Computing Zeros of Analytic Functions in the Complex Plane without using Derivatives

A new approach to evaluating all multiple complex roots of analytical function f(z) confined to the specified rectangular domain of complex plane has been developed and implemented in Fortran code. Generally f (z), despite being holomorphic function, does not have a closed analytical form thereby inhibiting explicit evaluation of its derivatives. The latter constraint poses a major challenge to implementation of the robust numerical algorithm. This work is at the instrumental level and provides an enabling tool for solving a broad class of eigenvalue problems and polynomial approximations.

Revealing the effect of angular correlation in the ground-state He wavefunction: a coincidence study of the transfer ionization process

A joint theoretical-experimental study of the transfer ionization process p + He -> H-0 + He2+ + e(-) is presented. For the first time all particles in the final state have been detected in triple coincidence. This fully differential measurement is in good agreement with a theoretical model where the target is described by a wavefunction containing both radial and angular correlation terms.

Angular distributions of electrons in photoionization of 3s subshell of atomic chlorine

R-matrix calculated photoelectron angular distribution asymmetry parameters, beta for Cl+ 3s3p(5) P-3(o) and 3s(2)3p(3) (D-2(o))3d P-1(o) final ionic states in photoionization of the ground state of atomic Cl are presented in the photon energy range from threshold to 80 eV. The results, characterized by prominent autoionization structures which are sensitive to multielectron correlations, are compared with those recently measured by Whitfield et al (Whitfield S B, Kehoe K, Krause M 0 and Caldwell C D 2000 Phys. Rev. Lett. 84 4818). Contrary to experiment and previous theoretical calculations, our detailed CIV3 structure calculation (Deb N C, Crothers D S F, Felfli Z and Msezane A Z 2002 J. Phys. B: At. Mol. Opt. Phys. submitted) has identified the lowest P-1(o) level of Cl+ as 3S(2)3p(3)(D-2(o))3d P-1(o) rather than 3s3p(5) P-1(o). The implications and consequences of the measured data for the 3s P-1(o) level are also discussed in the context of our calculated energies for Cl+ and beta for 3d P-1(o).

Glory and thresholds effects in H+D-2 reactive angular scattering

We analyse H + D-2 reactive angular scattering using the S- matrix elements obtained by Aoiz et al. and Althorpe et al. Enhancement of small angle scattering in the v' = 3

Semiclassical complex angular momentum theory and Pade reconstruction for resonances, rainbows, and reaction thresholds

A semiclassical complex angular momentum theory, used to analyze atom-diatom reactive angular distributions, is applied to several well-known potential (one-particle) problems. Examples include resonance scattering, rainbow scattering, and the Eckart threshold model. Pade reconstruction of the corresponding matrix elements from the values at physical (integral) angular momenta and properties of the Pade approximants are discussed in detail.

Angular distribution for the elastic scattering of electrons from Ar+(3s^2 3p^5 ^2P) above the first inelastic threshold

The measured angular differential cross section (DCS) for the elastic scattering of electrons from Ar+(3s2 3p5 2P) at the collision energy of 16 eV is presented. By solving the Hartree-Fock equations, we calculate the corresponding theoretical DCS including the coupling between the orbital angular momenta and spin of the incident electron and those of the target ion and also relaxation effects. Since the collision energy is above one inelastic threshold for the transition 3s2 3p5 2P–3s 3p6 2S, we consider the effects on the DCS of inelastic absorption processes and elastic resonances. The measurements deviate significantly from the Rutherford cross section over the full angular range observed, especially in the region of a deep minimum centered at approximately 75°. Our theory and an uncoupled, unrelaxed method using a local, spherically symmetric potential by Manson [Phys. Rev. 182, 97 (1969)] both reproduce the overall shape of the measured DCS, although the coupled Hartree-Fock approach describes the depth of the minimum more accurately. The minimum is shallower in the present theory owing to our lower average value for the d-wave non-Coulomb phase shift s2, which is due to the high sensitivity of s2 to the different scattering potentials used in the two models. The present measurements and calculations therefore show the importance of including coupling and relaxation effects when accurately modeling electron-ion collisions. The phase shifts obtained by fitting to the measurements are compared with the values of Manson and the present method.

Role of conformational constraints of position 7 of the disulphide bridge of h-alpha-CGRP derivatives in their agonist versus antagonist properties

Previous structure-activity studies have shown that the disulphide bridge of calcitonin gene-related peptide (CGRP) is important for the highly potent, CGRP receptor-mediated effects of this peptide. In this study penicillamine (Pen) was substituted for one or both of the cysteinyl residues to determine conformational and topographical properties of the disulphide bridge favourable for binding to CGRP receptors and/or receptor activation. Pen constrains the conformational flexibility of disulphide bridges in other peptides. Binding affinities were measured using a radioligand binding assay with membranes prepared from pig coronary arteries and I-125-h-alpha-CGRP. Functional effects were characterized using a previously reported pig coronary artery relaxation bioassay. The binding affinity of [Pen(2)]h-alpha-CGRP was not significantly different from that of h-alpha-CGRP. All other analogues showed reduced affinity for CGRP receptors. [Pen(2)]h-alpha-CGRP also caused relaxation of coronary arteries. The remaining analogues either caused relaxation with significantly reduced potency or failed to relax the arteries at concentrations up to 1 x 10(-5) M. All analogues that did not relax coronary arteries contained a D-Pen in position 7 and inhibited CGRP-induced relaxation. [D-Pen(2,7)]h-alpha- CGRP was the most potent antagonist with a K-B value of 630 nM. This affinity is similar to that of the classical CGRP receptor antagonist, h-alpha-CGRP(8-37), on these arteries (K-B, 212 nM). These studies show that modifying the topography of the disulphide bridge can cause large and variable effects on ligand binding and activation of CGRP receptors. The contribution of position 7 to the conformation and topography of the disulphide bridge of h-alpha-CGRP is crucial to the future design of agonists of CGRP receptors. Furthermore, position 7 is important for the development of new CGRP receptor antagonists with structures based on the whole sequence of h-alpha-CGRP.