arXiv subjects
Publications and source records attributed to D. Mukherjee.
Ab initio calculations have been carried out to study the magnetic dipole and electric quadrupole hyperfine structure constants of $^{205}$Pb$^+$. Many-body effects have been considered to all orders using the relativistic coupled-cluster theory in the singles, doubles and partial triples approximation. The trends of these effects are found to be different from atomic systems that have been studied earlier.
The low-lying n(=3,4,5)d $^2D_{5/2}$ 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 {\it 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 coupled-cluster method to cope with strongly interacting configurations.
We fix three natural numbers $k, n, N$, such that $n+k+1=N$, and introduce the notion of two dual arrangements of hyperplanes. One of the arrangements is an arrangement of $N$ hyperplanes in a $k$-dimensional affine space, the other is an arrangement of $N$ hyperplanes in an $n$-dimensional affine space. We assign weights $\al_1, ..., \al_N$ to the hyperplanes of the arrangements and for each of the arrangements consider the associated period matrices. The first is a matrix of $k$-dimensional hypergeometric integrals and the second is a matrix of $n$-dimensional hypergeometric integrals. The size of each matrix is equal to the number of bounded domains of the corresponding arrangement. We show that the dual arrangements have the same number of bounded domains and the product of the determinants of the period matrices is equal to an alternating product of certain values of Euler's gamma function multiplied by a product of exponentials of the weights.
The connections between the Random Phase Approximation (RPA) and Many-Body Perturbation Theory (MBPT) and its all order generalisation, the Coupled- Cluster Theory (CCT) have been explored. Explicit expressions have been derived for the electric dipole amplitudes for allowed and forbidden transitions induced by the parity non-conserving neutral weak interaction. The Goldstone diagrams associated with the RPA terms in both cases are shown to arise in MBPT and CCT and the numerical verification of this relationship is made for the allowed electric dipole transitions.
The electric quadrupole moment for the $4d ^2D_{5/2}$ state of $\mathrm{^{88}Sr^+}$, one of the most important candidates for an optical clock, has been calculated using the relativistic coupled-cluster theory. The result of the calculation is presented and the important many-body contributions are highlighted. The calculated electric quadrupole moment is $(2.94\pm0.07)ea_{0}^{2}$, where $a_{0}$ is the Bohr radius and $e$ the electronic charge while the measured value is $(2.6\pm0.3)ea_{0}^{2}$. This is so far the most accurate determination of the electric quadrupole moment for the above mentioned state.
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.
The magnetic dipole and electric quadrupole hyperfine constants of Aluminium ($^{27}Al$) atom are computed using the relativistic coupled cluster (CC) and unitary coupled cluster (UCC) methods. Effects of electron correlations are investigated using different levels of CC approximations and truncation schemes. The ionization potentials, excitation energies, transition probabilities, oscillator strengths and nuclear quadrupole moment are computed to assess the accuracy of these schemes. The nuclear quadrupole moment obtained from the present CC and UCC calculations in the singles and doubles approximations are 142.5 mbarn and 141.5 mbarn respectively. The discrepancies between our calculated IPs and EEs and their measured values are better than 0.3%. The other one-electron properties reported here are also in excellent agreement with the measurements.
We present the first formulation and application of relativistic unitary coupled cluster theory to atomic properties. The remarkable features of this theory are highlighted, and it is used to calculate the lifetimes of $5^{2}D_{3/2}$ and $6^{2}P_{3/2}$ states of $Ba^{+}$ and $Pb^{+}$ respectively. The results clearly suggest that it is very well suited for accurate \emph{ab initio} calculations of properties of heavy atomic systems.
We have employed the relativistic coupled cluster theory to calculate the magnetic dipole and electric quadrupole hyperfine constants for the ground and low lying excited states of singly ionized magnesium. Comparison with experimental and the other theoretical results are done and predictions are also made for a few low lying excited states which could be of interest. We have made comparative studies of the important many body effects contributing to the hyperfine constants for the different states of the ion.