Accounting for correlations with core electrons by means of the generalized relativistic effective core potentials: Atoms Hg and Pb and their compounds

A way to account for correlations between the chemically active (valence) and innermore (core) electrons in the framework of the generalized relativistic effective core potential (GRECP) method is suggested. The "correlated" GRECP's (CGRECP's) are generated for the Hg and Pb atoms. Only correlations for the external twelve and four electrons of them, correspondingly, should be treated explicitly in the subsequent calculations with these CGRECP's whereas the innermore electrons are excluded from the calculations. Results of atomic calculations with the correlated and earlier GRECP versions are compared with the corresponding all-electron Dirac-Coulomb values. Calculations with the above GRECP's and CGRECP's are also carried out for the lowest-lying states of the HgH molecule and its cation and for the ground state of the PbO molecule as compared to earlier calculations and experimental data. The accuracy for the vibrational frequencies is increased up to an order of magnitude and the errors for the bond lengths (rotational constants) are decreased in about two times when the correlated GRECP's are applied instead of earlier GRECP versions employing the same innercore-outercore-valence partitioning.Comment: 12 pages, 4 tables, the text of the paper was significantly improve

QED corrections to the parity-nonconserving 6s-7s amplitude in 133^{133}Cs

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 $\alpha Z$ 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 $\beta$, is $Q_W=-72.57(46)$ for $\beta = 26.957(51) a_{\rm B}^3$ and $Q_W=-73.09(54)$ for $\beta= 27.15(11)a_{\rm B}^3$. The first value deviates by $1.1\sigma$ from the prediction of the Standard Model, while the second one is in perfect agreement with it.Comment: 4 pages, 1 figure, 2 table

Radiative and correlation effects on the parity-nonconserving transition amplitude in heavy alkaline 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 $\alpha Z$ 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 $-$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 $1.1\sigma$ 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.Comment: 28 pages, 8 tables, 2 figure

Ground-state hyperfine structure of H-, Li-, and B-like ions in middle-Z region

The hyperfine splitting of the ground state of H-, Li-, and B-like ions is investigated in details within the range of nuclear numbers Z = 7-28. The rigorous QED approach together with the large-scale configuration-interaction Dirac-Fock-Sturm method are employed for the evaluation of the interelectronic-interaction contributions of first and higher orders in 1/Z. The screened QED corrections are evaluated to all orders in (\alpha Z) utilizing an effective potential approach. The influence of nuclear magnetization distribution is taken into account within the single-particle nuclear model. The specific differences between the hyperfine-structure level shifts of H- and Li-like ions, where the uncertainties associated with the nuclear structure corrections are significantly reduced, are also calculated.Comment: 22 pages, 11 tables, 2 figure

Dual kinetic balance approach to basis set expansions for the Dirac equation

A new approach to finite basis sets for the Dirac equation is developed. It solves the problem of spurious states and, as a result, improves the convergence properties of basis set calculations. The efficiency of the method is demonstrated for finite basis sets constructed from B splines by calculating the one-loop self-energy correction for a hydrogenlike ion.Comment: 14 pages, 1 tabl

Calculation of PandP_ and T_ odd effects in $"" sup 205_TIF including electron correlation

A method and codes for two-step correlation calculation of heavy-atom molecules have been developed, employing the generalized relativistic effective core potential and relativistic coupled cluster (RCC) methods at the first step, followed by nonvariational one-center restoration of proper four-component spinors in the heavy cores. Electron correlation is included for the first time in an ab initio calculation of the interaction of the permanent P,T-odd proton electric dipole moment with the internal electromagnetic field in a molecule. The calculation is performed for the ground state of TlF at the experimental equilibrium, R_e=2.0844 A, and at R=2.1 A, with spin-orbit and correlation effects included by RCC. Calculated results with single cluster amplitudes only are in good agreement (3% and 1%) with recent Dirac-Hartree-Fock (DHF) values of the magnetic parameter M; the larger differences occurring between present and DHF volume parameter (X) values, as well as between the two DHF calculations, are explained. Inclusion of electron correlation by GRECP/RCC with single and double excitations has a major effect on the P,T-odd parameters, decreasing M by 17% and X by 22%.Comment: 5 pages, REVTeX4 style Accepted for publication in Phys.Rev.Letter