Cross Sections For Inelastic Transitions Research Articles

Analyticity and the Global Information Field

The relation between analyticity in mathematics and the concept of a global information field in physics is reviewed. Mathematics is complete in the complex plane only. In the complex plane, a very powerful tool appears—analyticity. According to this property, if an analytic function is known on the countable set of points having an accumulation point, then it is known everywhere. This mysterious property has profound consequences in quantum physics. Analyticity allows one to obtain asymptotic (approximate) results in terms of some singular points in the complex plane which accumulate all necessary data on a given process. As an example, slow atomic collisions are presented, where the cross-sections of inelastic transitions are determined by branch-points of the adiabatic energy surface at a complex internuclear distance. Common aspects of the non-local nature of analyticity and a recently introduced interpretation of classical electrodynamics and quantum physics as theories of a global information field are discussed.

Cluster Model Analysis of Pion Elastic and Inelastic Scattering from 12C

Angular distributions of differential cross sections for the 12C(π±, π±)12C and 12C(π±, π±)12C* reactions at pion kinetic energy ranging from 50 to 260 MeV have been analyzed with the 3α-particle model of 12C. The model provides good fits to a wide range of data. Differential cross sections for inelastic transitions to the (2 + ; 4.44 MeV) and (3 − ; 9.64 MeV) states in 12C are computed and the deformation lengths δ2 and δ3 are extracted. It is found that the extracted deformation lengths are sensitive to the nuclear model used and similar to the corresponding values found with other probes and nuclear models.

Oscillator strengths and inelastic scattering of electrons from O II

Electron-collision excitation cross sections of inelastic transitions among the 28 LS terms of the 2s22p3, 2s2p4, 2s22p23s, 2s22p23p, 2s22p23d and 2s22p24s configurations of singly-ionized oxygen are calculated using the R-matrix method. The target states are represented by fairly extensive configuration-interaction wavefunctions which yield excitation energies, oscillator strengths and radiative lifetimes of excited states that agree well with available calculated and measured values. To assess the importance of electron correlation and coupling to higher excited states in the scattering calculation, the present 28-state calculation is compared with the earlier 11-state R-matrix theory. Our cross sections for the 2s22p3 4So-2s22p3 2Do and 2s22p3 4So-2s2p4 4P transitions show good agreement with the merged-beams energy-loss experiment and the 11-state R-matrix theory.

Quantum scattering studies of electronically inelastic collisions of CN (X 2Σ+, A 2Π) with He

Using recent ab initio interaction potential energy surfaces for the CN (X 2Σ+, A 2Π)+He system [H.-J. Werner, B. Follmeg, and M. H. Alexander, J. Chem. Phys. 89, 3139 (1988)], we have calculated fully quantum cross sections for inelastic transitions between individual rovibrational levels of the A 2Π and the X 2Σ+ states of CN. We have concentrated on the transitions studied experimentally by Dagdigian and co-workers for CN+Ar, namely transitions between the rotational levels of the A, v=8 and X, v′=12, the A, v=7 and X, v′=11, and the A, v=3 and X, v′=7 vibrational manifolds. In the case of the 8→12 and 7→11 transitions the cross sections are large (0.1–1 Å2), and the dependence on initial Λ doublet level and on final rotational quantum number displays the same subtle alternations as seen experimentally. In the case of the 3→7 transitions, for which the vibrational levels are energetically much more separated, the calculated cross sections for CN+He are extremely small (10−5 Å2), far smaller than observed experimentally for CN+Ar. In order to resolve this discrepancy, we have carried out some additional ab initio calculations for the CN+Ar system, but the change in the interelectronic coupling potential appears not to be large enough to explain the magnitude of the experimental cross sections.

Alignment and orientation of atomic orbitals in Na(3p)+Na+interactions

The authors use an efficient matrix propagator method to solve the coupled equations describing populations of the adiabatic states of Na2+ during a collision of Na+ with laser-excited Na(3p). Both straight-line and curved energy-conserving classical trajectories for the nuclei are used. Electronic motion is treated explicitly with a common translation factor. The radius at which the electronic angular momentum of a partially coherent mixture of Na(3p sigma u) and (3p pi u) becomes locked at the molecular axis is evaluated and the dependence of differential cross sections for inelastic transitions on the initial orbital alignment and orientation is discussed. The elementary mechanisms responsible for the observed effects are analysed numerically. Results are in qualitative agreement with recent experimental findings.

The Glauber approximation in molecular scattering. II. Rotational excitation by electron impact

The Glauber amplitudes for anisotropic potentials that originate from the local part of the electron–molecule interactions are examined in detail and presented in a final form which is directly suitable for numerical treatment. The various choices for the z axis are also examined and the one now most commonly employed in atomic scattering is selected. The case of rotational excitation from pure quadrupole scattering is examined for a wide variety of Q values and their effects on the form of the corresponding differential cross sections for inelastic transitions are discussed in detail.

Common trajectory methods for the calculation of differential cross sections for inelastic transitions in atom(ion)-atom collisions. I. General theory

Starting from a partial wave decomposition of the quantum-mechanical equations, a systematic development of the semiclassical theory of inelastic transitions in slow atom(ion)-atom collisions is presented. Both atomic and molecular representations are discussed. It is shown that the introduction of an average potential reduces the semiclassical equations to the well known impact parameter equations; the notions of the classical trajectory and the classical collision plane arise as a natural consequence of the semiclassical approximation. Expressions for the differential scattering cross sections for inelastic transitions are subsequently derived. The connection with the straight line eikonal approximation is discussed.

Common trajectory methods for the calculation of differential cross sections for inelastic transitions in atom(ion)-atom collisions. II. Application to proton-hydrogen scattering

For pt. I, see ibid., vol.8, no.2, 239 (1975). As an application of the semiclassical method presented in paper I, the elastic and inelastic, direct and exchange differential cross sections for proton-hydrogen collisions are calculated using a three-term molecular basis. The results of the common trajectory method are shown to agree with experiment (in the energy range 250-1000 eV) for relatively large angles, where the straight line eikonal method begins to show significant deviations. It is emphasized that the present treatment is not much more complicated numerically than the rectilinear model. A limit of validity to the straight line eikonal method is thus obtained. The sensitivity of the results to the explicit choice of trajectory is studied. The validity of the stationary phase approximation is tested in view of its popularity in other semiclassical treatments.