E. Ficocelli Varracchio

Atom–diatom scattering: An extension of the field theoretic approach and a computational assessment

In a recent paper the problem of atom–diatom scattering has been approached with a field‐theoretic formalism and an approximation scheme has been suggested for the optical and transition potentials, presiding elastic and inelastic processes, respectively. On the basis of experience gained from preliminary calculations, higher order approximations have been derived in this paper for the above mentioned effective potentials. New computations have been performed for a collinear collision model, with an exponential repulsive interaction potential and a harmonic oscillator representation for the molecule. The results obtained agree very well to the exact values of Secrest and Johnson, also for choices of the parameters where other approximate quantum mechanical treatments completely fail, suggesting that, in this extended scheme, the field theoretic scattering equations could be confidently applied to realistic three‐dimensional computations.

A new approach to the “sudden” collisional dynamics of atom-molecule systems

Abstract The sudden model of atom—molecule vibrotational scattering is generalized to introduce effects of nuclear relaxation. Ab initio corrections are obtained in the form of energy and space differentiations of an off-shell sudden T -matrix. The physical interpretation of the theory and a preliminary numerical application are considered.

Field-theoretical approach to vibrational excitation in atom—diatom collinear collisions

Abstract The field-theoretical atom—diatom scattering equations of Csanak have been tested numerically, assuming a collinear collision model, with an exponential repulsive interaction potential and with a harmonic oscillator approximation for the molecule. Dysons equation, in its integral form, has been solved obtaining orbitals representing the elastic scattering of an atom off the target and these Dysons orbitals have been used to evaluate a matrix element containing a transition potential. This has been obtained by approximating Bethe—Salpeters equation and yields directly the transition amplitudes for inelastic scattering. The results for single and multiple-jumps compare favourably with the exact values of Secrest and Johnson, and refinements of the model are suggested for further improvements.

Atom—molecule sudden theory of scattering: AB Initio corrections and range of validity of the collision model

Abstract The problem of describing atom—molecule vibro-rotational processes, within a sudden picture of scattering, is analyzed in a completely ab initio fashion. The resulting generalized infinite order sudden (GIOS) theory characteristically: (1) emphasizes the role of off-shell sudden T -matrices; (2) leads, from first principles, to corrective terms describing the influence of target motion. It is pointed out that, by means of such corrective terms, it is possible to define β( n ) coefficients, related to the (Δτr A /Δτr BC ) n power of (atomic/molecular) characteristic times for the process considered. A numerical analysis of such coefficients then leads to quantitative information on the validity of the sudden picture of energy transfer, for the process investigated. The theory is tested numerically by applying it to a collinear model of vibrational excitation.

Energy transfer in collisions of atoms with vibrationally (rotationally) excited molecules: a field-theoretical formulation and a numerical application

Abstract A field-theoretical approach to excited state—excited state transitions, in atom—diatom scattering, has been formulated. After showing that the S-matrix of these processes can be expressed in terms of a three particle Green function. Schwingers technique of functional differentiation has been applied to relate this to the one particle Green function and to obtain a functional equation for a transition potential, Ξ f“p connecting the initial and final states of the process. An explicit approximation for Ξ f“i has been derived and a numerical application made for a collinear collision model problem. The results seem to indicate the theory can be reliably used for single quantum transitions, up to energies corresponding to 4–5 open target channels, while double quantum transitions are generally underestimated by the present approximation to Ξ f←r particularly for slowly varying interaction potentials.

Off-shell adiabatic nuclei theory of e− -H2 rotational excitation

Abstract A recently proposed “off-shell” adiabatic nuclei theory is applied to rotational excitation. for the e − -H 2 system. The off-shell constraint on the T matrix is found able to remedy for the breakdown of the fixed-nuclei picture of scattering, at threshold for the process. A dynamical interpretation of the results obtained is outlined.

e+−H2 elastic scattering in the random phase approximation

Abstract The random phase approximation is applied to a description of elastic scattering, in the e + −H 2 system. The theory is in excellent agreement with experiment, up to the threshold for positronium (Ps) formation.

Unification of “post” and “prior” approximations in sudden theories of scattering

Abstract The “post” and “prior” forms of the scattering T-matrix are analyzed in the light of sudden mechanisms of atom-molecule vib-rotational energy transfer. It is pointed out that the corresponding approximations may be “unified” in a single “completely off-shell” T-matrix. Applications of the formalism to a rotational excitation problem are in good agreement with exact quantal calculations, also for multiquantum jumps.

Non Relativistic Field Theory in Few-Body Atomic Physics

A Field-Theoretic formulation of e+-atom scattering is considered, leading to a closed equation for the optical potential of the formalism. An RPA⊕Ladder approximation scheme is suggested and this is applied, numerically, to the e+-He system.

Theory of e - - Diatom Scattering at Low Energies

In this Lecture we want to consider e-- diatom collisions, in the low energy regime, e.g. essentially vibrorotational excitation processes, taking place in the ground electronic state of the diatom. As pointed out in recent reviews on the subject1-3, such a problem is of remarkable theoretical and technological relevance. Here we shall essentially be concerned with the theoretical aspects of such processes and, in particular, we shall mostly concentrate on a consideration of their “ab initio” treatment, along the lines explored in our research group, during the last few years.