Neutral uranium (U I) is a very difficult atom for theoretical calculations due to a large number of valence electrons, six, strong valence-valence and valence-core correlations, high density of states, and relativistic effects. Configuration-interaction many-body perturbation theory (CI-MBPT) can treat efficiently valence-core correlations and relativistic effects, but because the formalism was developed for Dirac-Hartree-Fock (DHF) starting potential that does not contain valence electrons, quite large CI space is needed to compensate for +6 charge of such a potential. Much more efficient is relativistic configuration-interaction (RCI) approach which uses relatively accurate starting DHF potential that includes some valence electrons to make the valence electron Hamiltonian diagonally dominated for some states. Here we report calculations of U I hyperfine constants of several low-energy states using the RCI method with the starting potential that includes four f valence electrons. With this starting potential, it is possible to use the single-configuration approximation or small basis sets to obtain quite accurate results for hyperfine structure constants. In fact, by scaling nuclear magnetic moment, the agreement for 5 levels was within 5\%, and a new magnetic moment can be recommended 0.43(2). The method can be further developed to include more extensive data sets to improve accuracy and can be applied to other atoms and for calculations of other properties, for example, relevant to fundamental symmetry tests.
We present the relativistic calculation of the hyperfine structure in pionic and kaonic atoms. A perturbation method has been applied to the Klein-Gordon equation to take into account the relativistic corrections. The perturbation operator has been obtained \textit{via} a multipole expansion of the nuclear electromagnetic potential. The hyperfine structure of pionic and kaonic atoms provide an additional term in the quantum electrodynamics calculation of the energy transition of these systems. Such a correction is required for a recent measurement of the pion mass.
Relativistic self-consistent-field calculations of the radial hyperfine integrals have been performed in the 4d-shell element ions. The comparison with available experimental results gives an estimate of configuration interaction effects in the hyperfine interaction in these ions. The results can also be used to derive nuclear moments from laserspectroscopic measurements of radioactive isotopes. PACS Numbers: 31.15.Ne, 31.30.Gs, 32.10.Fn
In previous work devoted to {\it ab initio} calculations of hyperfine structure constants in nitrogen and fluorine atoms, we observed sizeable relativistic effects, a priori unexpected for such light systems, that can even largely dominate over electron correlation. We observed that the atomic wave functions calculated in the Breit-Pauli approximation describe adequately the relevant atomic levels and hyperfine structures, even in cases for which a small relativistic $LS$-term mixing becomes crucial. In the present work we identify new levels belonging to the spectroscopic terms $2p^4(^3\!P) 3…
The mα^6(m/M) order corrections to the hyperfine splitting in the H_2^+ ion are calculated. That allows to reduce uncertainty in the frequency intervals between hyperfine sublevels of a given rovibrational state to about 10 ppm. Results are in good agreement with the high precision experiment carried out by Jefferts in 1969.
Energy levels, hyperfine interaction constants, and Landé $g_J$-factors are reported for n=2 states in beryllium-, boron-, carbon-, and nitrogen-like ions from relativistic configuration interaction calculations. Valence, core-valence, and core-core correlation effects are taken into account through single and double-excitations from multireference expansions to increasing sets of active orbitals. A systematic comparison of the calculated hyperfine interaction constants is made with values from the available literature.
The hyperfine interaction constants of the 2p4(3P)3p 2Do_{3/2,5/2}, 4Do_{1/2-7/2} and 4Po_{1/2-5/2} levels in neutral fluorine are investigated theoretically. Large-scale calculations are carried out using the multiconfiguration Hartree-Fock (MCHF) and Dirac-Hartree-Fock (MCDHF) methods. In the framework of the MCHF approach, the relativistic effects are taken into account in the Breit-Pauli approximation using non relativistic orbitals. In the fully relativistic approach, the orbitals are optimized using the Dirac-Coulomb Hamiltonian with correlation models inspired by the non relativistic ca…
Removal energies and hyperfine constants of the lowest four $ns, np_{1/2}$ and $np_{3/2}$ states in Na, K, Rb and Cs are calculated; removal energies of the n=7--10 states and hyperfine constants of the n=7 and 8 states in Fr are also calculated. The calculations are based on the relativistic single-double (SD) approximation in which single and double excitations of Dirac-Hartree-Fock (DHF) wave functions are included to all-orders in perturbation theory. Using SD wave functions, accurate values of removal energies, electric-dipole matrix elements and static polarizabilities are obtained, howe…
Hyperfine-structure constants of odd Ra$^{+}$ due to the interactions of nuclear magnetic dipole, electric quadrupole, and magnetic octupole moments with the electrons are investigated in the framework of relativistic coupled-cluster method within single- and double-excitation approximation. The calculated energies and magnetic dipole hyperfine-structure constants $A$ exhibit a good agreement with available experimental values. Combining with the experimental electric quadrupole hyperfine-structure constant, we also extracted the electric quadrupole moments $Q$ of $^{209,211,221,223}$Ra. Our $…
Hyperfine constants and anomalies of ground as well as few low lying excited states of $^{113,115,117}$In III are studied with highly correlated relativistic coupled-cluster theory. The ground state hyperfine splitting of $^{115}$In III is estimated to be 106.8 GHz. A shift of almost 1.9 GHz of the above frequency has been calculated due to modified nuclear dipole moment. This splitting result shows its applicability as communication band and frequency standards at $10^{-11}$ sec. Correlations study of hyperfine constants indicates a few distinct features of many-body effects in the wave-funct…
We present an experimental and theoretical investigation of the polarizabilities and hyperfine constants of D_J states in 133Cs for J=3/2 and J=5/2. New experimental values for the hyperfine constant A are obtained from level-crossing signals of the (7,9,10)D_5/2 states of 133Cs and precise calculations of the tensor polarizabilities alpha_2. The results of relativistic many-body calculations for scalar and tensor polarizabilities of the (5-10)D_3/2 and (5-10)D_5/2 states are presented and compared with measured values from the literature. Calculated values of the hyperfine constants A for the…
This work presents accurate {\it ab initio} determination of the magnetic dipole (M1) and electric quadrupole (E2) hyperfine structure constants for the ground and a few low-lying excited states in $^{67}$Zn$^{+}$, which is one of the interesting systems in fundamental physics. The coupled-cluster (CC) theory within the relativistic framework has been used here in this calculations. Long standing demands for a relativistic and highly correlated calculations like CC can be able to resolve the disagreements among the lifetime estimations reported previously for a few low-lying states of Zn$^{+}$…
Accurate predictions of hyperfine structure (HFS) constants are important in many areas of chemistry and physics, from the determination of nuclear electric and magnetic moments to benchmarking of new theoretical methods. We present a detailed investigation of the performance of the relativistic coupled cluster method for calculating HFS constants withing the finite-field scheme. The two selected test systems are $^{133}$Cs and $^{137}$BaF. Special attention has been paid to construct a theoretical uncertainty estimate based on investigations on basis set, electron correlation and relativistic…
We have developed an all-particle Fock-space relativistic coupled-cluster method to calculate the properties of two-valence atoms and ions. Using the method we compute the properties associated with hyperfine induced $^1S_0 - ^3P^o_0$ clock transition in Al$^+$. Our result of the $^3P^o_0$ metastable state life time, $20.20 \pm 0.91$ s, is in excellent agreement with the experimental value, $20.60 \pm 1.4$ s [Phys. Rev. Lett. {\bf 98}, 220801 (2007)]. Our studies show that the contributions from the triple excitations, and the corrections from the Breit interaction and QED effects are essentia…
Multiconfiguration Hartree-Fock (MCHF) and multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations are performed for the $2p^{5}~^{2}P^{o}$, $2p^4(^{3}P)3s~^{4}P$, $2p^4(^{3}P)3s~^{2}P$ and $2p^4(^{3}P)3p~^{4}S^o$ states of $^{19}$F~I to determine their hyperfine constants. Several computing strategies are considered to investigate electron correlation and relativistic effects. High-order correlation contributions are included in MCHF calculations based on single and double multireference (SD-MR) expansions. The largest components of the single reference MCHF wave functions are selected to …
The multi-configuration Dirac-Hartree-Fock method was employed to calculate the total and excitation energies, oscillator strengths and hyperfine structure constants for low-lying levels of Sm I. In the first-order perturbation approximation, we systematically analyzed correlation effects from each electrons and electron pairs. It was found that the core correlations are of importance for physical quantities concerned. Based on the analysis, the important configuration state wave functions were selected to constitute atomic state wave functions. By using this computational model, our excitatio…
We report the magnetic dipole and electric quadrupole hyperfine coupling constants of 6 P_{3/2} state of ^{133} Cs(I= {7/2}) obtained from the relativistic coupled cluster (RCC) method. To our knowledge, no prior electric quadrupole hyperfine CC calculation is available for ^{133} Cs(6 P_{3/2}) state. Our computed magnetic dipole (A) and electric quadrupole (B) coupling constants are in excellent agreement with the experiment.
This work is an ab initio study of the 2p3 4So_3/2, and 2Do_{3/2,5/2} states of C- and 2p2 3P_{0,1,2}, 1D_2, and 1S_0 states of neutral carbon. We use the multi-configuration Hartree-Fock approach, focusing on the accuracy of the wave function itself. We obtain all C- detachment thresholds, including correlation effects to about 0.5%. Isotope shifts and hyperfine structures are calculated. The achieved accuracy of the latter is of the order of 0.1 MHz. Intra-configuration transition probabilities are also estimated.
We demonstrate an iterative scheme for coupled-cluster properties calculations without truncating the dressed properties operator. For validation, magnetic dipole hyperfine constants of alkaline Earth ions are calculated with relativistic coupled-cluster and role of electron correlation examined. Then, a detailed analysis of the higher order terms is carried out. Based on the results, we arrive at an optimal form of the dressed operator. Which we recommend for properties calculations with relativistic coupled-cluster theory.
$^{229}$Th is a promising candidate for developing a nuclear optical clock and searching the new physics beyond the standard model. Accurate knowledge of the nuclear properties of $^{229}$Th is very important. In this work, we calculate hyperfine-structure constants for the first four states of $^{229}$Th$^{3+}$ using the relativistic coupled-cluster method based on the Gauss basis set. The no-pair Dirac-Coulomb-Breit Hamiltonian with the lowest-order quantum electrodynamics (QED) correction is the starting point, together with all linear and non-linear terms of single and double excitations a…
Energy levels of 30 low-lying states of Lu2+ and allowed electric-dipole matrix elements between these states are evaluated using a relativistic all-order method in which all single, double and partial triple excitations of Dirac-Fock wave functions are included to all orders of perturbation theory. Matrix elements are critically evaluated for their accuracy and recommended values of the matrix elements are given together with uncertainty estimates. Line strengths, transition rates and lifetimes of the metastable 5d(3/2) and 5d(5/2) states are calculated. Recommended values are given for stati…
This work presents a first time accurate calculation of the magnetic dipole hyperfine structure constants for the ground state and some low-lying excited states of Pb$^+$. By comparing different levels of approximation with experimental results, we demonstrate the importance of correlation effects which reach beyond lower order relativistic many body perturbation theory. Employing relativistic coupled-cluster theory we obtain a quantitative understanding of the core-polarization and correlation effects inherent in this system and observe completely different trends compared to $Ba^+$.
Precision calculations of the fine and hyperfine structure of muonic atoms are performed in a relativistic approach and results for muonic 205 Bi, 147 Sm, and 89 Zr are presented. The hyperfine structure due to magnetic dipole and electric quadrupole splitting is calculated in first order perturbation theory, using extended nuclear charge and current distributions. The leading correction from quantum electrodynamics, namely vacuum polarization in Uehling approximation, is included as a potential directly in the Dirac equation. Also, an effective screening potential due to the surrounding elect…
This work presents accurate ab initio determination of the hyperfine splitting for the ground state and few low-lying excited states of 113Cd+; important candidates for the frequency standard in the microwave region, using coupled-cluster theory (CC) in the relativistic framework. The calculated hyperfine splitting are well in agreement with recent experimental results. We have also carried out the lifetimes of the 5p2P1=2 and 5p2P3=2 states, which are in well agreement with recent experimental result (Moehring et al., PRA 73 023413, 2006). The roles of different electron correlation effects i…
NRQED approach to the fine and hyperfine structure corrections of order m$α$ 6 and m$α$ 6 (m/M)-Application to the hydrogen atom The NRQED approach is applied to the calculation of relativistic corrections to the fine and hyperfine structure of hydrogenlike atoms at orders m$α$ 6 and m$α$ 6 (m/M). Results are found to be in agreement with those of the relativistic theory. This confirms that the derived NRQED effective potentials are correct, and may be used for studying more complex atoms or molecules. Furthermore, we verify the equivalence between different forms of the NRQED Lagrangian used …
This article deals with the general implementation of 4-component spinor relativistic extended coupled cluster (ECC) method to calculate first order property of atoms and molecules in their open-shell ground state configuration. The implemented relativistic ECC is employed to calculate hyperfine structure (HFS) constant of alkali metals (Li, Na, K, Rb and Cs), singly charged alkaline earth metal atoms (Be+, Mg+, Ca+ and Sr+) and molecules (BeH, MgF and CaH). We have compared our ECC results with the calculations based on restricted active space configuration interaction (RAS-CI) method. Our re…
The Z-vector method in the relativistic coupled-cluster framework is employed to calculate the parallel and perpendicular components of the magnetic hyperfine structure constant of a few small alkaline earth hydrides (BeH, MgH, and CaH) and fluorides (MgF and CaF). We have compared our Z-vector results with the values calculated by the extended coupled-cluster (ECC) method reported in Phys. Rev. A 91 022512 (2015). All these results are compared with the available experimental values. The Z-vector results are found to be in better agreement with the experimental values than those of the ECC va…
The values of nuclear electric quadrupole moment are different by about 7% for 87Sr nucleus between the recommended value [N. J. Stone, At. Data Nucl. Data Tables 111-112, 1 (2016); P. Pyykko, Mol. Phys. 116, 1328 (2018)] and earlier results [e.g. A. M. Matensson-Pendrill, J. Phys. B: At. Mol. Opt. Phys. 35, 917 (2002); K. Z. Yu et al., Phys. Rev. A 70, 012506 (2004)]. In this work, we reported a new value, Q(87Sr) = 328(4) mb, making use of our calculated electric field gradients produced by electrons at nucleus in combination with experimental values for hyperfine structures of the 5s5p 3P1,…
The relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) and the non-relativistic multiconfiguration Hartree-Fock (MCHF) methods have been employed to calculate the magnetic dipole and electric quadrupole hyperfine structure constants of zinc. The calculated electric field gradients for the $ 4s 4p \,\, ^3 \! P^o_{1} $ and $ 4s 4p \,\, ^3 \! P^o_{2} $ states, together with experimental values of the electric quadrupole hyperfine structure constants, made it possible to extract a nuclear electric quadrupole moment $ Q(^{67}{\rm Zn}) = 0.122(10) $ b. The error bar has been evaluated in a q…
We are reinvestigating the hyperfine structure of sodium using a fully relativistic multiconfiguration approach. In the fully relativistic approach, the computational strategy somewhat differs from the original nonrelativistic counterpart used in Jönsson et al. (Phys. Rev. A 53 (1996) 4021). Numerical instabilities force us to use a layer-by-layer approach that has some broad unexpected effects. Core correlation is found to be significant and therefore requires to be described in an adequate orbital basis. The natural-orbital basis provides an interesting alternative to the orbital basis from …
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.
Relativistic and QED corrections are calculated for the hyperfine splitting (hfs) in the $2S_{1/2}$ ground state of $^{9}$Be$^+$ ions with an exact account for electronic correlations. The achieved accuracy is sufficient to determine the finite nuclear size effects from the comparison to the experimental hfs value. The obtained results establish the ground to determine the neutron halo in $^{11}$Be.
The Z-vector method in the relativistic coupled-cluster framework is used to calculate magnetic hyperfine structure constant ($A_J$) of alkali metals and singly charged alkaline earth metals in their ground state electronic configuration. The Z-vector results are in very good agreement with the experiment. The $A_J$ values of Li, Na, K, Rb, Cs, Be$^{+}$, Mg$^{+}$, Ca$^{+}$, and Sr$^{+}$ obtained in the Z-vector method are compared with the extended coupled-cluster results taken from Phys. Rev. A 91, 022512 (2015). The same basis and cutoff are used for the comparison purpose. The comparison sh…
Accurate calculations of the fine and hyperfine splitting of the 2P state in Li and Be$^+$ isotopes using the explicitly correlated Hylleraas basis set are presented. Theoretical predictions including the mixing of $P_{1/2}$ and $P_{3/2}$ states, relativistic and quantum electrodynamics effects on hyperfine interactions, are compared with experimental values. It is concluded that precise spectroscopic determination of the nuclear magnetic moments requires elimination of nuclear structure effects by combining measurements for two different states.
Relativistic Calculation of Energies, Transition Parameters Hyperfine Structure, Landé g$_J$ and Isotope shifts factors for Ar$^{7+}$, Kr$^{25+}$ and Xe$^{43+}$ ions
Relativistic corrections to the hyperfine splitting are calculated for the triplet $2^3S_1$ state of the helium isotope He$^3$. High precision variational wave functions are employed, where the electron-electron correlations are well accounted for. Due to the unknown nuclear structure a comparison with the experimental result is performed via He$^{3+}$ hyperfine splitting. Surprisingly, the second order contribution due to Fermi interaction, in spite of the additional small factor $m/M$, is very significant.
The four-component relativistic Fock space coupled cluster method is used to describe the magnetic hyperfine interaction in low-lying electronic states of the KCs molecule. Both diagonal and off-diagonal matrix elements as functions of the internuclear separation $R$ are calculated within the finite-field scheme. The resulting matrix elements exhibit very weak dependence on $R$ for the separations exceeding 8 Å, whereas in the vicinity of the ground-state equilibrium the deviation of molecular HFS matrix elements from the atomic values reaches 15\%. The dependence of the computed HFS couplings…
The relativistic Breit Hamiltonian between electrons is transformed into an effective vector potential ${\bf A}_i$ for the $i.$th electron, ${\bf A}_i$ having the structure of a recoil--corrected hyperfine operator. Apart from a small three--body operator, the Dirac--Breit equation is now easier applied to relativistic magnetic properties of complex systems.
A complete effective Hamiltonian for relativistic corrections at orders $mα^6$ and $mα^6(m/M)$ in a one-electron molecular system is derived from the NRQED Lagrangian. It includes spin-independent corrections to the energy levels and spin-spin scalar interactions contributing to the hyperfine splitting, both of which had been studied previously. In addition, corrections to electron spin-orbit and spin-spin tensor interactions are newly obtained. This allows improving the hyperfine structure theory in the hydrogen molecular ions. Improved values of the spin-orbit hyperfine coefficient are calcu…
Determination of nuclear moments for many nuclei relies on the computation of hyperfine constants, with theoretical uncertainties directly affecting the resulting uncertainties of the nuclear moments. In this work we improve the precision of such method by including for the first time an iterative solution of equations for the core triple cluster amplitudes into the relativistic coupled-cluster method, with large-scale complete basis sets. We carried out calculations of the energies and magnetic dipole and electric quadrupole hyperfine structure constants for the low-lying states of 229Th^(3+)…
A large-scale relativistic configuration-interaction (CI) calculation is performed for the magnetic-dipole and the electric-quadrupole hyperfine structure splitting in ^{7,6}Li and ^9Be^+. Numerical results for the 2^2S, 3^2S, 2^2P_{1/2}, and 2^2P_{3/2} states are reported. The CI calculation based on the Dirac-Coulomb-Breit Hamiltonian is supplemented with separate treatments of the QED, nuclear-magnetization distribution, recoil, and negative-continuum effects.
We have developed an all particle Fock-space relativistic coupled-cluster method for two-valence atomic systems. We then describe a scheme to employ the coupled-cluster wave function to calculate atomic properties. Based on these developments we calculate the excitation energies, magnetic hyperfine constants and electric dipole matrix elements of Sr, Ba and Yb. Further more, we calculate the electric quadrupole HFS constants and the electric dipole matrix elements of Sr$^+$, Ba$^+$ and Yb$^+$. For these we use the one-valence coupled-cluster wave functions obtained as an intermediate in the tw…
We apply relativistic many-body methods to compute static differential polarizabilities for transitions inside the ground-state hyperfine manifolds of monovalent atoms and ions. Knowing this transition polarizability is required in a number of high-precision experiments, such as microwave atomic clocks and searches for CP-violating permanent electric dipole moments. While the traditional polarizability arises in the second-order of interaction with the externally-applied electric field, the differential polarizability involves additional contribution from the hyperfine interaction of atomic el…
Hyperfine induced $1s2s ^1S_0 \to 1s^2 ^1S_0$ M1 transition probabilities of He-like ions have been calculated from relativistic configuration interaction wavefunctions including the frequency independent Breit interaction and QED effects. Present results for {$^{151}$}Eu and {$^{155}$}Gd are in good agreement with previous calculations [Phys. Rev. A {\bf 63}, 054105 (2001)]. Electronic data are given in terms of a general scaling law in $Z$ that, given isotopic nuclear spin and magnetic moment, allows hyperfine induced decay rates to be estimated for any isotope. The results should be helpful…
Investigating Role of Electron Correlation Effects via Triple Excitations for Precise Evaluation of Energies and Hyperfine Structure Constants in $^{23}$Na
Physical Research Laboratory（物理研究实验室）；Indian Institute of Technology Gandhinagar（甘地纳加尔印度理工学院）
We have investigated energies, magnetic dipole hyperfine structure constants ($A_{hyf}$) and electric dipole (E1) matrix elements of a number of low-lying states of the triply ionized tin (Sn$^{3+}$) by employing relativistic coupled-cluster theory. Contributions from the Breit interaction and lower-order quantum electrodynamics (QED) effects in determination of above quantities are also given explicitly. These higher-order relativistic effects are found to be important for accurate evaluation of energies, while QED contributions are seen to be contributing significantly to the determination o…
This work presents precise calculations of important electromagnetic transition amplitudes along with detail of their many-body correlations using relativistic coupled cluster method. Studies of hyperfine interaction constants, useful for plasma diagnostic, with this correlation exhaustive many-body approach are another important area of this work. The calculated oscillator strengths of allowed transitions, amplitudes of forbidden transitions and lifetimes are compared with the other theoretical results wherever available and they show a good agreement. Hyperfine constants of different isotope…
The influence of hyperfine interactions on the tune-out wavelengths of the $^{39,40,41}$K isotopes of the potassium atom was investigated. The hyperfine interaction of the $4s_{1/2}$ state result in a shift and splitting of the primary tune-out wavelength near 769 nm. The $4s_{1/2}$ ground state hyperfine splittings of the primary tune-out were almost equal to the hyperfine splittings of the ground states. The splittings in the wavelengths were 0.0008, 0.0027 and 0.0005 nm for $^{39}$K, $^{40}$K and $^{41}$K respectively. The hyperfine splitting of the $np_{J}$ levels leads to the creation of …
To search for the temporal variation of the fundamental constants one needs to know dependence of atomic transition frequencies on these constants. We study the dependence of the hyperfine structure of atomic $s$-levels on nuclear radius and, via radius, on quark masses. An analytical formula has been derived and tested by the numerical relativistic Hartree-Fock calculations for Rb, Cd$^+$, Cs, Yb$^+$ and Hg$^+$. The results of this work allow the use of the results of past and future atomic clock experiments and quasar spectra measurements to put constrains on time variation of the quark mass…
We report first configuration interaction calculations of hyperfine constants A_\parallel and the effective electric field W_d acting on the electric dipole moment of the electron, in two excited electronic states of ^{207}PbO. The obtained hyperfine constants, A_\parallel = -3826 MHz for the a(1) state and A_\parallel = 4887 MHz for the B(1) state, are in very good agreement with the experimental data, -4113 MHz and 5000 \pm 200 MHz, respectively. We find W_d = -(6.1 ^{+1.8}_{-0.6}) 10^{24} Hz/(e cm) for a(1), and W_d = (8.0 \pm 1.6) 10^{24} Hz/(e cm) for B(1). The obtained values are analyze…
We present highly correlated multi-configuration Hartree-Fock (MCHF) calculations of the hyperfine structure of the 3p5 2Po_J levels of {33}S- and {35,37}Cl. We obtain a good agreement with observation. The hyperfine structure of the neutral sulfur {33}S 3p4 3P_J lowest multiplet that has never been measured to the knowledge of the authors, is also estimated theoretically. We discuss some interesting observations made on the description of the atomic core in MCHF theory.
A large-scale configuration-interaction (CI) calculation is reported for the hyperfine splitting of the 2^2S and 3^2S states of ^7Li and ^9Be^+. The CI calculation based on the Dirac-Coulomb-Breit Hamiltonian is supplemented with a separate treatment of the QED, nuclear-size, nuclear-magnetization distribution, and recoil corrections. The nonrelativistic limit of the CI results is in excellent agreement with variational calculations. The theoretical values obtained for the hyperfine splitting are complete to the relative order of α^2 and improve upon results of previous studies.
We calculate energies and hyperfine structure constants A and B for low-lying levels of $^{173}$Yb. The latter is treated as a two-electron atom. To account for valence-valence correlations the configuration interaction method is used. Valence-core correlations are accounted for within the many-body perturbation theory which is used to construct effective two-electron operators in the valence space.
Atomic quadrupole moments and hyperfine constants of the metastable $^2 D_{3/2, 5/2}$ states of Ca$^+$, Sr$^+$, Ba$^+$, Yb$^+$, and Hg$^+$ are calculated by the multiconfiguration Dirac-Hartree-Fock and relativistic configuration-interaction methods. For Hg$^+$, the configuration is $5d^9 6s^2$. For the other ions, the configuration consists of a single $d$-electron outside a set of closed shells. Current interest in the quadrupole moments of these states is due to the fact that optical transitions of these ions may be useful as references for frequency standards. Energy shifts of the metastab…
Searching for an accurate optical clock which can serve as a better time standard than the present day atomic clock is highly demanding from several areas of science and technology. Several attempts have been made to built more accurate clocks with different ion species. In this article we discuss the electric quadrupole and hyperfine shifts in the $5d^{9}6s^{2} ^{2}D_{5/2}(F=0,m_{F}=0)\leftrightarrow5d^{10}6s ^{2}S_{1/2}(F=2,m_{F}=0)$ clock transition in $ ^{199}Hg^{+}$, one of the most promising candidates for next generation optical clocks. We have applied Fock-space unitary coupled-cluster…
This study addresses the effect of the magnetic hyperfine interaction on the relativistic H1s wave functions. These are used to calculate the electric, magnetic, and confinement force densities acting on the 1s electron. The magnetic field couples Dirac equations for different angular momenta. These are solved numerically for the hyperfine singlet and triplet, as well as for a classical magnetic dipole. In the singlet ground state the hyperfine interaction shifts the electron density toward the proton. A similar shift is found for the classical dipole, and an opposite shift for the triplet. Th…
Roles of electron correlation effects in the determination of attachment energies, magnetic dipole hyperfine structure constants and electric dipole (E1) matrix elements of the low-lying states in the singly charged cadmium ion (Cd$^+$) 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…
Parity- and time-reversal-symmetry violating interaction constants required for the interpretation of a recent measurement (arXiv:1704.07928 [physics.atom-ph]) of corresponding symmetry violations in the $Ω=1$ (${^3Δ}_1$) science state of the HfF$^+$ molecular ion are reported. Using a relativistic four-component all-electron multi-reference configuration interaction model the nucleon-electron scalar-pseudoscalar interaction constant is determined as $W_S = 20.0$ [kHz]. An updated result for the electron electric-dipole-moment effective electric field of $|E_{\text{eff}}| = 22.7 \left[\frac{\r…
