A New Approach To Relativistic Gaussian Basis Functions: Theory And Applications

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 theor and other correlated theories.Comment: RevTex (15 pages) one figur

Differentially Private Model Selection with Penalized and Constrained Likelihood

In statistical disclosure control, the goal of data analysis is twofold: The released information must provide accurate and useful statistics about the underlying population of interest, while minimizing the potential for an individual record to be identified. In recent years, the notion of differential privacy has received much attention in theoretical computer science, machine learning, and statistics. It provides a rigorous and strong notion of protection for individuals' sensitive information. A fundamental question is how to incorporate differential privacy into traditional statistical inference procedures. In this paper we study model selection in multivariate linear regression under the constraint of differential privacy. We show that model selection procedures based on penalized least squares or likelihood can be made differentially private by a combination of regularization and randomization, and propose two algorithms to do so. We show that our private procedures are consistent under essentially the same conditions as the corresponding non-private procedures. We also find that under differential privacy, the procedure becomes more sensitive to the tuning parameters. We illustrate and evaluate our method using simulation studies and two real data examples

Theoretical studies of the atomic transitions in boron-like ions: Mg VIII, Si X and S XII

In this paper, we have carried out the calculations of the weighted oscillator strengths and the transition probabilities for a few low-lying transitions of boron-like ions: Mg VIII, Si X and S XII which are astrophysically important, particularly, in the atmospheres of the solar corona. We have employed an all-order relativistic many-body theory called the relativistic coupled-cluster theory to calculate very precisely these atomic quantities of astrophysical interest. We have reported for the first time the transition probabilities for some forbidden transitions which are unavailable in the literature; either theoretically or experimentally. We also discuss the physical effects associated with these transitions. Our data can be used for the identification of spectral lines arising from the coronal atmospheres of Sun and Sun-like stars having an extended corona.Comment: 8 pages, 4 table

Theoretical spectroscopic studies of the atomic transitions and lifetimes of low-lying states in Ti IV

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 (E1) transition amplitudes of few transitions with recent many-body calculations by different groups. We have also carried out the calculations for the lifetimes of the low-lying states of Ti IV. A long lifetime is found for the first excited 3d$^{2}D_{5/2}$ state, which suggested that Ti IV may be one of the useful candidates for many important studies. Most of the results reported here are not available in the literature, to the best of our knowledge.Comment: 15 pages submitted to J. Phys.

Spectacular Role of Electron Correlation in the Hyperfine Interactions in 2D5/2^2D_{5/2} States in Alkaline Earth Ions

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.Comment: Submitted to Physical Review Letters, 3 figures and 5 table

Comparative studies of the magnetic dipole and electric quadrupole hyperfine constants for the ground and low lying excited states of ^{25}Mg^{+}

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.Comment: 3 figures, Late