Bearing Coupling Research Articles

Volume effects for pion two-point functions in constant electric and magnetic fields

We compute finite volume effects relevant for lattice QCD simulations using quantized background fields. Focusing on constant electric and magnetic fields on a periodic lattice, we determine volume corrections to pion two-point functions using chiral perturbation theory. Among such corrections are the finite volume shifts to the electric and magnetic polarizabilities, which are numerically shown to be non-negligible. We additionally find that all terms in the single-particle effective action can be renormalized by infrared effects. This includes Born couplings to the pion current and total charge-squared, which can be renormalized due to the nature of gauge invariance on a torus.

Quasifree kaon photoproduction on nuclei

Investigations of the quasifree reaction A( γ, KY)B are presented in the distorted wave impulse approximation (DWIA). For this purpose, we present a revised tree-level model of elementary kaon photoproduction that incorporates hadronic form factors consistent with gauge invariance, uses SU(3) values for the Born couplings and uses resonances consistent with multichannel analyses. The potential of exclusive quasifree kaon photoproduction on nuclei to reveal details of the hyperon–nucleus interaction is examined. Detailed predictions for the coincidence cross section, the photon asymmetry, and the hyperon polarization and their sensitivities to the ingredients of the model are obtained for all six production channels. Under selected kinematics these observables are found to be sensitive to the hyperon–nucleus final-state interaction. Some polarization observables are found to be insensitive to distortion effects, making them ideal tools to search for possible medium modifications of the elementary amplitude.

Non-adiabatic coupling of the 11A' and 21A' states of ozone in the vicinity of their conical intersection and construction of diabatic states

The 11A' and 21A' states of ozone are known to have a conical intersection near 83° in C2v, the intersection seam continuing into asymmetric geometries. We have calculated ab initio the symmetric stretch, antisymmetric stretch and bend components of the Born couplings between these states in the vicinity of the intersection seam, using MRD-CI wavefunctions and an analytical gradient formalism. All three components are significant and sharply peaked near the intersection seam. The non-adiabatic couplings in the vicinity of the energetically accessible conical intersection are expected to be important in understanding the spectroscopy of ozone in the region of the Huggins band. The conical nature of the intersection is illustrated. The singularity in the couplings is eliminated by constructing quasidiabatic states. Different diabatization schemes are discussed and compared. The quasidiabatic states are shown to have distinct characteristics.

Density functional theory of born couplings: Consequences for electron flow in Jahn–Teller molecules and superconductors

AbstractThe dynamics of Jahn–Teller systems has recently been discussed in terms of generalized electronic charge and current densities in nuclear‐coordinate space. The introduction of the electronic phase as a function of both electronic and nuclear coordinates, in addition to the electronic density, was a crucial component of this formulation. Here, a densitybased treatment of Born couplings is derived from first‐principles quantum mechanics beyond the Born–Oppenheimer approximation. Because of the degenerate electronic configuration of a Jahn–Teller molecule, there are an infinite number of ways in which the charge distribution can be oriented for the same energy, leading to a vanishing bond hardness for the molecule in the symmetric nuclear configuration. Further, the moving nuclear framework serves as the perturbation necessary to define the orientation of the charge density, leading to unhindered rotation of the charge cloud. This leads to the dynamical Jahn–Teller problem, namely, the coupling of electronic and nuclear motions through the Born coupling terms. Applications to superconductivity theory are discussed. © 1995 John Wiley & Sons, Inc.

Nonadiabatic coupling of the 1 1A″ and 2 1A″ states of ozone

We report the results of ab initio calculations of the nonadiabatic Born coupling terms for the two lowest-lying singlet A″ excited states of ozone ( 1 A 2 and 1 B 1 in C 2v symmetry) whose electronic potential energy surfaces exhibit a crossing at a bond angle near 120°. Since photoexcitation from the ground state to these A″ states is believed to be responsible for the Chappuis band of ozone, determination of the nonadiabatic coupling terms in the molecular Hamiltonian is therefore likely to be of importance in understanding the predissociative features of the spectrum. The nuclear derivative coupling matrix elements are computed between ab initio electronic wavefunctions obtained from multi-reference configuration interaction (MRD-CI) calculations in a basis of configuration state functions constructed from MCSCF orbitals. The first-derivative nonadiabatic coupling terms are calculated analytically in a manner similar to the calculation of analytic energy gradients, thereby avoiding the cumbersome numerical differentiation of CI and SCF coefficients. The calculated analytical derivative coupling matrix elements are used to determine a suitable transformation to a quasidiabatic basis.

Constraints on coupling constants through charged Σ photoproduction

The few available data for the reactions $\gamma p \rightarrow K^{0} \Sigma^{+}$ and $\gamma n \rightarrow K^{+} \Sigma^{-}$ are compared to models developed for the processes $\gamma p \rightarrow K^{+} \Sigma^{0}$ and $\gamma p \rightarrow K^{+} \Lambda$. It is found that some of these phenomenological models overpredict the measurements by up to a factor of 100. Fitting the data for all of these reactions leads to drastically reduced Born coupling constants.

Density functional theory for Jahn–Teller systems

AbstractThe first discussion of the dynamics of Jahn–Teller systems in terms of the electronic density as the fundamental variable was given by W.J. Clinton in 1960, where the degenerate electronic configuration of a Jahn–Teller molecule was interpreted in terms of the infinite number of ways in which the charge distribution can be oriented for the same energy. The moving nuclear framework serves as the perturbation necessary to define the orientation of the charge density, with no activation energy required to put the charge cloud into motion. Recently, this notion of the electronic charge cloud in a Jahn–Teller molecule sweeping out the potential surface over which the nuclei move has found mathematical expression in our work in terms of a generalized electronic current density in nuclear‐coordinate space [N. Sukumar and B.M. Deb, Int. J. Quantum Chem. 40, 501 (1991)]. The introduction of the electronic phase as a function of both electronic and nuclear coordinates, in addition to the electronic density, is a crucial component of this formulation. In the present work, the density‐based treatment is extended to the nonadiabatic situation, with the Born couplings interpreted as nonadiabatic currents in parameter space. Abelian and non‐Abelian gauge transformations of these currents are discussed. © John Wiley & Sons, Inc.

Comment on "Electromagnetic production of kaons"

We comment on a recent paper from Adelseck and Wright in which kaon photoproduction and electroproduction data have been fit within a diagrammatic model. The importance of the resonance ${K}_{1}$(1280) in recovering the canonical Born coupling constants is questioned.

A b i n i t i o evaluation of the Born correction, Born couplings, and higher derivative matrix elements with Gaussian-lobe orbitals

Formulation of the expectations of eight operators required for the evaluation of the Born corrections, the Born couplings, and higher derivatives of the Born–Oppenheimer wave functions are derived for the case of a Gaussian-lobe orbital (GLO) basis. The relative simplicity of these analytical formulas is a special advantage of GLO and reduces the computer time in these calculations. Some operators treated here require a modification of the Slater rules. As examples of applications of these techniques, ab initio calculations of the orbital stresses and the Born corrections for the ground state X 1Σ+g and excited states 1Σ+g(II), C, C′ 3Πu, and 3Πu(II) of N2 are reported. The obtained results show that the Born correction near the avoided crossing region strongly depends upon the nuclear separation; in this region configuration interaction makes an important contribution.

The nuclear displacement operator and formulation of the Born couplings of molecular Born–Oppenheimer wave functions

The nuclear displacement operator (NDO) for Born–Oppenheimer electronic wave functions (BOEWF) is introduced and some recurrence formulas are obtained. The formulas for Born couplings and higher derivatives of BOEWF with respect to nuclear coordinates are derived from very general considerations and relations among these quantities are given. The series form, exponential, and integral forms of the NDO are exhibited. Particularly, it is proven that for the two-state systems the NDO has a very simple form by which it is convenient to study two-state dynamical processes. It is shown that the NDO satisfies a differential equation which is analogous to that for the time-evolution operator in the presence of a time-dependent perturbation. The physical meanings of these two operators are compared. It is demonstrated that the NDO is uniquely determined by the vector Born coupling matrix, and that the nuclear motion may be analyzed in terms of a local non-Abelian gauge transformation.