Relativistic coupled-cluster (RCC) calculations have been performed to estimate the electromagnetic forbidden transition probabilities, oscillator strengths and lifetimes of many low-lying states of five times ionized molybdenum (Mo VI). Contributions from the Breit interaction up to the first order of perturbation have been examined. Our results are in good agreement with the available other reported theoretical and experimental results. A long lifetime about 4.9854 s of the first excited state, 4d $^2D_{5/2}$, has been predicted which can be a very useful criteria in the doping process of thin films. Correlations trends from various RCC terms to the transition amplitude calculations are discussed.
The results of ab initio calculation of E1 amplitudes, lifetimes,and polarizabilities for several low-lying levels of ytterbium are reported. The effective Hamiltonian for the valence electrons has been constructed in the frame of CI+MBPT method and solutions of many electron equation are found.
We use the configuration interaction method and many-body perturbation theory to perform accurate calculations of energy levels, transition amplitudes, and lifetimes of low-lying states of barium and radium. Calculations for radium are needed for the planning of measurements of parity and time invariance violating effects which are strongly enhanced in this atom. Calculations for barium are used to control the accuracy of the calculations.
Electric quadrupole (E2) and magnetic dipole (M1) transition amplitudes among the low-lying states of quadruply ionized vanadium V$^{4+}$, important in various field of experimental and astrophysics are presented very accurately. Most of these results are reported for the first time in the literature. Relativistic coupled-cluster theory with single, double and leading triple excitations has been employed for these calculations. Estimation of different correlation effects arising through the above formalism have been highlighted by studying core and valence electrons excitations to the excited …
We demonstrate a hybrid method based on field ionization and state-selective de-excitation capable of measuring the lifetimes of high-lying Rydberg states. For nS Rydberg states of Rb atoms with principal quantum number $60\leq n\leq88$, we measure both the individual target state lifetimes and those of the ensemble of Rydberg states populated via black-body radiation-induced transitions. We find good overall agreement with numerical calculations of the expected lifetimes in both cases. However, for the target state lifetimes, we find a local deviation towards shorter lifetimes for states arou…
Relativistic coupled-cluster(RCC) theory has been employed to calculate the life time of the $6 ^2P_{3/2}$ state of single ionized lead($^{207}Pb$) to an accurac y of 3% and compared with the corresponding value obtained using second order r elativistic many-body perturbation theory(RMBPT). This is one of the very few ap plications of this theory to excited state properties of heavy atomic systems. C ontributions from the different electron correlation effects are given explicitl y.
The first metastable triplet state of HeH$^+$ was found to be present in ion beam experiments, with its lifetime estimated to be between hundreds of milliseconds and thousand of seconds. In this work, we use {\it ab initio} methods to evaluate the radiative lifetimes of the six vibrational levels of the $a\ ^3Σ^+$ of HeH$^+$. The transition $a\ ^3Σ^+ \rightarrow X \ ^1Σ^+$ is spin-forbidden, but acquires intensity through spin-orbit interaction with the singlet and triplet $Π$ states. Large scale CASSCF/MRCI calculations using an adapted basis set were performed to determine the potential ener…
We present an ab initio study of the HeH$^+$ molecule. Using the quantum chemistry package MOLPRO and a large adapted basis set, we have calculated the adiabatic potential energy curves of the first 20 $^1 Σ^+$, 19 $^3Σ^+$, 12 $^1Π$, 9 $^3Π$, 4 $^1Δ$ and 2 $^3Δ$ electronic states of the ion in CASSCF and CI approaches. The results are compared with previous works. The radial and rotational non-adiabatic coupling matrix elements as well as the dipole moments are also calculated. The asymptotic behaviour of the potential energy curves and of the various couplings between the states is also studi…
The astrophysically important electric quadrupole (E2) and magnetic dipole (M1) transitions for the low-lying states of triply ionized titanium (Ti IV) are calculated very accurately using a state-of-art all-order many-body theory called Coupled Cluster (CC) theory in the relativistic frame-work. Different many-body correlations of the CC theory has been estimated by studying the core and valence electron excitations to the unoccupied states. The calculated excitation energies of different states are in very good agreement with the measurements. Also we compare our calculated electric dipole (…
We propose a method for obtaining effective lifetimes of scattering electronic states for avoiding the artificially confinement of the wave function due to the use of incomplete basis sets in time-dependent electronic-structure calculations of atoms and molecules. In this method, using a fitting procedure, the lifetimes are extracted from the spatial asymptotic decay of the approximate scattering wave functions obtained with a given basis set. The method is based on a rigorous analysis of the complex-energy solutions of the Schr{ö}dinger equation. It gives lifetimes adapted to any given basis …
We report a new technique to determine the van der Waals coeffcients of lithium (Li) atoms based on the relativistic coupled-cluster theory. These quantities are determined using the imaginary parts of the scalar dipole and quadrupole polarizabilities, which are evaluated using the approach that we have proposed in [1]. Our procedure is fully ab initio, and avoids the sum-over-the-states method. We present the dipole and quadrupole polarizabilities of many of the low-lying excited states of Li. Also, the off-diagonal dipole and quadrupole polarizabilites between some of the low-lying states of…
Two different theoretical methods have been used to complete a new calculation of polarizability in the thallium 6p_{1/2}, 7s, and 7p_{1/2} states. The predictions of the two methods agree to within 1% for the 6p_{1/2} and 7s states and 2% for 7p_{1/2} state. We find that the theoretical expression for the 6p_{1/2} - 7s transition polarizability difference is dominated (greater than 90% contribution) by mixing of the 7s state with the 7p_{1/2} and 7p_{3/2} states. By comparing the theoretical expression to an existing Stark shift measurement [Doret et al., Phys. Rev. A 66, 052504 (2002)], new,…
The hyperfine constants of the levels 2p2(3P)3s 4P_J, 2p2(3P)3p 4Po_J and 2p2(3P)3p 4Do_J, deduced by Jennerich et al. [Eur. Phys. J. D 40 (2006) 81] from the observed hyperfine structures of the transitions 2p2(3P)3s 4P_J - 2p2(3P)3p 4Po_J' and 2p2(3P)3s 4P_J - 2p2(3P)3p 4Do_J' recorded by saturation spectroscopy in the near-infrared, strongly disagree with the ab initio values of Jönsson et al. [J. Phys. B: At. Mol. Opt. Phys. 43 (2010) 115006]. We propose a new interpretation of the recorded weak spectral lines. If the latter are indeed reinterpreted as crossover signals, a new set of exper…
We present here the results of our relativistic many-body calculations of various properties of the first six low-lying excited states of indium. The calculations were performed using the relativistic coupled-cluster method in the framework of the singles, doubles and partial triples approximation. We obtain a large lifetime ~10s for the [4p^6]5s^2 5p_{3/2} state, which had not been known earlier. Our precise results could be used to shed light on the reliability of the lifetime measurements of the excited states of atomic indium that we have considered in the present work.
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$^{+}$…
The lifetimes of the lower-lying vibrational states of ultralong-range strontium Rydberg molecules comprising one ground-state 5s2 1S0 atom and one Rydberg atom in the 5s38s 3S1 state are reported. The molecules are created in an ultracold gas held in an optical dipole trap and their numbers determined using field ionization, the product electrons being detected by a microchannel plate. The measurements show that, in marked contrast to earlier measurements involving rubidium Rydberg molecules, the lifetimes of the low-lying molecular vibrational states are very similar to those of the parent R…
We employ a technique that combines the configuration interaction method with the singles-doubles coupled-cluster method to perform calculation of the energy levels, transition amplitudes, lifetimes, g-factors, and magnetic dipole and electric quadrupole hyperfine structure constants for many low-lying states of neutral actinium. We find very good agreement with existing experimental energy levels and make accurate predictions for missing levels. It has been noted that some of the levels have been previously misidentified; our analysis supports this claim. If spectroscopy is performed with act…
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…
Ab initio calculations of $^{229}$Th band-to-band internal conversion rate in $^{229}$ThO$_2$
University of Nevada, Reno（内华达大学里诺分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of Manchester（曼彻斯特大学）；University of California Los Angeles（加州大学洛杉矶分校）
To support efforts on cooling and trapping of alkaline-earth atoms and designs of atomic clocks, we performed ab initio relativistic many-body calculations of electric-dipole transition amplitudes between low-lying states of Mg, Ca, and Sr. In particular, we report amplitudes for ^1P_1 --> ^1S_0, ^3S_1, ^1D_2$, for ^3P_1 --> ^1S_0, ^1D_2, and for ^3P_2 --> ^1D_2 transitions. For Ca, the reduced matrix element <4s4p, ^1P_1 ||D|| 4s^2, ^1S_0> is in a good agreement with a high-precision experimental value deduced from photoassociation spectroscopy [Zinner et al., Phys.Rev.Lett., v.85, 2292 (2000…
Recently a breakthrough has been achieved in laser-spectroscopic studies of short-lived radioactive compounds with the first measurements of the radium monofluoride molecule (RaF) UV/vis spectra. We report results from high accuracy \emph{ab initio} calculations of the RaF electronic structure for ground and low-lying excited electronic states. Two different methods agree excellently with experimental excitation energies from the electronic ground state to the $^2Π_{1/2}$ and $^2Π_{3/2}$ states, but lead consistently and unambiguously to deviations from experimental-based adiabatic transition …
We have employed the relativistic coupled-cluster theory to calculate the electric dipole matrix elements in the singly ionized barium (Ba$^+$) and radium (Ra$^+$). Matrix elements of Ba$^+$ are used to determine the light-shift ratios for two different wavelengths on which recent experiments are carried out. By combining the measured light-shift ratios and our calculations, we are able to estimate possible errors associate with the used matrix elements in Ba$^+$. Static polarizabilities of the low-lying states and lifetimes of the first excited P-states are also determined using these matrix …
The atomic states of the W IX (W8+) tungsten ion lying below the W9+ ionisation threshold have been studied theoretically, employing the multiconfiguration Dirac-Hartree-Fock method with configuration interaction. The level electronic structures and their energies are presented. The electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) radiative transitions have been computed in order to calculate the radiative lifetimes of given states. Transition wavelengths, energies, and decay rates are also presented for selected high-intensity E1 transitions. …
We report calculation of the energy spectrum and the spectroscopic properties of the superheavy element ion: Rf^+. We use the 4-component relativistic Dirac-Coulomb Hamiltonian and the multireference configuration interaction (MRCI) model to tackle the complex electronic structure problem that combines strong relativistic effects and electron correlation. We determine the energies of the ground and the low-lying excited states of Rf+, which originate from the 7s^26d^1, 7s^16d^2, 7s^27p^1, and 7s^16d^17p^1 configurations. The results are discussed vis-à-vis the lighter homologue, Hf^+ ion. We a…
Using the relativistic coupled-cluster method, we have calculated ionization potentials, E1 matrix elements and dipole polarizabilities of many low-lying states of Ca$^+$. Contributions from the Breit interaction are given explicitly for these properties. Polarizabilities of the ground and the first excited d-states are determined by evaluating the wave functions that are perturbed to first order by the electric dipole operator and the black-body radiation shifts are estimated from these results. We also report the results of branching ratios and lifetimes of the first excited p-states using b…
We tabulate spontaneous emission rates for all possible 811 electric-dipole-allowed transitions between the 75 lowest-energy states of Ca I. These involve the $4sns$ ($n=4-8$), $4snp$ ($n=4-7$), $4snd$ ($n=3-6$), $4snf$ ($n=4-6$), $4p^2$, and $3d4p$ electronic configurations. We compile the transition rates by carrying out ab initio relativistic calculations using the combined method of configuration interaction and many-body perturbation theory. The results are compared to the available literature values. The tabulated rates can be useful in various applications, such as optimizing laser cool…
Auger-Meitner processes are electronic decay processes of energetically low-lying vacancies. In these processes, the vacancy is filled by an electron of an energetically higher lying orbital, while another electron is simultaneously emitted to the continuum. In low-lying orbitals relativistic effects can not even be neglected for light elements. At the same time lifetime calculations are computationally expensive. In this context, we investigate which effect spin-orbit coupling has on Auger-Meitner decay widths and aim for a rule of thumb for the relative decay widths of initial states split b…
Transition properties such as oscillator strengths, transition rates, branching ratios and lifetimes of many low-lying states in the doubly ionized scandium (Sc III) are reported. A relativistic method in the coupled-cluster framework has been employed to incorporate the electron correlation effects due to the Coulomb interaction to all orders by considering all possible singly and doubly excited electronic configurations conjointly with the leading order triply excited configurations in a perturbative approach. Present results are compared with the previously reported results for the transiti…
We report ab initio calculations of the X $^2 Σ_{u}^+ $ and B $^2 Σ_{g}^+$ states of the Be$_{2}^+$ dimer. Full valence configuration interaction calculations were performed using the aug-cc-pVnZ basis sets and the results were extrapolated to the CBS limit. Core-core, core-valence effects are included at the CCSDT/MTsmall level of theory. Two local minima, separated by a large barrier, are found in the expected repulsive B $^2 Σ_{g}^+$ state. Spectroscopic constants have been calculated and good agreement is found with the recent measurements of Merritt et al. Bound vibrational levels, transi…
We report an ab initio study on the rovibronic spectroscopy of the closed-shell diatomic molecule phosphorous mononitride, PN. The study considers the nine lowest electronic states, $X\,{}^{1}Σ^{+}$, $A\,{}^{1}Π$, $C\,{}^{1}Σ^{-}$, $D\,{}^{1}Δ$, $E\,{}^{1}Σ^{-}$, $a\,{}^{3}Σ^{+}$, $b\,{}^{3}Π$, $d\,{}^{3}Δ$ and $e\,{}^{3}Σ^{-}$ using high level electronic structure theory and accurate nuclear motion calculations. The ab initio data cover 9 potential energy, 14 spin-orbit coupling, 7 electronic angular momentum coupling, 9 electric dipole moment and 8 transition dipole moment curves. The Duo nu…
This work reports new experimental radiative lifetimes and calculated oscillator strengths for transitions of astrophysical interest in singly ionized cobalt. More precisely, nineteen radiative lifetimes in Co+ have been measured with the time-resolved laser-induced fluorescence technique using one- and two-step excitations. Out of these, seven belonging to the high lying 3d$^7$($^4$F)4d configuration in the energy range 90697 - 93738 cm$^{-1}$ are new, and the other twelve from th3d$^7$($^4$F)F)4p configuration with energies between 45972 and 49328 cm$^{-1}$1 are compared with previous measur…
We report \textit{ab initio} calculations of the X $^2 Σ_{u}^+$, A $^2Π_u$ and B $^2 Σ_{g}^+$ states of the Ca$_{2}^+$ dimer. All electron CAS+MRCI calculations are performed for the X $^2 Σ_{u}^+$ and B $^2 Σ_{g}^+$ states, while valence CAS+MRCI calculations using an effective core potential are used to describe the A $^2Π_u$ state. A double well is found in the B $^2 Σ_{g}^+$ state. Spectroscopic constants, vibrational levels, transition moments and radiative lifetimes are calculated for the most abundant isotope of calcium ($^{40}$Ca). The static dipole and quadrupole polarizabilities, and…
We report lifetime measurements of the 6 levels in the 3d6(5D)4d e6G term in Fe ii at an energy of 10.4 eV, and f -values for 14 transitions from the investigated levels. The lifetimes were measured using time-resolved laser-induced fluorescence on ions in a laser-produced plasma. The high excitation energy, and the fact that the levels have the same parity as the the low-lying states directly populated in the plasma, necessitated the use of a two-photon excitation scheme. The probability for this process is greatly enhanced by the presence of the 3d6(5D)4p z6F levels at roughly half the energ…
Two lowest-energy odd-parity atomic levels of actinium, 7s^27p 2P^o_1/2, 7s^27p 2P^o_3/2, were observed via two-step resonant laser-ionization spectroscopy and their respective energies were measured to be 7477.36(4) cm^-1 and 12 276.59(2) cm^-1. The lifetimes of these states were determined as 668(11) ns and 255(7) ns, respectively. In addition, these properties were calculated using a hybrid approach that combines configuration interaction and coupled-cluster methods in good agreement. The data are of relevance for understanding the complex atomic spectra of actinides and for developing effi…
Relativistic many-body perturbation theory is applied to study properties of ions of the francium isoelectronic sequence. Specifically, energies of the 7s, 7p, 6d, and 5f states of Fr-like ions with nuclear charges Z = 87 - 100 are calculated through third order; reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for 7s - 7p, 7p - 6d, and 6d - 5f electric-dipole transitions; and 7s - 6d, 7s - 5f, and 5f_5/2 - 5f_7/2 multipole matrix elements are evaluated to obtain the lifetimes of low-lying excited states. Moreover, for the ions Z = 87 - 92 calculati…
We report ab initio relativistic correlation calculations of potential curves and electric dipole transition moments for ten low-lying electronic states, effective electric field on the electron, hyperfine constants and radiative lifetimes for the $^3Δ_1$ state of cation of the heavy transition metal fluoride HfF$^+$, which it is suggested to be used in experiments to search for the electric dipole moment of the electron. It is obtained that HfF$^+$ has deeply bound $^1Σ^+$ ground state; its dissociation energy is $D_e=6.4$ eV. The $^3Δ_1$ state is obtained as the relatively long-lived, with l…
Radiative Association of Ag and H: Formation of AgH from Ab Initio Calculations
Taiyuan University of Science and Technology（太原科技大学）；Henan Normal University（河南师范大学）；Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）
Atomic properties of the 24 low-lying ns, np, nd, nf, and ng states in Th IV ion are calculated using the high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of electric-dipole matrix elements, oscillator strengths, transition rates, and lifetimes. Scalar polarizabilities of the ground and six excited states (5f_j, 6d_j, 7p_j, and 7s), and tensor polarizabilities of the 5f_j, 6d_j, 7p_{3/2} states of Th IV are e…
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 …
Relativistic ab initio study on the spectroscopic and radiative properties of the lowest states and modeling of the optical cycles for the LiFr molecule
Anomalously enhanced lifetimes of low angular momentum Rydberg states in singly charged alkaline-earth metal ions
Institut für Theoretische Physik and Center for Integrated Quantum Science and Technology, Universität Tübingen（蒂宾根大学理论物理研究所与集成量子科学与技术中心）；School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham（诺丁汉大学物理与天文学学院及量子非平衡系统数学与理论物理中心）
The thorium nucleus with mass number $A=229$ has attracted much interest because its extremely low lying first excited isomeric state at about $8$eV opens the possibility for the development of a nuclear clock. However, neither the exact energy of this nuclear isomer nor properties, such as nuclear magnetic dipole and electric quadrupole moment are known to a high precision so far. The latter can be determined by investigating the hyperfine structure of thorium atoms or ions. Due to its electronic structure and the long lifetime of the nuclear isomeric state, Th$^{2+}$ is especially suitable f…
The determination of the electron neutrino mass by electron capture in $^{163}$Ho relies on a precise understanding of the deexcitation of a core hole after an electron capture event. We here present an \textit{ab intio} calculation of the electron capture spectrum in $^{163}$Ho, including all intra-atomic decay channels into bound-states. We use theoretical methods developed for the calculation of core level spectroscopy on correlated electron compounds. Our comparison critically tests the reality of these theories. We find that relativistic interactions beyond the Dirac equation, i.e. quantu…
