Variational Methods in Electron-Atom Scattering TheoryThe investigation of scattering phenomena is a major theme of modern physics. A scattered particle provides a dynamical probe of the target system. The practical problem of interest here is the scattering of a low energy electron by an N-electron atom. It has been difficult in this area of study to achieve theoretical results that are even qualitatively correct, yet quantitative accuracy is often needed as an adjunct to experiment. The present book describes a quantitative theoretical method, or class of methods, that has been applied effectively to this problem. Quantum mechanical theory relevant to the scattering of an electron by an N-electron atom, which may gain or lose energy in the process, is summarized in Chapter 1. The variational theory itself is presented in Chapter 2, both as currently used and in forms that may facilitate future applications. The theory of multichannel resonance and threshold effects, which provide a rich structure to observed electron-atom scattering data, is presented in Chapter 3. Practical details of the computational implementation of the variational theory are given in Chapter 4. Chapters 5 and 6 summarize recent appli cations of the variational theory to problems of experimental interest, with many examples of the successful interpretation of complex structural fea tures observed in scattering experiments, and of the quantitative prediction of details of electron-atom scattering phenomena. |
Contents
Quantum Mechanics of ElectronAtom Scattering | 1 |
Variational Theory | 25 |
Computational Technique | 73 |
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1)-electron approximation asymptotic form basis functions basis set Bethe-Goldstone bound bound-state boundary condition Burke Callaway channel orbitals close-coupling calculations close-coupling equations closed-channel coefficients computed configuration continuum basis functions corresponding curve defined by Eq derived differential cross section dipole effective eigenchannel eigenfunctions eigenphases eigenvalues elastic cross section elastic scattering electron scattering electron-atom scattering excitation cross section experimental data Figure formalism given by Eq Green's function Hamiltonian Hartree-Fock included indices Kohn formula LeDourneuf Lippmann-Schwinger equation matrix elements optical potential orbital functions orthogonal parameter phase shifts Phys polarizability polarization potential polarized orbital quadratically integrable quantum numbers R-matrix s-wave scattering wave function Schrödinger equation Schwinger shown in Fig Sinfailam and Nesbet Slater determinants solution stationary structure symmetric target atom Thomas and Nesbet two-electron values variational calculations variational method variational principle vectors virtual excitations wave function width zero ра