Rydberg Collision Theories

Abstract

Collisionsscattering theoryRydberg atom collisions involving atoms or molecules in Rydberg orbitals are important in understanding a wide range of phenomena from the spectra of astrophysical objects, such as planetary nebulae and interstellar gas clouds, and industrial plasmas on Earth, to Bose-Einstein condensates and multi-qubit logic gates in quantum computing. This Chapter collects together many of the equations used to study theoretically the collisional properties of both charged and neutral particles with atoms and molecules in Rydberg states or orbitals, from thermal energies to ultra-cold temperatures, including the impulse approximation, binary encounter approximation and the Born approximation. Also covered are many new asymptotic methods and working formulae suitable for numerical computation, as well as models using scattering lengths and effective ranges. Readers interested in the basic quantum mechanical properties of Rydberg states may consult Chap. 15 . The theoretical techniques used to study Rydberg collisions complement and supplement the eigenfunction expansion approximations used for collisions with target atoms and molecules in their ground (n = 1) or first few excited states (n > 1), as discussed in Chap. 49 . Direct application of eigenfunction expansion techniques to Rydberg collisions, wherein the target particle can be in a Rydberg orbital with principal quantum number in the range n ≥ 100, is prohibitively difficult due to the need to compute numerically and store wave functions with n3, or more, nodes. For n = 100 this amounts to ≈ 106 nodes for each of the wave functions represented in the eigenfunction expansion. Therefore, a variety of approximate scattering theories have been developed to deal specifically with the peculiarities of Rydberg collisions. Experiments in the ultracold regime, via the use of lasers and magnetic traps, has allowed access to aspects of many-body physics using collisions of Rydberg atoms in a gas that were previously inaccessible in condensed matter and nuclear physics. For the second edition of the Handbook we have changed the title of the chapter to reflect the broader array of theories now being used, in particular, in ultra-cold collisions of Rydberg atoms and the study of their universal properties. scattering theoryclassicalscattering theorysemiclassicalsemiclassical approximationMOTmagneto-optical traps (MOT)