On Regge trajectories for ion-atom and atom-atom potentials

Abstract

Some properties of Regge trajectories for interatomic potentials of the Lennard-Jones type are considered. An exact differential equation for the trajectories is derived. An approximation similar to the rigid rotator and neglect of centrifugal distortion approximation allows this equation to be integrated and predicts a linear relation between Re (An ~) and the energy E. A semiclassical analysis complements the formal analysis and gives a physical interpretation to the integration constant Re Cn as well as to Im An : Re Cn is related to the vibrational states of the potential and Im An is related to the angle of rotation of the atoms about each other. A numerical example is presented for a Lennard-Jones (6, 4) potential, with parameters approximating low energy H+-Ar elastic scattering.

Calculation of angular distributions in complex angular momentum theories of elastic scattering

“…In equations (14) and (15), it can be seen that a logarithmic factor is present, and that the terms am ~4) are O(m-5). As noted previously, the expression (14) and (15) differs from the corresponding formula in [21] in certain of its signs and in the equation for R 4.…”

“…The CERN subroutine can also be used for the exact results of w 4. Downloaded by [New York University] at 00: 23 21 July 2015 However, this subroutine is not widely available whereas equations (14) and (15) are readily programmed on a computer. The CERN subroutine took 0.029 s to calculate [P~(-cos 0)[' at 35 angles for v= (3.0, 3.0) on the CDC 7600 computer at the University of Manchester Regional Computer Centre.…”

“…Equations (14) and (15) are used in w 4 to calculate accurate values for Pv(-cos 0). The number of terms needed in the summation depends strongly on v and 0.…”

“…(-cos 0), and to approximate the background integral [10][11][12][13][14][15][16][17]38]. We are concerned in this paper with the calculation of Pz.…”

Orbiting resonances and bound states in molecular scattering

“…Although these phenomena can be quite naturally interpreted in the framework of scattering theory [6], their semiclassical nature calls for a more refined analysis, mainly geometrical, which has been partially performed by several authors, and notably by Berry [7,8,9]. In this spirit, it has been also advocated the use of the complex angular momentum plane polology, especially by Bosanac [10,11,12], Connor [13,14] and Nussenzveig (see in particular his book [15] and the references quoted therein). In the latter approach, however, some problems remain, and a detailed phenomenological analysis is in part still missing.…”