Working group report: Collider Physics

This is summary of the activities of the working group on collider physics in the IXth Workshop on High Energy Physics Phenomenology (WHEPP-9) held at the Institute of Physics, Bhubaneswar, India in January 2006. Some of the work subsequently done on these problems by the subgroups formed during the workshop is included in this report.     

Calculation of molecular geometries by SCF perturbation theory

An SCF perturbation method for investigating the effects of an arbitrary change in nuclear configuration on the electronic structure of a molecule is reported. Illustrative calculations for CO₂ and CH₃OH are presented. It is found that, when taken to second order, the error in the calculated change in energy which results from a change in nuclear configuration is typically in the range of 0.1 to 7%.     

On the singularity of Green's tensor for a perfectly conducting semi-infinite cone

This paper is intended to clarify a misunderstanding concerningthe source singularity of the electric Green's tensor for aperfectly conducting semi-infinite cone of circular cross-section.Tai's series expansion of the Green's tensor is known to lacka singular term at the source region. Jones has reconstructedthe solution to this problem and has pointed out the differencebetween his result and that of Tai. The aim of our paper isto demonstrate that, although Jones's closed-form solution iscorrect, there is a mistake in his comparison with Tai's seriessolution. We conclude that one of the two additional singularterms that Jones claims as missing from Tai's formula must beomitted. Besides, we compare Jones's closed-form solution withSmyshlyaev's solution to the very same problem. We concludethat the magnetic field expressions given by Jones and Smyshlyaevcoincide, but a singular term is missing from Smyshlyaev's expressionfor the electric field.     

A symmetry problem in polymer calculations

It is shown by a symmetry argument that the band gap in a symmetric polyene must be zero in the restricted single determinant approximation. Spurious band gaps can arise in SCF calculations when the symmetry of the lattice is not reflected in the lattice sums. The consequences of this symmetry problem are discussed.     

SCF perturbation calculations on metalloporphyrins

The influence of metal ion on the oxidation and ionisation potentials of metalloporphyrins is investigated by the simple electrostatic model using SCF perturbation theory. The zero order wavefunctions are obtained from PPP and CNDO/2 methods. The wide variations in redox potentials with metal and the relative insensitivity of the optical transitions with metal are very well accounted for by the perturbation approach.     

Self consistent field perturbation theory for Frenkel and charge transfer states of hydrogen bonded crystals

Comparison is presented of energies, oscillator strengths, and polarization directions calculated using the dipole length and dipole velocity formulas for the lowest 4–7ππ ^* transitions in eight 6π-electron molecules of C _s symmetry using various amounts of CI, from singly excited configurations only (SCI) to complete CI (CCI), and also using the time-dependent Hartree-Fock (TDHF) method. The standard simple PPP approximation was used. For the strongest transitions, SCI and especially TDHF give results in fairly good agreement with CCI. For weaker transitions both SCI and TDHF give similar results, quite different from the CCI solutions. Rational methods for selecting a small number of configurations needed to reproduce correct order of excited states (SECI-1) or a somewhat larger number reproducing correct order, energies, oscillator strengths and polarization directions of transitions (SECI-2) are presented. Both, and particularly the latter, give similar results from both dipole length or dipole velocity formulas when Linderberg's relation is used for matrix elements of the linear momentum operator and in this respect resemble the TDHF and CCI methods for which both formulas necessarily give identical results.     

Microwave-Assisted Synthesis of Aryl Amide Bonds on Solid Phase

A novel microwave-assisted synthesis of a library of triarylamides has been undertaken on the solid-phase.     

Scattering by small defects in the neighbourhood of a fluid-solid interface

The scattering of incident plane elastic waves by a varietyof different defects that lie upon a fluid-solid interface isconsidered here using matched asymptotic expansions. The expansionscheme is developed in terms of a parameter , the ratio of typicaldefect length scale to a typical wavelength of the incidentfield, taken to be small. Three different canonical situations occur and these are illustratedvia three specific examples treated here: a rigid strut, anedge crack, and a rigid strip. In each case the leading-ordermatching is performed to identify the leading-order contributionof the defect to the acoustic field in the far field. In particular,each defect is identified with a source of dipole response ininterfacial stress of displacement. It is shown in the limit as s<<s1 that in the inner problemsthe fluid and solid pieces uncouple in a particularly convenientmanner allowing analytical solutions to be deduced. These arethen matched with appropriate outer solutions.