The permanent electric dipole moment of the X 2 Σ + electronic ground state of the strontium mono... more The permanent electric dipole moment of the X 2 Σ + electronic ground state of the strontium monofluoride molecule is calculated using a relativistic coupled cluster method. Our result is compared with those of other calculations and that of experiment. Individual contributions arising from different physical effects are presented. The result obtained suggests that the relativistic coupled cluster method used in the present work is capable of yielding accurate results for the permanent electric dipole moments of molecules for which relativistic effects cannot be ignored.
We report on a theoretical analysis of the suitability of the 7s 2 S 1/2 ↔ 6d 2 D 3/2 transition ... more We report on a theoretical analysis of the suitability of the 7s 2 S 1/2 ↔ 6d 2 D 3/2 transition in singly ionized radium to measure parity nonconservation, in the light of an experiment planned at the KVI of the University of Groningen. Relativistic coupled-cluster theory has been employed to perform an ab initio calculation of the parity-nonconserving electric dipole amplitude of this transition, including single, double, and leading triple excitations. We discuss the prospects for a sub-1% precision test of the electroweak theory of particle physics.
Heavy polar diatomic molecules are the primary tools for searching for the T-violating permanent ... more Heavy polar diatomic molecules are the primary tools for searching for the T-violating permanent electric dipole moment of the electron (eEDM). Valence electrons in some molecules experience extremely large effective electric fields due to relativistic interactions. These large effective electric fields are crucial to the success of polar-molecule-based eEDM search experiments. Here we report on the results of relativistic ab initio calculations of the effective electric fields in a series of molecules that are highly sensitive to an eEDM, the mercury monohalides (HgF, HgCl, HgBr,and HgI). We study the influence of the halide anions on E eff , and identify HgBr and HgI as interesting candidates for future electric dipole moment search experiments.
One of the most successful ab initio, highly correlated all-order many-body methods, the relativi... more 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 Â 10 À4) and branching ratio (1.80) of these doublet lines matches well with the recent empirical and semiempirical calculations. Subject headings: atomic data-methods: analytical
We report the result of our ab initio calculation of the 6s 2 S 1/2 → 5d 2 D 3/2 parity nonconser... more We report the result of our ab initio calculation of the 6s 2 S 1/2 → 5d 2 D 3/2 parity nonconserving electric dipole transition amplitude in 137 Ba + based on relativistic coupled-cluster theory. Considering single, double and partial triple excitations, we have achieved an accuracy of less than one percent. If the accuracy of our calculation can be matched by the proposed parity nonconservation experiment in Ba + for the above transition, then the combination of the two results would provide an independent non accelerator test of the Standard Model of particle physics.
Ionization potentials ͑IP's͒ are evaluated for various excited states of Tl using the relativisti... more Ionization potentials ͑IP's͒ are evaluated for various excited states of Tl using the relativistic coupled cluster ͑CCCD͒ theory in the even-parity pair channel approximation ͑CCSD-EPC͒. An average accuracy below half a percent is reached. The effect of deep core electrons on the core-valence correlations is investigated. It is found that electrons in the third subshell (nϭ3) modify the IP's of the 6p orbitals by 100 cm Ϫ1. By comparison with calculations made in the linearized CCSD ͑LCCSD͒ approximation it is demonstrated that nonlinear contributions are mandatory to reach an accuracy below half a percent for the 6p 1/2 orbital.
We present a new hybrid method to solve the relativistic Hartree-Fock-Roothan equations where the... more We present a new hybrid method to solve the relativistic Hartree-Fock-Roothan equations where the one-and two-electron radial integrals are evaluated numerically by defining the basis functions on a grid. This procedure reduces the computational costs in the evaluation of two-electron radial integrals. The orbitals generated by this method are employed to compute the ionization potentials, excitation energies and oscillator strengths of alkali-metal atoms and elements of group IIIA through second order many-body perturbation theory (MBPT). The computed properties are in excellent agreement with the experiment and other correlated theories.
A fully relativistic restricted active space configuration interaction method is employed to comp... more A fully relativistic restricted active space configuration interaction method is employed to compute the P , T-odd interaction constant W s for the ground ͑ 2 ⌺ 1/2 ͒ state of YbF and BaF molecules, which yield the results W s = −41.2 kHz and −9.7 kHz for YbF and BaF, respectively. Our present estimated results of the P , T-odd interaction constant W s is in reasonable agreement with previous calculations.
We report a new technique to determine the van der Waals coefficients of lithium (Li) atoms based... more We report a new technique to determine the van der Waals coefficients 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 Li are calculated.
Using the relativistic coupled-cluster method, we have calculated ionization potentials, E1 matri... more 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 both the calculated and experimental wavelengths and compare them with their measured values.
We present our calculations of the electric dipole and quadrupole matrix elements for transitions... more We present our calculations of the electric dipole and quadrupole matrix elements for transitions between low-lying bound states of Ba ϩ that are relevant for parity nonconservation studies using the relativistic coupled-cluster method. The results compare well with the experimental data. We have also computed the electric dipole transition matrix elements between many high-lying excited states.
Atomic properties involving the low-lying excited 2 D 3/2,5/2 states in alkaline-earth-metal ions... more Atomic properties involving the low-lying excited 2 D 3/2,5/2 states in alkaline-earth-metal ions are of current interest in many different applications ranging from tests of physics beyond the standard model to astrophysics. We have used the relativistic coupled-cluster theory to perform accurate calculations of the lifetimes of the lowest excited 2 D 3/2 and 2 D 5/2 states in singly ionized calcium, strontium, and barium. The importance of electron correlation in these calculations is emphasized. Our results are compared with the available experimental and theoretical data.
The low-lying n(=3,4,5)d 2 D 5/2 states alkaline earth ions are of vital importance in a number o... more The low-lying n(=3,4,5)d 2 D 5/2 states alkaline earth ions are of vital importance in a number of different physical applications. The hyperfine structure constants of these states are characterized by unusually strong electron correlation effects. Relativistic coupled-cluster theory has been employed to carry out ab initio calculations of these constants. The role of the all order core-polarization effects was found to be decisive in obtaining good agreement of the results of our calculations with accurate measurements. The present work is an apt demonstration of the power of the coupledcluster method to cope with strongly interacting configurations.
It is widely believed that the standard model of particle physics is just an intermediate step in... more It is widely believed that the standard model of particle physics is just an intermediate step in understanding the properties of the elementary physics in nature and the interactions between them. Over the past twenty years, studies of the parity nonconservation in atomic systems based on nonaccelerator methods have made remarkable progress. An experiment to measure parity nonconservation in singly ionized barium has been proposed as an independent test of the standard model. We have employed the relativistic coupled-cluster theory to calculate the parity nonconserving 6s 2 S 1/2 → 5d 2 D 3/2 transition amplitude and associated properties. We have also shown contributions from various intermediate states which play a significant role in the determination of this transition amplitude.
We investigate electric quadrupole hyperfine structure constant (B) results in 135 Ba + and 137 B... more We investigate electric quadrupole hyperfine structure constant (B) results in 135 Ba + and 137 Ba + and compare their ratios with the reported measurements of the ratio between the nuclear quadrupole moment (Q) values of these isotopes. We carry out confidence tests for the reported experimental B values and calculations of B/Q from the present work. Inconsistencies in the experimental B values are observed in both the isotopes from different experiments performed using the same techniques. The present calculations are carried out using an all order relativistic many-body theory considering only single and double excitations in the coupled-cluster ansatz. After a detailed analysis of the results, the values of Q we obtain for 135 Ba and 137 Ba are 0.153(2)b and 0.236(3)b, respectively, which differ by about 4% from the currently referred precise values.
The present work tests the suitability of the narrow transitions 7s 2 S 1/2 → 6d 2 D 3/2 and 7s 2... more The present work tests the suitability of the narrow transitions 7s 2 S 1/2 → 6d 2 D 3/2 and 7s 2 S 1/2 → 6d 2 D 5/2 in Ra + for optical frequency standard studies. Our calculations of the lifetimes of the metastable 6d states using the relativistic coupled-cluster theory suggest that they are sufficiently long for Ra + to be considered as a potential candidate for an atomic clock. This is further corroborated by our studies of the hyperfine interactions, dipole and quadrupole polarizabilities and quadrupole moments of the appropriate states of this system.
Journal of Theoretical and Computational Chemistry, 2005
This review article deals with some case studies of relativistic and correlation effects in atomi... more This review article deals with some case studies of relativistic and correlation effects in atomic systems. After a brief introduction to relativistic many-electron theory, a number of applications ranging from correlation energy to parity non-conservation in atoms are considered. There is a special emphasis on relativistic coupled-cluster theory as most of the results presented here are based on it.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2004
Relativistic coupled-cluster(RCC) theory has been employed to calculate the lifetime of the 6 2 P... more Relativistic coupled-cluster(RCC) theory has been employed to calculate the lifetime of the 6 2 P 3/2 state of single ionized lead(207 P b) to an accuracy of 3% and compared with the corresponding value obtained using second order relativistic many-body perturbation theory(RMBPT). This is one of the very few applications of this theory to excited state properties of heavy atomic systems. Contributions from the different electron correlation effects are given explicitly.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2005
The relativistic coupled-cluster theory has been employed to calculate the magnetic dipole and el... more The relativistic coupled-cluster theory has been employed to calculate the magnetic dipole and electric quadrupole hyperfine structure constants for the stable isotopes 45 Sc and 89 Y. The role of electron correlation is found to be very important. The trend exhibited by these effects is rather different from previously studied single valence atomic systems.
The permanent electric dipole moment of the X 2 Σ + electronic ground state of the strontium mono... more The permanent electric dipole moment of the X 2 Σ + electronic ground state of the strontium monofluoride molecule is calculated using a relativistic coupled cluster method. Our result is compared with those of other calculations and that of experiment. Individual contributions arising from different physical effects are presented. The result obtained suggests that the relativistic coupled cluster method used in the present work is capable of yielding accurate results for the permanent electric dipole moments of molecules for which relativistic effects cannot be ignored.
We report on a theoretical analysis of the suitability of the 7s 2 S 1/2 ↔ 6d 2 D 3/2 transition ... more We report on a theoretical analysis of the suitability of the 7s 2 S 1/2 ↔ 6d 2 D 3/2 transition in singly ionized radium to measure parity nonconservation, in the light of an experiment planned at the KVI of the University of Groningen. Relativistic coupled-cluster theory has been employed to perform an ab initio calculation of the parity-nonconserving electric dipole amplitude of this transition, including single, double, and leading triple excitations. We discuss the prospects for a sub-1% precision test of the electroweak theory of particle physics.
Heavy polar diatomic molecules are the primary tools for searching for the T-violating permanent ... more Heavy polar diatomic molecules are the primary tools for searching for the T-violating permanent electric dipole moment of the electron (eEDM). Valence electrons in some molecules experience extremely large effective electric fields due to relativistic interactions. These large effective electric fields are crucial to the success of polar-molecule-based eEDM search experiments. Here we report on the results of relativistic ab initio calculations of the effective electric fields in a series of molecules that are highly sensitive to an eEDM, the mercury monohalides (HgF, HgCl, HgBr,and HgI). We study the influence of the halide anions on E eff , and identify HgBr and HgI as interesting candidates for future electric dipole moment search experiments.
One of the most successful ab initio, highly correlated all-order many-body methods, the relativi... more 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 Â 10 À4) and branching ratio (1.80) of these doublet lines matches well with the recent empirical and semiempirical calculations. Subject headings: atomic data-methods: analytical
We report the result of our ab initio calculation of the 6s 2 S 1/2 → 5d 2 D 3/2 parity nonconser... more We report the result of our ab initio calculation of the 6s 2 S 1/2 → 5d 2 D 3/2 parity nonconserving electric dipole transition amplitude in 137 Ba + based on relativistic coupled-cluster theory. Considering single, double and partial triple excitations, we have achieved an accuracy of less than one percent. If the accuracy of our calculation can be matched by the proposed parity nonconservation experiment in Ba + for the above transition, then the combination of the two results would provide an independent non accelerator test of the Standard Model of particle physics.
Ionization potentials ͑IP's͒ are evaluated for various excited states of Tl using the relativisti... more Ionization potentials ͑IP's͒ are evaluated for various excited states of Tl using the relativistic coupled cluster ͑CCCD͒ theory in the even-parity pair channel approximation ͑CCSD-EPC͒. An average accuracy below half a percent is reached. The effect of deep core electrons on the core-valence correlations is investigated. It is found that electrons in the third subshell (nϭ3) modify the IP's of the 6p orbitals by 100 cm Ϫ1. By comparison with calculations made in the linearized CCSD ͑LCCSD͒ approximation it is demonstrated that nonlinear contributions are mandatory to reach an accuracy below half a percent for the 6p 1/2 orbital.
We present a new hybrid method to solve the relativistic Hartree-Fock-Roothan equations where the... more We present a new hybrid method to solve the relativistic Hartree-Fock-Roothan equations where the one-and two-electron radial integrals are evaluated numerically by defining the basis functions on a grid. This procedure reduces the computational costs in the evaluation of two-electron radial integrals. The orbitals generated by this method are employed to compute the ionization potentials, excitation energies and oscillator strengths of alkali-metal atoms and elements of group IIIA through second order many-body perturbation theory (MBPT). The computed properties are in excellent agreement with the experiment and other correlated theories.
A fully relativistic restricted active space configuration interaction method is employed to comp... more A fully relativistic restricted active space configuration interaction method is employed to compute the P , T-odd interaction constant W s for the ground ͑ 2 ⌺ 1/2 ͒ state of YbF and BaF molecules, which yield the results W s = −41.2 kHz and −9.7 kHz for YbF and BaF, respectively. Our present estimated results of the P , T-odd interaction constant W s is in reasonable agreement with previous calculations.
We report a new technique to determine the van der Waals coefficients of lithium (Li) atoms based... more We report a new technique to determine the van der Waals coefficients 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 Li are calculated.
Using the relativistic coupled-cluster method, we have calculated ionization potentials, E1 matri... more 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 both the calculated and experimental wavelengths and compare them with their measured values.
We present our calculations of the electric dipole and quadrupole matrix elements for transitions... more We present our calculations of the electric dipole and quadrupole matrix elements for transitions between low-lying bound states of Ba ϩ that are relevant for parity nonconservation studies using the relativistic coupled-cluster method. The results compare well with the experimental data. We have also computed the electric dipole transition matrix elements between many high-lying excited states.
Atomic properties involving the low-lying excited 2 D 3/2,5/2 states in alkaline-earth-metal ions... more Atomic properties involving the low-lying excited 2 D 3/2,5/2 states in alkaline-earth-metal ions are of current interest in many different applications ranging from tests of physics beyond the standard model to astrophysics. We have used the relativistic coupled-cluster theory to perform accurate calculations of the lifetimes of the lowest excited 2 D 3/2 and 2 D 5/2 states in singly ionized calcium, strontium, and barium. The importance of electron correlation in these calculations is emphasized. Our results are compared with the available experimental and theoretical data.
The low-lying n(=3,4,5)d 2 D 5/2 states alkaline earth ions are of vital importance in a number o... more The low-lying n(=3,4,5)d 2 D 5/2 states alkaline earth ions are of vital importance in a number of different physical applications. The hyperfine structure constants of these states are characterized by unusually strong electron correlation effects. Relativistic coupled-cluster theory has been employed to carry out ab initio calculations of these constants. The role of the all order core-polarization effects was found to be decisive in obtaining good agreement of the results of our calculations with accurate measurements. The present work is an apt demonstration of the power of the coupledcluster method to cope with strongly interacting configurations.
It is widely believed that the standard model of particle physics is just an intermediate step in... more It is widely believed that the standard model of particle physics is just an intermediate step in understanding the properties of the elementary physics in nature and the interactions between them. Over the past twenty years, studies of the parity nonconservation in atomic systems based on nonaccelerator methods have made remarkable progress. An experiment to measure parity nonconservation in singly ionized barium has been proposed as an independent test of the standard model. We have employed the relativistic coupled-cluster theory to calculate the parity nonconserving 6s 2 S 1/2 → 5d 2 D 3/2 transition amplitude and associated properties. We have also shown contributions from various intermediate states which play a significant role in the determination of this transition amplitude.
We investigate electric quadrupole hyperfine structure constant (B) results in 135 Ba + and 137 B... more We investigate electric quadrupole hyperfine structure constant (B) results in 135 Ba + and 137 Ba + and compare their ratios with the reported measurements of the ratio between the nuclear quadrupole moment (Q) values of these isotopes. We carry out confidence tests for the reported experimental B values and calculations of B/Q from the present work. Inconsistencies in the experimental B values are observed in both the isotopes from different experiments performed using the same techniques. The present calculations are carried out using an all order relativistic many-body theory considering only single and double excitations in the coupled-cluster ansatz. After a detailed analysis of the results, the values of Q we obtain for 135 Ba and 137 Ba are 0.153(2)b and 0.236(3)b, respectively, which differ by about 4% from the currently referred precise values.
The present work tests the suitability of the narrow transitions 7s 2 S 1/2 → 6d 2 D 3/2 and 7s 2... more The present work tests the suitability of the narrow transitions 7s 2 S 1/2 → 6d 2 D 3/2 and 7s 2 S 1/2 → 6d 2 D 5/2 in Ra + for optical frequency standard studies. Our calculations of the lifetimes of the metastable 6d states using the relativistic coupled-cluster theory suggest that they are sufficiently long for Ra + to be considered as a potential candidate for an atomic clock. This is further corroborated by our studies of the hyperfine interactions, dipole and quadrupole polarizabilities and quadrupole moments of the appropriate states of this system.
Journal of Theoretical and Computational Chemistry, 2005
This review article deals with some case studies of relativistic and correlation effects in atomi... more This review article deals with some case studies of relativistic and correlation effects in atomic systems. After a brief introduction to relativistic many-electron theory, a number of applications ranging from correlation energy to parity non-conservation in atoms are considered. There is a special emphasis on relativistic coupled-cluster theory as most of the results presented here are based on it.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2004
Relativistic coupled-cluster(RCC) theory has been employed to calculate the lifetime of the 6 2 P... more Relativistic coupled-cluster(RCC) theory has been employed to calculate the lifetime of the 6 2 P 3/2 state of single ionized lead(207 P b) to an accuracy of 3% and compared with the corresponding value obtained using second order relativistic many-body perturbation theory(RMBPT). This is one of the very few applications of this theory to excited state properties of heavy atomic systems. Contributions from the different electron correlation effects are given explicitly.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2005
The relativistic coupled-cluster theory has been employed to calculate the magnetic dipole and el... more The relativistic coupled-cluster theory has been employed to calculate the magnetic dipole and electric quadrupole hyperfine structure constants for the stable isotopes 45 Sc and 89 Y. The role of electron correlation is found to be very important. The trend exhibited by these effects is rather different from previously studied single valence atomic systems.
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Papers by Bhanu Das