A perturbation method for the complex angular momentum poles of the multichannel S‐matrix is developed. The inelastic residues of the S‐matrix are also treated in a similar fashion. It is shown that the poles and residues are the second order in coupling between the channels. The closed channel Regge poles are also discussed and it is shown that their contribution in the perturbation series is finite, regardless of the asymptotic behavior of potential.

A semiclassical perturbation method for the inelastic S matrix is described. The channels are transformed into a set of the eigenstates and it is assumed that the transition between them is small. The perturbation is the matrix which diagonalizes the coupling matrix. It is shown that such a series is independent of h/; hence the limit h/ →0 of the S matrix can be calculated. A special case of the weak coupling is also discussed.

An analysis of the differential cross section in the presence of orbiting is given. It is shown that the Regge representation of the scattering amplitude is particularly useful for such a case. The orbiting oscillations in the cross section of H-Hg are very pronounced and they can be described by only a few Regge poles. The velocity averaging can be done with ease and in the presence of orbiting can substantially change the differential cross section.

A simple formulation of orbiting is provided by using the Regge theory. A closed formula for the elastic total cross section is given, both for identical and non-identical particle collisions. It is shown that a single Regge pole can reproduce quantitatively an entire structure of orbiting resonances for a wide range of energy. This is supported by detailed calculation on the system H2-Kr, for which the total cross section has been measured. The resulting expressions are used to calculate explicitly the effect of velocity averaging of the total cross section.

An analysis of the Regge representation of the elastic scattering amplitude is given. The background term is discussed in detail showing that, for large-angle scattering, its contribution is non-oscillatory and represents reflection from the core of a potential. It is shown that the direct reflection term cannot be ignored, although in low-energy collision the Regge pole contribution is dominant. However, in high-energy collisions, it may be the sole contribution to the large-angle differential cross section. This is confirmed in one example, with the explicit calculation of the Regge-pole and background term contributions to the scattering amplitude. The background term is dominant in the forward direction, representing diffraction and forward glory. On the other hand, the Regge-pole contribution can be neglected in first order.

A method for solving the Schrodinger equation is given. It is specially developed for applications in atomic (short wavelength) collisions. The method is also useful for calculating Regge poles, without having to define the potential for complex coordinate. The stability of the method is discussed.

Abstract A graph theoretical method is developed which enables to calculate the contribution of a particular ring to the total π-electron energy of a conjugated molecule.

Exact quantum-mechanical close-coupling and approximate calculations are presented for Ne + N2 collisions using a model potential. The approximate calculations were performed using an exponential semi-classical distorted wave approximation (ESCDW) which is outlined in the paper. The ESCDW approximation involves the evaluation of the same integrals as the standard distorted wave approximation. The former method, however, in contrast to the latter, yields a unitary S matrix and therefore conserves particle flux. The exponentiation process is shown to lead to dramatic improvements in the calculated cross sections for the present system. Cross sections evaluated using the ESCDW approximation compare very well with exact ones over the entire range of thermally accessible energies. Total and differential rotationally inelastic cross sections are presented and their variation with energy is examined. The dependence of the cross sections on the number of coupled channels included in the calculations is also inves...

Differential cross-sections for collisions of molecules in the thermal energy range normally oscillate rapidly with angle, the oscillations becoming more rapid with increasing relative kinetic energy. The angular resolution in crossed molecular beam experiments is generally insufficient to resolve these rapid oscillations. A method is proposed for averaging differential cross-sections over small angular ranges without actually evaluating them at many angles. The method permits the calculation of averaged cross-sections, which are much more directly comparable with the experimentally determined ones than those evaluated without averaging. Illustrative calculations are presented for three examples : one for elastic scattering (Ar + Kr) and two for rotationally inelastic scattering (Ar + CsF and Ne + N2). When the differential cross-section oscillates rapidly, as it does in the first two cases, it requires less computational effort to plot the relatively smoothly varying averaged differential cross-section t...

A variational calculation has confirmed earlier suggestions that 4He3 has a bound state. The partial wave expansion of Simonov was found to be slowly convergent and by this method no bound state was obtained although there was clear evidence that He3 would be closer to a stable bound state than He2. A variational wave function based directly on interparticle separations and the use of Morse-potential eigenfunctions was rapidly convergent and gave a lower limit to the binding energy of 0·63 K.