4,022 research outputs found
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
Photoacoustic Spectroscopy and Characterization of some High Temperature Superconducting Oxide (HITSO) Materials
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 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 States in Alkaline Earth Ions
The low-lying n(=3,4,5)d 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
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