Collisions in External Fields

Before considering molecular collisions in external fields, it is useful to make a few comments about the general features of molecule-field interactions. Some of... 

The quantum theory of molecular collisions in external fields described in this chapter is based on the solutions of the time-independent Schrodinger equation. The scattering formalism considered here can be used to calculate the collision properties of molecules in the presence of static electric or magnetic fields as well as in nonresonant AC fields. In the latter case, the time-dependent problem can be reduced to the time-independent one by means of the Floquet theory, discussed in the previous section. We will consider elastic or inelastic but chemically nonreac-tive collisions of molecules in an external field. The extension of the formalism to reactive scattering problems for molecules in external fields has been described in Ref. [12]. 

Most of the recent literature on molecular collisions in external fields [1-3, 9, 10, 15, 16, 18, 19, 21, 23, 25, 27-84, 92] is focused on collisions of molecules at low and ultralow temperatures. As mentioned in the introduction, it is at temperatures < 10 K that strong electromagnetic fields are expected to have a noticeable effect on the scattering properties of molecules. The coupled-channel calculations... 

H. Rinneberg J. Neukammer M. Kohl A. Konig K. Vietzke H. Hieronymus and H.-J. Grabka (1988) Atomic Spectra and Collisions in External Fields K.T. Taylor, M.H. Nayfeh and C.W. Clark Eds. Plenum Press, New York... 

A. Holle, J. Main, G. Wiebusch, H. Rottke, K.H. Welge Laser spectroscopy of the diamagnetic hydrogen atom in the chaotic region . In Atomic Spectra and Collisions in External Fields, ed. by K.T. Taylor, M.H. Nayfeh, C.W. Clark (Plenum, New York 1988)... 

In principle, the choice of the basis states (p ) is arbitrary as long as the basis set spans the entire Hilbert space. In the following subsections, we will discuss three choices of the basis set relevant for collision problems in external fields. 

In order to simplify the evaluation of the matrix elements entering Eq. (8.35) for collision problems in external fields, Krems and Dalgarno [18] proposed to... 

The total angular momentum basis is thus computationally more efficient, even for collision problems in external fields. There is a price to pay for this. The expressions for the matrix elements of the collision Hamiltonian for open-shell molecules in external fields become quite cumbersome in the total angular momentum basis. Consider, for example, the operator giving the interaction of an open-shell molecule in a 51 electronic state with an external magnetic field. In the uncoupled basis (8.43), the matrix of this operator is diagonal with the matrix elements equal to Mg, where is the projection of S on the magnetic field axis. In order to evaluate the matrix elements of this operator in the coupled basis, we must represent the operator 5 by spherical tensor of rank 1 (Sj = fl theorem [5]... 

Describe the theory for quantum scattering calculations of cross sections for molecular collisions in external electromagnetic fields. 

The processes by which photon absorption may produce ions are (1) direct ionization, (2) autoionization, and (3) ion-pair formation. (Processes that depend on collisions or external fields are not included here.) In direct ionization, electron ejection occurs directly upon photon absorption, i.e., no intermediate state is indicated and the process may... 

The perturbations exerted by external electromagnetic fields on molecular energy levels are often larger than the kinetic energy of molecules at temperatures below 1K. Collisions of molecules in a cold gas may therefore be significantly affected by the presence of external fields. The purpose of this chapter is to discuss the effects of external fields on dynamics of molecular collisions at cold and ultracold temperatures and outline the prospects for new discoveries in the research of molecule-field interactions at low temperatures. The experimental work on collision dynamics of low-temperature molecules in external fields may lead to the development of the research field of cold controlled chemistry [4] and we will particularly focus the discussion on mechanisms for external field control of intermolecular interactions. Most of the results presented are based on rigorous quantum-mechanical calculations. The quantum theory of molecular collisions in the presence of external fields is described in Chapter 1. 

Once the Fock operators have been constructed from a set of MSOs, this matrix equation is linear in its unknowns. Its coefficients are dependent on time in a way determined by the forces driving the electrons. These forces are the nuclear Coulomb potentials in molecular collisions or dynamics, but they could also be weak external fields. 

Together with Eq. (66), this equation describes exactly the linear response of the system to an external field, with arbitrary initial conditions. Its physical meaning is very simple and may be explained precisely as for Eq. (66) 32 the evolution of the velocity distribution results in two effects (1) the dissipative collisions between the particles which are described by the same non-Markoffian collision operator G0o(T) 35 1 the field-free case and (2) the acceleration of the particles due to the external field. As we are interested in a linear theory, this acceleration only affects the zeroth-order distribution function It is... 

As discussed by M. Shapiro and R Brumer in the book Quantum Control of Molecular Processes, there are two general control strategies that can be applied to harness and direct molecular dynamics optimal control and coherent control. The optimal control schemes aim to find a sef of external field parameters that conspire - through quantum interferences or by incoherent addition - to yield the best possible outcome for a specific, desired evolution of a quantum system. Coherent control relies on interferences, constructive or destructive, that prohibit or enhance certain reaction pathways. Both of these control strategies meet with challenges when applied to molecular collisions. 

This question can be answered by means of scattering experiments for molecules in fields [1-3] or accurate calculations of the scattering matrices for collisions of molecules in nonperturbative external fields. The purpose of this chapter is to describe the theory for such calculations and present selected results illustrating the effects of external electromagnetic fields on molecular collisions at low temperatures. 

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