Radial Couplings Research Articles

Calculation of diabatic states from molecular properties

Presents a formal analysis of the variation of molecular properties in the vicinity of an avoided crossing. It is shown that the crossing can be characterised by a molecular property; the conditions which that property should meet are indicated. A method of considerably reducing radial couplings and obtaining diabatic wavefunctions have been developed. An explicit example is presented to illustrate the method.

Calculation of radial couplings between approximate wavefunctions in atomic collisions. II

For pt.I see ibid., vol.10, no.5, p.861 (1977). A generalisation of a scheme, proposed by Macias and Riera (pt.1) to calculate radial couplings which appear in the molecular approach to atomic collisions, is presented for two-centre expansions of the wavefunctions. An example is chosen to show the efficiency of the method, and the effect of linear dependence in the basis set on the energies and couplings is studied.

Calculation of radial couplings between approximate wavefunctions in atomic collisions

A method is presented for the calculation of the radial coupling matrix elements which occur in the molecular approach to atomic collisions. The formalism is based on the earlier work of Bratos (1958) and provides a local method of evaluating analytically radial couplings between approximate wavefunctions when a Gaussian basis is used. The cases of CI and SCF molecular calculations are treated explicitly. Some examples of strong and weak radial couplings are chosen to show the efficiency of the procedure and an approximate formula is tested for the case of coupling between SCF orbitals.

Theoretical investigation of the nonadiabatic interactions and the translational factors in proton-hydrogen collisions

The interaction in the (${p}^{+}$, H) collision system is examined in terms of the exact ${\mathrm{H}}_{2}^{+}$ and H electronic states. The nonadiabatic interactions between the ${\mathrm{H}}_{2}^{+}$ electronic states which asymptotically go to the $n=1$ or $n=2$ atomic states are calculated together with the corresponding translational contributions. The question concerning the choice of the space-fixed and rotating atomic bases is investigated in relation to the long-range interactions. The adiabatic-diabatic question is discussed in connection with the noncrossing rule and dynamic correlations between the separated and united atomic states. With the aid of the calculated interactions, the coupling hypothesis, which states that the nonadiabatic transitions are directly correlated with the closest approach of the electronic state energies, is examined. The characteristic features of the radial and rotational couplings are discussed in a phase-interference model.

Interference effects in 43S and 41S excitation, in He+on He collisions at low energies

Differential cross sections for 43S and 41S excitation of He in He+ on He collisions have been measured in the energy range 94 eV-120 eV and in the angular range 8-17 degrees (in the laboratory frame) by detecting, in delayed coincidence, the scattered ions and the emitted photons ( lambda =5047 AA, 4713 AA). Relative values of the corresponding total cross sections have also been determined, from 60 eV up to 3 keV. Below 400 eV they oscillate in opposite phase as functions of energy. This behaviour can be explained by the Rosenthal model a long range crossing (at 36 bohr) makes the inelastic amplitudes produced by radial couplings interfere at the inner crossing points (1.3 bohr). A double system of oscillations is observed in the differential cross sections. It is interpreted as Stueckelberg interference, coming from inner crossings, combined with a nuclear symmetry interference effect. Calculations of the differential and total cross sections have been carried out and satisfactory agreement between calculated and measured cross sections is obtained.

Calculation of radial couplings in collision of slow atoms

A method, similar to the Born−Oppenheimer approximation for bound molecular states, is developed for the calculation of radial coupling matrix elements. (AIP)