The current state of the theory and its application to low-energy electron-molecule collisions is reviewed. The emphasis is on elastic scattering and vibrational and rotational excitation of small diatomic and polyatomic molecules. New and traditional theoretical approaches are described, and the results of calculations are compared with existing experimental measurements.

The theory of electron-molecule collisions

Publisher Summary This chapter discusses the R-matrix concept of atomic processes. The R-matrix method was first introduced by Wigner and Eisenbud with a fundamental idea that configuration space describes the scattered particle, and the target is divided into two regions. In the internal region (r

The R-Matrix Theory of Atomic Processes

On an “equivalent quadrature” calculation of matrix elements of (z − p2/2m)−1 using an L2 expansion technique

L2 series solution of the relativistic Dirac–Morse problem for all energies

By exploiting the soluble infinite tridiagonal (Jacobi)-matrix problem generated by evaluating a zero-order scattering Hamiltonian H0 in a certain L2 basis set, we obtain phase shift, wave functions, etc., which are exact for a full Hamiltonian H in which only the potential V is approximated. Only bound–bound (L2) matrix elements of the Hamiltonian and finite matrix manipulations are needed. The method is worked out here for s-wave scattering using Laguerre basis functions. Kato improvement of the results and necessary generalizations to many channels are treated.

New L 2 approach to quantum scattering: Theory

It is shown that the Fredholm determinant for the Lippmann-Schwinger equation may be computed for complex energies using only ${L}^{2}$ basis functions. Analytic continuation to the real axis in the $E+i\ensuremath{\epsilon}$ limit gives elastic scattering phase shifts over a continuous range of energies, showing that it is not necessary to explicitly enforce asymptotic boundary conditions for numerical scattering computations, and suggesting that elastic electron-atom or -ion scattering information may be obtained using standard bound-state configuration-interaction methods.

T.N. Rescigno

Papers

Computation of Elastic Scattering Phase Shifts via Analytic Continuation of Fredholm Determinants Constructed Using an L 2 Basis