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The growing interest in atomic structures of moderately stripped alkali-like ions in the diagnostic study and modeling of astrophysical and laboratory plasma makes an accurate many-body study of atomic properties inevitable. This work presents transition line parameters in the absence or presence of plasma atmosphere for astrophysically important candidates Ar7+, Kr7+, Xe7+, and Rn7+. We employ relativistic coupled-cluster (RCC) theory, a well-known correlation exhaustive method. In the case of a plasma environment, we use the Debye Model. Our calculations agree with experiments available in the literature for ionization potentials, transition strengths of allowed and forbidden selections, and lifetimes of several low-lying states. The unit ratios of length and velocity forms of transition matrix elements are the critical estimation of the accuracy of the transition data presented here, especially for a few presented for the first time in the literature. We do compare our findings with the available recent theoretical results. Our reported data can be helpful to the astronomer in estimating the density of the plasma environment around the astronomical objects or in the discovery of observational spectra corrected by that environment. The present results should be advantageous in the modeling and diagnostics laboratory plasma, whereas the calculated ionization potential depression parameters reveal important characteristics of atomic structure.

We conduct a theoretical study of the creation and dynamics of vortices in a two-dimensional binary Bose-Einstein condensate with a mass imbalance between the species. To initiate the dynamics, we use one or two rotating paddle potentials in one species, while the other species is influenced only via the interspecies interaction. In both species, the number and the dominant sign of the vortices are determined by the rotation frequency of the paddle potential. Clusters of positive and negative vortices form at a low rotation frequency comparable to that of the trap when using the single paddle potential. In contrast, vortices of the same sign tend to dominate as the rotation frequency of the paddle increases, and the angular momentum reaches a maximum value at a paddle frequency, where the paddle velocity becomes equal to the sound velocity of the condensate. When the rotation frequency is sufficiently high, the rapid annihilation of vortex-antivortex pairs significantly reduces the number of vortices and antivortices in the system. For two paddle potentials rotating in the same direction, the vortex dynamics phenomenon is similar to that of a single paddle. However, when the paddle potentials are rotated in the opposite direction, both positive and negative signed vortices occur at all rotational frequencies. At the low rotation frequencies, the cluster of like-signed vortices produces the $k^{-5/3}$ and $k^{-3}$ power laws in the incompressible kinetic energy spectrum at low and high wavenumbers, respectively, a hallmark of the quantum turbulent flows., Comment: 14 pages, 13 figures

In this work, we present a scheme of a two-photon interaction to calculate magic wavelengths for the 62S12 − 52D32,52 clock transitions of Ba+ ion employing the relativistic coupled-cluster method. These magic wavelengths can be essential inputs to achieve better accuracy in the future ionic clock experiments. In this paper, we further show an application of a two-photon interaction to the spin-mixing processes, |0,0⟩↔|+1,−1⟩ and |0,0⟩↔|−1,+1⟩, of an ultra-cold spin-1 mixture of 137Ba+ ions and 87Rb atoms. We determine the protocols for selecting these spin-mixing oscillations by changing the strength and frequencies of the externally applied magnetic field and laser beams, respectively.

We observe experimentally the spontaneous formation of star-shaped surface patterns in driven Bose-Einstein condensates. Two-dimensional star-shaped patterns with $l$-fold symmetry, ranging from quadrupole ($l=2$) to heptagon modes ($l=7$), are parametrically excited by modulating the scattering length near the Feshbach resonance. An effective Mathieu equation and Floquet analysis are utilized, relating the instability conditions to the dispersion of the surface modes in a trapped superfluid. Identifying the resonant frequencies of the patterns, we precisely measure the dispersion relation of the collective excitations. The oscillation amplitude of the surface excitations increases exponentially during the modulation. We find that only the $l=6$ mode is unstable due to its emergent coupling with the dipole motion of the cloud. Our experimental results are in excellent agreement with the mean-field framework. Our work opens a new pathway for generating higher-lying collective excitations with applications, such as the probing of exotic properties of quantum fluids and providing a generation mechanism of quantum turbulence., 5 pages, 4 figures

We theoretically investigate the out-of-equilibrium dynamics in a binary Bose-Einstein condensate confined within two-dimensional box potentials. One species of the condensate interacts with a pair of oppositely wound, but otherwise identical Laguerre-Gaussian laser pulses, while the other species is influenced only via the interspecies interaction. Starting from the Hamiltonian, we derive the equations of motion that accurately delineate the behavior of the condensates during and after the light-matter interaction. Depending on the number the helical windings (or the magnitude of topological charge), the species directly participating in the interaction with lasers is dynamically segmented into distinct parts which collide together as the pulses gradually diminish. This collision event generates nonlinear structures in the related species, coupled with the complementary structures produced in the other species, due to the interspecies interaction. The long-time dynamics of the optically perturbed species is found to develop the Kolmogorov-Saffman scaling law in the incompressible kinetic energy spectrum, a characteristic feature of the quantum turbulent state. However, the same scaling law is not definitively exhibited in the other species. This study warrants the usage of Laguerre-Gaussian beams for future experiments on quantum turbulence in Bose-Einstein condensates., Comment: 15 pages, 9 figures

The present paper determines the precise values of magic wavelengths corresponding to the clock transitions ${5}^{2}S\text{--}{4}^{2}D$ of the ${\mathrm{Y}}^{2+}$ ion at the levels of both fine and hyperfine structures due to the external light beams having linear as well as circular polarization. To calculate the dynamic polarizabilities of the associated states of the transitions, we employ the sum-over-states technique, where the dominating and correlation sensitive part of the sum is evaluated using a highly correlated relativistic coupled-cluster theory. The estimated magic wavelengths of the light beams have substantial importance to cool and trap the ion using a blue-detuned trapping scheme. We also present the tune-out wavelengths, which are useful in state-insensitive trapping and cooling. The vector component of a total polarizability, which is induced by a circularly polarized light only, can provide additional magic wavelengths. Considerable effects of hyperfine interaction on the values of polarizabilities and number of magic wavelengths divulge the importance of precise estimations of hyperfine-structure splitting.

Experiments with vortex beams have shown a surge of interest in controlling cold atoms. Most of the controlling protocols are dominated by circularly polarized light due to its ability to induce vector polarization at atoms, which is impossible for paraxial linearly polarized light. Here we develop a theory for frequency dependent polarizability of an atomic state interacting with a focused linearly polarized vortex beam. The naturally induced spin-orbit coupling in this type of linearly polarized beam produces vector component of the valence polarizability to an atomic state, obeying the total angular momentum conservation of the beam. The theory is employed on $^{87}$Sr$^{+}$ ion to accurately calculate the magic wavelengths for the clock transitions and tune-out wavelengths for the clock states using relativistic coupled-cluster method. The induced vector component in the dynamic polarizability due to the linearly polarized focused vortex beam promotes fictitious magnetic field to the atomic state. We demonstrate that this fictitious magnetic field, depending on the focusing angle and OAM of the beam, improves the flexibility of the coherent heteronuclear spin oscillations in a spin-1 mixture of $^{87}$Rb and $^{23}$Na atoms., Comment: 20 pages, 4 figures

A theory of dynamic polarizability for trapping relevant states of Sr\(^+\) is presented here when the ions interact with a focused optical vortex. The coupling between the orbital and spin angular momentum of the optical vortex varies with focusing angle of the beam and is studied in the calculation of the magic wavelengths for \(5s_{{1}/{2}}\rightarrow 4d_{{3}/{2}, {5}/{2}}\) transitions of Sr\(^+\). The initial state of our interest here is \(5s_{{1}/{2}}\) with \(m_J = -1/2\) of which is different possible trapping state compare to our recent work on Sr\(^+\) [Phys. Rev. A 97, 022511 (2018)]. We find a variation in magic wavelengths and the corresponding polarizabilities with different combinations of orbital and spin angular momentum of the vortex beam. The variation is very significant when the wavelengths of the beam are in the infrared region of the electromagnetic spectrum. The calculated magic wavelengths will help the experimentalists to trap the ion for performing the high-precision spectroscopic measurements.

Here we report on accurate ab initio calculations to study astrophysically important electromagnetic transition parameters among different low-lying states of Sn IV. Our ab initio calculations are based on the sophisticated relativistic coupled-cluster theory, which almost exhausts many important electron correlations. To establish the accuracy of the calculations, we compare our results with the available experiments and estimates the transition amplitudes in length and velocity gauged forms. Most of these allowed and forbidden transition wavelengths lie in the infrared region, and they can be observed in the different cool stellar and interstellar media. For the improvement of uncertainty, we use experimental energies to the estimations of the above transition parameters. The presented data will be helpful to find the abundances of the ion in different astrophysical and laboratory plasma., Comment: 7 pages

We present the theory of microscopic interaction of the spin-orbit coupled focused Laguerre-Gaussian (LG) beam with the two-component Bose-Einstein condensate (BEC), composed of two hyperfine states of $^{87}$Rb in a harmonic trap. We have shown that Raman Rabi frequency distributions over the inter-component coupling identify phase separation coupling strength. A significant enhancement of side-band transitions due to non-paraxial nature of vortex beam is observed for particular values of inter-component coupling around 1.25 and 0.64 in unit of 5.5nm for $10^5$ and $10^6$ number of atoms, respectively. The uncertainty in the estimation of these coupling strengths is improved with the focusing angles of the beam. We discuss an experimental scheme to verify this non-paraxial effect on ultra-cold atoms., Comment: 15 pages, 7 figures, Journal of Physics Communications 2018

The density profiles of trapped two-component Bose-Einstein condensates (BEC) and its microscopic interaction with Laguerre Gaussian (LG) beam are studied. We consider the $^{87}$Rb BEC in two hyperfine spin components. The wavelength of the LG beam is assumed to be comparable to the atomic de-Broglie wavelength. Competitions between intra- and inter-component interactions produce interesting density structures of the ground state of BEC. We demonstrate vortex-antivortex interference and its dependence on the inter-component interactions and Raman transitions., Comment: 14 pages, 30 figures

Isotope shifts (ISs) of ${D}_{1}\phantom{\rule{4.pt}{0ex}}(ns\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}\ensuremath{\rightarrow}np\phantom{\rule{0.16em}{0ex}}^{2}P_{1/2})$ and ${D}_{2}\phantom{\rule{4.pt}{0ex}}(ns\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}\ensuremath{\rightarrow}np\phantom{\rule{0.16em}{0ex}}^{2}P_{3/2})$ transitions for the first three elements of the K isoelectronic sequence are calculated with all-order correlated relativistic coupled-cluster theory. To get precise ab initio results, all the orbitals of the reference states have been optimized by a linear regression technique. Some of the important IS estimations reported here were not available in literature. Interesting features of odd-even staggering and magic neutron number effects are also observed in the case of volume shift calculations. Energy-level corrections for a few levels due to a change in the nuclear model from a point nucleus to a Fermi nucleus have been studied with interesting correlation features and compared with other theoretical results available in literature.

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 relativistic coupled cluster theory is employed to calculate electric quadrupole (E2) transition probabilities among the doublet states of Mg II which are of interest in astrophysical problems. This is the first time a highly correlated fully ab initio method has been used to compute these quantities for this particular ion. The line strengths and transition probabilities of a number of different transitions are reported and compared with those available in the literature.

We investigated Boettger’s screened nuclear potential approximation for the spin–orbit interaction (SNSO) in the context of the Douglas–Kroll approach to relativistic Kohn–Sham theory. We extended the approximation to second-order terms and evaluated it for various atomic and molecular properties (spin–orbit splittings, g -tensor shifts, bond lengths, vibrational frequencies and binding energies) and compared the SNSO results with those of a self-consistent relativistic treatment of the electron–electron (ee) interaction. The SNSO approximation is comparable in computational effort to the model based on the nuclear potential only, but delivers molecular results that agree well with those of the more exact ee treatment.

The relativistic coupled cluster theory is employed to calculate the hyperfine structure of the 2S 1/2, 2P 1/2, 2P 3/2, 2D 3/2 and 2D 5/2 states of singly ionized calcium. The importance of correlation effects is highlighted. Our results are compared with other theoretical calculations and experiments.

One of the most successful ab initio, highly correlated all-order many-body methods, the relativistic coupled cluster theory, is employed to calculate excitation energies of the doublet states of Mg+ and allowed transitions among them that are of interest in astrophysical problems. We have also calculated oscillator strength for the 3s-4p doublet transitions, which is improved over the existing results. These transition lines have been sought after in astronomical observations because they represent the best column density identifier in the interstellar medium. Our calculated oscillator strength (9.3 × 10-4) and branching ratio (1.80) of these doublet lines matches well with the recent empirical and semiempirical calculations.

Previous studies show that within paraxial limit and electric dipole approximations, the orbital angular momentum (OAM) of a Laguerre–Gaussian (LG) beam rotates the whole atom about the beam axis but does not affect the internal electronic motion. The contribution of the Gaussian part of the LG beam profile to the angular momentum exchange is not usually taken into account. In this paper, we develop a theory which shows that not only the OAM of a LG beam, but also the geometry of the beam cross section, plays an important role in the electronic lowest-order transitions in the interaction of the beam with a trapped Rydberg atom, due to the large span of its electronic wavefunctions. In this interaction, the standard dipole selection rules do not hold and our results show that the otherwise forbidden transitions can become sufficiently probable.

A physics-based analytical modeling for the gas sensor application of AlGaN/GaN heterostructure Schottky diode has been investigated for high linearity and sensitivity of the device. The heterointerface and surface properties are exploited here. The dependency of 2DEG on the surface charge, which is dependent on the Si 3 N 4 passivation layer, is mainly utilized to model the device. The simulation of Schottky diode has been performed in the TCAD tool and I-V curves are generated. From the I-V curves, 54% response has been recorded in presence of 500 ppm gas and at biasing voltage of 0.95 Volts.

In this paper, we have calculated parity nonconserving electric dipole amplitudes of the hyperfine components for the transitions between the ground and first excited states of ${}^{137}{\mathrm{Ba}}^{+}$ and ${}^{87}{\mathrm{Sr}}^{+}$ using sum-over-states technique. The results are presented to extract the constants associated with the nuclear spin-dependent amplitudes from experimental measurements. The wave functions to calculate the most dominant part of the sums are constructed using highly correlated coupled-cluster theory based on the Dirac-Coulomb-Gaunt Hamiltonian.

Exchange of orbital angular momentum between Laguerre-Gaussian beam of light and center-of-mass motion of an atom or molecule is well known. We show that orbital angular momentum of light can also be transferred to the internal electronic or rotational motion of an atom or a molecule provided the internal and center-of-mass motions are coupled. However, this transfer does not happen directly to the internal motion, but via center-of-mass motion. If atoms or molecules are cooled down to recoil limit then an exchange of angular momentum between the quantized center-of-mass motion and the internal motion is possible during interaction of cold atoms or molecules with Laguerre-Gaussian beam. The orientation of the exchanged angular momentum is determined by the sign of the winding number of Laguerre-Gaussian beam. We have presented selective results of numerical calculations for the quadrupole transition rates in interaction of Laguerre-Gaussian beam with an atomic Bose-Einstein condensate to illustrate the underlying mechanism of light orbital angular momentum transfer. We discuss how the alignment of diatomic molecules will facilitate to explore the effects of light orbital angular momentum on electronic motion of molecules., Accepted in Phys. Rev. A

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-functions in and near the nuclear region of this ion. Astrophysically important forbidden transition amplitudes are estimated for the first time in the literature to our knowledge. The calculated oscillator strengths of few allowed transitions are compared with recent experimental and theoretical results wherever available., 11 pages, 4 figures

In this paper we present a new method of generating a relativistic basis set for atomic Dirac–Fock (DF) orbitals. Here, all the occupied and a few low-lying unoccupied DF orbital wavefunctions of atoms obtained from the finite basis set expansion approach are replaced by orbital wavefunctions obtained from numerical solutions. We compare this with the Gaussian basis set generation by employing orbitals obtained from both the approaches in a coupled cluster method and computing the ionization potential and oscillator strengths for Mg + and Ca + using the above two different bases. The new method is found to be more appropriate for high-precision calculations.

We have applied the highly correlated ab initio effective valence shell Hamiltonian (Hv) method to determine the energy difference between the cyclic and linear isomers of propynlidyne (C3H). Calculations are also described for the vertical excitation energies, ionization potentials, electron affinities, dipole moments, oscillator strengths, and some harmonic vibrational frequencies, which are all determined using the third order Hv method. Computations at both the experimental and theoretically optimized geometries are used to illustrate the geometrical dependence of the computed properties. The Hv optimized geometry is obtained using a two-configurational reference function describing the two dominant resonance structures. Our third-order vertical excitation energy to the lowest excited state in the cyclic isomer, dipole moments, and ground state isomer conformational energy difference are all in good agreement with experiment and with other highly correlated many-body calculations. The computations for...

Atomic transition lines of neutral calcium were first found in solar spectrum as early as the middle of the 19th century, when the 4227-A line was identified along with the famous singly ionized H and K lines @1#. Neutral calcium lines have also been observed in all types of stellar and interstellar spectra, such as late-type dwarf stars. The crude abundance of Ca I (l56717.7 A ) has been observed in Am binaries@2#. To confirm those identifications and to find new lines, one has to depend on atomic experimental data or computational data based on theoretical models of the calcium atom. The abundances of neutral calcium in these astronomical bodies depend on the oscillator strengths of those lines, which come from the excitation energies of various levels and transition moments among those levels. The difficulty in accurately estimating transition energies and oscillator strengths of neutral calcium atom arises mainly due to the following reasons: ~a! The precise computation of transition energies and oscillator strengths requires a balanced description of the ground and excited states. ~b! The use of an inadequate basis leads to difficulties in describing the excited states and an unbalanced treatment of dynamical correlation and polarization effects. The problems due to basis set inadequacy can be removed partially by enlarging the basis for small and moderate-sized atomic and molecular systems. Here, the size extensivity @3# of the theory plays an important role in handling the proper treatment of electron correlation, and in that way it properly treats the differential correlation energies of the interacting ~initial and final states! zeroth-order states. It ensures that the state energies scale linearly with the number of electrons in a rigorous way. The accuracy of the computed excitation energy depends mostly upon the quality of the unoccupied valence orbitals in which excitation occurs. The traditional choice of some unoccupied valence orbitals from a ground-state selfconsistent-field ~SCF! computation introduces V N orbitals that are best suited for describing negative ions, and not lowlying excited states. Thus the valence orbitals, those that are not occupied in the ground-state SCF, should be taken as more representative orbitals suitable for excited states. One possible choice emerges from the restricted single excitation configuration interaction procedure@4#, where excitations are only permitted from the highest occupied orbitals. A simpler and often equivalent approaches involves using improved virtual orbitals ~IVO’s !@ 5 #in the H v valence space or reference space. Here the IVO’s are generated by single orbital SCF optimization in which the Fock operator is defined by promoting an electron from the highest occupied orbital to the orbital being optimized, while all the previously determined orbitals are kept frozen. Alternatively this can be accomplished by a unitary transformation @6#. The IVO orbital energies obtained in this way are lower than those evaluated from the traditional SCF procedure due to the absence of an extra Coulomb operator in the former procedure. For example, in a neutral calcium atom H v calculation, the twoorbital (4 s,4p) minimal reference space is produced by the sequence

In this paper, we have described electron-correlation trends in the calculations of the hyperfine $A$ and $B$ constants for a few elements belonging to the Na isoelectronic sequence. The hyperfine $A$ and $B/Q$ values of the ground state $3s$ ${}^{2}{S}_{1/2}$ and the excited states $3p$ ${}^{2}{P}_{1/2}$, $3p$ ${}^{2}{P}_{3/2}$, $3d$ ${}^{2}{D}_{3/2}$, and $3d$ ${}^{2}{D}_{5/2}$ of the ions from Si${}^{3+}$ to V${}^{12+}$ are presented. The influence of the Breit interaction in the unretarded approximation to these hyperfine values is reported briefly. With increasing atomic number of this sequence, the variations of the different correlation contributing terms such as core correlations, core polarizations, and pair correlations are discussed in the framework of the relativistic coupled-cluster theory. The electron-correlation effect relative to the Dirac-Fock value in the hyperfine $A$ constants of the $3d$ ${}^{2}{D}_{3/2,5/2}$ states follows unusual trends with increasing ionization. The relative pair-correlation effect influences the hyperfine constants of the fine-structure states of a term in an identical way at each species of this sequence. The presented relativistic coupled-cluster results are found to agree excellently with the other available results for a few ions.

In this paper, the $E1$, $E2$, and $M1$ transition amplitudes are calculated along with the hyperfine $A$ and $B$ constants of doubly ionized gallium using the relativistic coupled-cluster approach. Electron correlations and the Gaunt interactions are considered to all orders using the coupled-cluster theory in a relativistic framework and their contributions are discussed explicitly in the calculations of all these amplitudes. Some interesting features of the correlation effects on the Gaunt interactions are noticed in the calculations of the hyperfine constants. The lifetimes of some low-lying states are also calculated using the transition amplitudes obtained by the present theory and the experimental transition energies. The calculated $E1$ transition amplitudes and lifetimes are in good agreement with the results obtained by the other theories and experiment. The hyperfine splitting of the ground states of ${}^{71}$Ga iii and ${}^{69}$Ga iii are found to be about 35 and 27.5 GHz, respectively, which shows the importance of these isotopes for the possible use of microwave frequency standards. The calculated hyperfine constants are associated with linewidth estimations of some transition lines in the visible and ultraviolet regions of electromagnetic spectrum.

In this paper, we study electron correlation and Gaunt interaction effects in ionization potentials (IPs) and hyperfine constants A of $2p{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2}$ and $2p{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{3/2}$ states along with fine structure splitting (FSS) between them for the boron isoelectronic sequence using the relativistic coupled-cluster method. The range of atomic number $z$ is taken from 8 to 21. The Gaunt contributions can be calculated at both the Dirac-Fock and the coupled-cluster levels from our presentation. Calculated IPs and FSS are compared with the results of the National Institute of Standards and Technology. Important correlation contributions like the core correlation, core polarization, and pair correlation effects are studied for hyperfine constants A. Many distinct features of the correlation and relativistic effects are observed in these studies.

This work presents accurate ab initio determination of the hyperfine splitting for the ground state and a few low-lying excited states of 113 Cd + ; important candidate for the frequency standard in the microwave region, using coupled-cluster theory (CC) in the relativistic framework. The hyperfine energy splittings, calculated first time in literature, are in good agreement with the recent experimental results. We have also carried out the lifetimes of the 5p 2 P1/2 and 5p 2 P3/2 states, which are in good agreement with the available experimental results. The role of different electron correlation effects in the determination of these quantities are discussed and their contributions are presente in the CC terms.

We report electric quadrupole $(E2)$ and magnetic dipole $(M1)$ transition amplitudes of the first few low-lying states of quadruply ionized vanadium $({\mathrm{V}}^{4+})$, which are important in various experimental applications and astrophysics. To our knowledge, most of these presented results are determined for the first time in the literature. A relativistic multireference Fock-space coupled-cluster theory with single $(S)$, double $(D)$, and partial triple $(T)$ excitations is employed to compute the forbidden transition probabilities and lifetimes of the low-lying states in ${\mathrm{V}}^{4+}$. Estimations of different correlation effects arising through the above formalism have been highlighted by investigating core and valence electron excitations. A long lifetime is found for the first excited $3d\phantom{\rule{0.2em}{0ex}}^{2}D_{5∕2}$ state, which suggests that ${\mathrm{V}}^{4+}$ may be one of the useful candidates for many important studies.

We report the results of our relativistic coupled cluster singles, doubles, and partial triples calculations of the ionization potentials (IP) and excitation energies (EE) for different low-lying levels of ${\mathrm{Ba}}^{+}$. The accuracies of the IP's and EE's are approximately 0.2% and 1%, respectively. The inclusion of the triple excitations were crucial to achieve this degree of precision.

The multiconfiguration Dirac-Fock method, based on the extended optimal level approximation, is used to calculate magnetic quadrupole transitions $(M2)$ from ${2s2p(}^{3}{P}_{2})$ to ${2s}^{2}{(}^{1}{S}_{0})$ states in berylliumlike ions. The calculation of this transition for $Zg6$ uses the Dirac-Fock Hamiltonian which is necessary for highly ionized atoms. The Breit interaction is treated as a first-order perturbation, and its non-negligible contributions to the excitation energies for heavier ions are highlighted. Some of the $M2$ transition probabilities results presented in this paper are calculated for the first time, to our knowledge.

In this paper, we report on weighted oscillator strengths of E1 transitions and transition probabilities of E2 transitions among different low-lying states of triply ionized germanium using highly correlated relativistic coupled cluster (RCC) method. Due to the abundance of Ge IV in the solar system, planetary nebulae, white dwarf stars, etc., the study of such transitions is important from an astrophysical point of view. The weighted oscillator strengths of E1 transitions are presented in length and velocity gauge forms to check the accuracy of the calculations. We find excellent agreement between calculated and experimental excitation energies. Oscillator strengths of few transitions, wherever studied in the literature via other theoretical and experimental approaches, are compared with our RCC calculations.

We reply here to comments by A E Kingston on our paper (Mandal et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 055701). Some of them are addressed by correcting our mistakes, and others are clarified by scientific arguments.

We report here 'allowed' and 'forbidden' electromagnetic transition amplitudes among various low lying states of doubly ionized Thallium (T12+) using relativistic coupled cluster method based on Dirac-Fock hybrid basis functions. These transitions are of importance in astrophysics and plasma research. The effect of core correlation, pair correlation and core polarization on these transitions are estimated.

We have determined the amplitudes for Stark-induced (SI) transitions, of current interest in atomic physics and astrophysics, between mixed states dominated by same parity configurations of some low-lying states of singly ionized calcium. Well established Relativistic Coupled cluster (RCC) method has been used for the spectroscopic study of these transitions. This method has proved to be a very useful tool for rigorous electron correlation studies. We compare our results with experimental data for allowed electric dipole transition amplitudes and energies and also with other theoretical studies.