnetic TlF molecule, where the T,P-odd effects are produced by the nuclear Schiff moment. We argue that measurements in molecules with MQMs may provide improved limits on the strength of T,P-odd nuclear forces, on the proton, neutron and quark EDMs, on quark chromo-EDMs, and on the QCD $theta$-term and CP-violating quark interactions.
Ionization potentials, excitation energies, transition properties, and hyperfine structure constants of the low-lying $3p^6 3d^{9} ^2D_{5/2}$, $3p^6 3d^{9} ^2D_{3/2}$, $3p^5 3d^{10} ^2P_{3/2}$ and $3p^5 3d^{10} ^2P_{1/2}$ atomic states of the Co-like highly-charged ions such as Y$^{12+}$, Zr$^{13+}$, Nb$^{14+}$, Mo$^{15+}$, Tc$^{16+}$, Ru$^{17+}$, Rh$^{18+}$, Pd$^{19+}$, Ag$^{20+}$ and Cd$^{21+}$ are investigated. The singles and doubles approximated relativistic coupled-cluster theory in the framework of one electron removal Fock-space formalism is employed over the Dirac-Hartree-Fock calculations to account for the electron correlation effects for determining the aforementioned properties. Higher-order relativistic corrections due to the Breit interaction and quantum electrodynamics effects in the evaluation of energies are also quantified explicitly. Our estimated values are compared with the other available theoretical calculations and experimental results, which are found to be in good agreement with each other.
We present high accuracy relativistic coupled cluster calculations of the P-odd interaction coefficient $W_A$ describing the nuclear anapole moment effect on the molecular electronic structure. The molecule under study, BaF, is considered a promising candidate for the measurement of the nuclear anapole moment, and the preparation for the experiment is now underway [Altunas et al., Phys. Rev. Lett. 120, 142501 (2018)]. Influence of various computational parameters (size of the basis set, treatment of relativistic effects, and treatment of electron correlation) on the calculated $W_A$ coefficient is investigated and a recommended value of 147.7 Hz with an estimated uncertainty of 1.5% is proposed.
Roles of electron correlation effects in the determination of attachment energies, magnetic dipole hyperfine structure constants and electric dipole (E1) matrix elements of the low-lying states in the singly charged cadmium ion (Cd$^+$) have been analyzed. We employ the singles and doubles approximated relativistic coupled-cluster (RCC) method to calculate these properties. Intermediate results from the Dirac-Hartree-Fock approximation, second-order many-body perturbation theory and considering only the linear terms of the RCC method are given to demonstrate propagation of electron correlation effects in this ion. Contributions from important RCC terms are also given to highlight importance of various correlation effects in the evaluation of these properties. At the end, we also determine E1 polarizabilities ($alpha^{E1}$) of the ground and $5p ^2P_{1/2;3/2}$ states of Cd$^+$ in the {it ab initio} approach. We estimate them again by replacing some of the E1 matrix elements and energies from the measurements to reduce their uncertainties so that they can be used in the high precision experiments of this ion.
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