Improved LeRoy-Bernstein near-dissociation expansion formula. Tutorial application to photoassociation spectroscopy of long-range states

NDE (Near-dissociation expansion) including LeRoy-Bernstein formulas are improved by taking into account the multipole expansion coefficients and the non asymptotic part of the potential curve. Applying these new simple analytical formulas to photoassociation spectra of cold alkali atoms, we improve the determination of the asymptotic coefficient, reaching a 1% accuracy, for long-range relativistic potential curve of diatomic molecules.Comment: This article is part of Daniel Comparat's PhD thesis available at http://tel.ccsd.cnrs.fr

Duo: a general program for calculating spectra of diatomic molecules

Duo is a general, user-friendly program for computing rotational, rovibrational and rovibronic spectra of diatomic molecules. Duo solves the Schr\"{o}dinger equation for the motion of the nuclei not only for the simple case of uncoupled, isolated electronic states (typical for the ground state of closed-shell diatomics) but also for the general case of an arbitrary number and type of couplings between electronic states (typical for open-shell diatomics and excited states). Possible couplings include spin-orbit, angular momenta, spin-rotational and spin-spin. Corrections due to non-adiabatic effects can be accounted for by introducing the relevant couplings using so-called Born-Oppenheimer breakdown curves. Duo requires user-specified potential energy curves and, if relevant, dipole moment, coupling and correction curves. From these it computes energy levels, line positions and line intensities. Several analytic forms plus interpolation and extrapolation options are available for representation of the curves. Duo can refine potential energy and coupling curves to best reproduce reference data such as experimental energy levels or line positions. Duo is provided as a Fortran 2003 program and has been tested under a variety of operating systems

Calculation of Franck-Condon Factors for a Number of Band Systems of Diatomic Molecules Using Hua Potential

ABSTRACT: This work deals with the calculation of Franck-Condon factors using Hua potential function for the first time. The advantages of this function have been mentioned, and the numerical methods are used to obtain Franck-Condon factors for the following band systems

Theory for Molecular Tests of Fundamental Physics

Even today, fundamental difficulties remain in the understanding of our universe. Among those are inexplicable phenomena like the enormous excess of matter over anti-matter (baryon asymmetry) — connected to the question why is there matter at all — or dark matter (DM) and dark energy which are invoked to explain the structure and evolution of our universe, and problems like the unification of quantum theory with gravity. In order to take a step closer to resolving such issues, it is important to test the known laws of physics, summarized in the standard models of particle physics (SM) and cosmology (ΛCDM model), as accurately as possible. Direct experimental tests of the SM can be carried out with high energies at large colliders like the LHC at CERN, and direct tests of the ΛCDM model are usually performed at large observatories like LIGO. In contrast, the theoretical foundations of chemistry are mostly well understood. Hence, molecules are theoretically and experimentally well controllable. Thus, measurements in standard-sized laboratories with ultra-high precision are possible, so that the less well understood laws of physics can be tested. Such low-energy experiments provide indirect tests of the standard models in the realm of chemistry by probing the fundamental symmetries of nature. Therewith, these tests are complementary to direct tests of the laws of physics in cosmology or high-energy physics. In this cumulative thesis quantum chemical methods are developed and applied to design new experiments and improve existing experiments that employ molecules for tests of fundamental symmetries and, therewith, search for new physics beyond the standard models (BSM). A simultaneous violation of parity and time-reversal symmetry (P,T) is closely connected to baryon asymmetry. P,T-violation appears in a larger amount in unifying BSM theories than in the SM itself. P,T-violation on the elementary particle level is relativistically enhanced in heavy atoms and heavy-elemental molecules and results in permanent electric dipole moments (EDMs) of atoms and molecules which are non-vanishing in the limit of vanishing electric fields. In the first part of this thesis, P,T-violations in diatomic and small polyatomic molecules are studied in order to find well-suited candidates for a first measurement of a permanent EDM. Within this study relativistic effects as well as effects due to the chemical environment of the heavy atom are systematically analyzed. Furthermore, the effects of various fundamental sources of P,T-violation that contribute to the P,T-odd EDM of a molecule are studied. It is discussed, how these sources can be disentangled from experiments that aim to measure the permanent EDMs of different molecules. Among this research one of the first calculations of P,T-odd effects in polyatomic molecules is presented. In the second part of this thesis, the applicability of chiral molecules as sensitive probes for P-violating cosmic fields is demonstrated. P-violating cosmic fields are predicted in several cold DM (CDM) models as well as in the standard model extension (SME) that allows for local Lorentz invariance violation (LLIV). LLIV appears in several theories that aim to unify quantum theory and gravity. It is shown that well-chosen chiral molecules containing heavy elements can improve present limits on P-odd interactions of electrons with cosmic fields by at least two orders of magnitude. This renders chiral molecules particularly interesting for searches for BSM physics. In order to guide future searches for candidate molecules, challenges that may appear in the theoretical description or the design of experiments are discussed. In the last part of this thesis, the possibilities to use a clock transition in the iodine molecule to limit LLIV are explored in cooperation with the BOOST collaboration. Quantum chemical studies of such effects in iodine are presented. These calculations are essential for an estimate of the expected sensitivity of the BOOST satellite mission, which employs the iodine molecular clock as probe for LLIV

Highly Excited States of Small Molecules and Negative Atomic Ions

Excited states of atoms and molecules exhibit a rich array of diverse phenomena. This dissertation examines two exotic states of atoms at such excited levels: Rydberg molecules and atomic negative ions. Rydberg molecules are formed by a Rydberg atom and one or more ground state atoms, and can be highly polar due to their unusual electronic wave functions and enormous bond lengths. This dissertation expands the theory of these molecules by studying the formation and structure of polyatomic molecules, multichannel Rydberg molecules formed from divalent atoms, and spin effects and relativistic interactions. It also details intermolecular forces between Rydberg molecules, their manipulation via external fields, and their dependence on the intricacies of electron-atom scattering. This electron-atom interaction is also the main component of the latter portion of this thesis, which studies doubly excited states of alkali negative ions in very polarizable and nearly degenerate atomic states. Photodetachment of these states reveals electron correlation and long-range forces stemming from their high excitation

Stability of Topological States and Crystalline Solids

From the alignment of magnets to the melting of ice, the transition between different phases of matter underpins our exploitation of materials. Both a quantum and a classical phase can undergo an instability into another state. In this thesis, we study the stability of matter in both contexts: topological states and crystalline solids. We start with the stability of fractional quantum Hall states on a lattice, known as fractional Chern insulators. We investigate, using exact diagonalization, fractional Chern insulators in higher Chern bands of the Harper-Hofstadter model, and examine the robustness of their many-body energy gap in the effective continuum limit. We report evidence of stable states in this regime; comment on two cases associated with a bosonic integer quantum Hall effect; and find a modulation of the correlation function in higher Chern bands. We next examine the stability of molecules using variational and diffusion Monte Carlo. By incorporating the matrix of force constants directly into the algorithms, we find that we are able to improve the efficiency and accuracy of atomic relaxation and eigenfrequency calculation. We test the performance on a diverse selection of case studies, with varying symmetries and mass distributions, and show that the proposed formalism outperforms existing restricted Hartree-Fock and density functional theory methods. Finally, we analyze the stability of three-dimensional crystals. We note that for repulsive Coulomb crystals of point nuclei, cubic systems have a zero matrix of force constants at second order. We investigate this by constructing an analytical model in the tight-binding approximation, and present a phase diagram of the most stable crystal structures, as we tune core and valence orbital radii. We reconcile our results with calculations in the nearly free electron regime, as well as current research in condensed matter and plasma physics.Funded by the Engineering and Physical Sciences Research Council under grant no. EP/M506485/1

References, Appendices & All Parts Merged

Includes: Appendix MA: Selected Mathematical Formulas; Appendix CA: Selected Physical Constants; References; EGP merged file (all parts, appendices, and references)https://commons.library.stonybrook.edu/egp/1007/thumbnail.jp