Optical Kerr and Cotton-Mouton effects in atomic gases: a quantum-statistical study

Theory of the birefringence of the refractive index in atomic diamagnetic dilute gases in the presence of static electric (optical Kerr effect) and magnetic (Cotton-Mouton effect) fields is formulated. Quantum-statistical expressions for the second Kerr and Cotton-Mouton virial coefficients, valid both in the low and high temperature regimes, are derived. It is shown that both virial coefficients can rigorously be related to the difference of the fourth derivatives of the thermodynamic (pressure) virial coefficient with respect to the strength of the non-resonant optical fields with parallel and perpendicular polarizations and with respect to the external static (electric or magnetic) field. Semiclassical expansions of the Kerr and Cotton-Mouton coefficients are also considered, and quantum corrections up to and including the second order are derived. Calculations of the second Kerr and Cotton-Mouton virial coefficients of the helium-4 gas at various temperatures are reported. The role of the quantum-mechanical effects and the convergence properties of the semiclassical expansions are discussed. Theoretical results are compared with the available experimental data.Comment: 26 pages, 5 figure

A time-resolution study with a plastic scintillator read out by a Geiger-mode Avalanche Photodiode

In this work we attempt to establish the best time resolution attainable with a scintillation counter consisting of a plastic scintillator read out by a Geiger-mode Avalanche Photodiode. The measured time resolution is inversely proportional to the square root of the energy deposited in the scintillator, and scales to 18ps (sigma) at 1MeV. This result competes with the best ones reported for photomultiplier tubes.Comment: 8 pages, 8 figure

Formation of deeply bound ultracold Sr_2 molecules by photoassociation near the ^1S + ^3P_1 intercombination line

We predict feasibility of the photoassociative formation of Sr_2 molecules in arbitrary vibrational levels of the electronic ground state based on state-of-the-art ab initio calculations. Key is the strong spin-orbit interaction between the c^3\Pi_u, A^1\Sigma_u^+ and B^1\Sigma_u^+ states. It creates not only an effective dipole moment allowing free-to-bound transitions near the ^1S + ^3P_1 intercombination line but also facilitates bound-to-bound transitions via resonantly coupled excited state rovibrational levels to deeply bound rovibrational levels of the ground X^1\Sigma_g^+ potential, with v" as low as v"=6. The spin-orbit interaction is responsible for both optical pathways. Therefore, those excited state levels that have the largest bound-to-bound transition moments to deeply bound ground state levels also exhibit a sufficient photoassociation probability, comparable to that of the lowest weakly bound excited state level previously observed by Zelevinsky et al. [Phys. Rev. Lett. 96, 203201 (2006)]. Our study paves the way for an efficient photoassociative production of Sr_2 molecules in ground state levels suitable for experiments testing the electron-to-proton mass ratio.Comment: 11 pages, 10 figure

Combining Slater-type orbitals and effective core potentials

We present a general methodology to evaluate matrix elements of the effective core potentials (ECPs) within one-electron basis set of Slater-type orbitals (STOs). The scheme is based on translation of individual STO distributions in the framework of Barnett-Coulson method. We discuss different types of integrals which naturally appear and reduce them to few basic quantities which can be calculated recursively or purely numerically. Additionally, we consider evaluation of the STOs matrix elements involving the core polarisation potentials (CPP) and effective spin-orbit potentials. Construction of the STOs basis sets designed specifically for use with ECPs is discussed and differences in comparison with all-electron basis sets are briefly summarised. We verify the validity of the present approach by calculating excitation energies, static dipole polarisabilities and valence orbital energies for the alkaline earth metals (Ca, Sr, Ba). Finally, we evaluate interaction energies, permanent dipole moments and ionisation energies for barium and strontium hydrides, and compare them with the best available experimental and theoretical data.Comment: submitted to Phys. Rev.

Calculation of Araki-Sucher correction for many-electron systems

In this paper we consider the evaluation of the Araki-Sucher correction for arbitrary many-electron atomic and molecular systems. This contribution appears in the leading order quantum electrodynamics corrections to the energy of a bound state. The conventional one-electron basis set of Gaussian-type orbitals (GTOs) is adopted; this leads to two-electron matrix elements which are evaluated with help of generalised the McMurchie-Davidson scheme. We also consider the convergence of the results towards the complete basis set. A rigorous analytic result for the convergence rate is obtained and verified by comparing with independent numerical values for the helium atom. Finally, we present a selection of numerical examples and compare our results with the available reference data for small systems. In contrast with other methods used for the evaluation of the Araki-Sucher correction, our method is not restricted to few-electron atoms or molecules. This is illustrated by calculations for several many-electron atoms and molecules.Comment: submitted to Phys. Rev.

Long-range interactions between an atom in its ground S state and an open-shell linear molecule

Theory of long-range interactions between an atom in its ground S state and a linear molecule in a degenerate state with a non-zero projection of the electronic orbital angular momentum is presented. It is shown how the long-range coefficients can be related to the first and second-order molecular properties. The expressions for the long-range coefficients are written in terms of all components of the static and dynamic multipole polarizability tensor, including the nonadiagonal terms connecting states with the opposite projection of the electronic orbital angular momentum. It is also shown that for the interactions of molecules in excited states that are connected to the ground state by multipolar transition moments additional terms in the long-range induction energy appear. All these theoretical developments are illustrated with the numerical results for systems of interest for the sympathetic cooling experiments: interactions of the ground state Rb($^2$S) atom with CO($^3\Pi$), OH($^2\Pi$), NH($^1\Delta$), and CH($^2\Pi$) and of the ground state Li($^2$S) atom with CH($^2\Pi$).Comment: 30 pages, 3 figure