The Atmosphere and Ionosphere pp 1-67 | Cite as

# Rydberg States of Atoms and Molecules in a Field of Neutral Particles

## Abstract

This book is devoted to the modern methods of calculating the energy eigenvalues of Rydberg atoms *A*** and molecules *XY*** perturbed by neutral particles of a medium and to the results of studying the interaction processes with them. Numerous applications in plasma chemistry, aeronomy, and astrophysics have contributed to conducting this study. These methods are based on the use of integral variant of the theory utilizing Green’s function approach. Because of the closeness to the continuum boundary, these energies cannot be properly described in terms of the standard quantum chemistry. When the radius of electronic cloud of excited states is large enough (i.e., \(R{_{{\rm{c}}\;}} = 2\,{n^2} \gg \hskip-1.2pt1\), where *n* is the principal quantum number), they cannot be regarded as isolated even in the case of a rarefied gas. The spectral distortion is the strongest when the number *N* of perturbing neutral particles falling into this region exceeds unity. This chapter is divided into four main parts.

In the first part, the generalized method of finite-radius potential (FRP) is discussed. This method self-consistently takes into account the short- and long-range interactions in the two-center system under consideration. It adequately describes the scattering of a weakly bound electron by the ion core and a perturbing atom with nonzero angular momenta *l* and *L* with respect to these centers, thereby allowing the theory to be extended to the intermediate (on the order of and less than electron wavelength \(\lambda \propto n\)) interatomic distances \(R\). As an application of the theory, the detailed analysis is performed for the behavior of the potential energy surfaces (PESs) of a system composed of a highly excited atom \(A^{\ast\ast}\;(n, \, l)\) and a neutral atom *В* with the filled electronic shell. It is demonstrated that the inclusion of nonzero momentum \(L\) for the \({e^{-} } - B\) scattering results in the additional splitting of the PES into the separate groups of interacting terms classified by the projection *m* of electronic angular momentum *l* on the quasimolecular axis. At distances \(R \gg n\), the FRP method exactly transforms to the zero-radius pseudopotential (ZRP) model and, correspondingly, to the asymptotic theory in which the PESs acquire a simple analytic form. It turns out that, at large values \(n \gg 1\), the ZRP method is valid up to the distances \(R\sim \, n.\)

In the second part, the specific features of the diabatic and adiabatic PESs are discussed by taking into account the dissociative, covalent, and ion configurations. The potentialities and disadvantages of the existing ab initio approaches are analyzed. The matching method is suggested, which allows a unique self-consistent picture devoid of the above-mentioned disadvantages to be obtained for the terms. As an illustration, the potential curves are calculated for the \(n l\, \left( { {}^{2s + 1}\Lambda } \right)\) states of the \({\hbox{Na}}^{\ast\ast} + {\hbox{He}}\) quasimolecule (\(n, \, \,l\,\), and \(\Lambda\) are the principal quantum number, angular momentum, and its projection on the molecular axis, respectively, and *S* is the spin of the system), and a detailed comparison with the computational results of other authors is carried out.

The interaction of *ХY*** with a neutral particle *M* includes the interactions with both ion and a weakly bound electron. The former is characterized by small impact parameters, whereas the latter has large impact parameters. As a result, the total scattering cross-sections can appreciably exceed the gas-kinetic values. The material is presented in terms of the PES of the \(XY^{\ast\ast} + M\) system followed by the description of the dynamics of processes (1.1a–e) within the framework of the integral variant of the multichannel quantum defect (MQD) theory using the renormalized Lippmann–Shwinger equation technique. Such a formulation of the MQD theory allows one to obtain a convenient representation for Green’s function of a highly excited molecule, which opens up wide possibilities for various applications.

In the fourth part, the many-center perturbation of the atomic Rydberg states is analyzed for the situation wherein two (or more) perturbing neutral centers fall inside the electronic cloud. The behavior of Rydberg atom in a dense medium is considered with allowance for the influence of finite number *N* of the neutral particles chaotically distributed in its volume. The stochastic approach is proposed for the solution to this problem.

## Keywords

Atom−molecular processes Elementary chemical reactions## Notes

### Acknowledgment

This work was supported by Russian Foundation for Basic Research, project N. 10-03-00737.

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