Doctor of Philosophy (Ph.D.)
John B Delos
A systematic study of the photoabsorption spectra of highly excited hydrogen and alkali atoms in electric fields is presented, based on the semiclassical closed-orbit theory. In most respects, hydrogen and alkali atoms behave similarly, because the excited alkali atoms have a single electron outside of a small ionic core, and the core only produces small shifts of energy levels and small phase shifts of scattered wave functions.;For hydrogen, the classical motion of the excited electron is regular and closed orbits can be enumerated. Above the zero-field ionization threshold, the system is rather simple. There is only one closed orbit, called the parallel orbit, which goes out from the Coulomb center along the electric field and later returns to the center. This orbit is unstable. Nevertheless, the orbit and its repetitions produce recurrences in time, that lead to oscillations in the absorption spectrum. Comparisons between theory and experiments show good agreement.;Below threshold, the parallel orbit becomes stable and, as the energy decreases, many other orbits bifurcate out of it. These closed orbits form orderly patterns, and the associated recurrences are most clear if the absorption spectrum is measured using a scaled-variables method and its Fourier transform, the recurrence spectrum, is computed. Bifurcations are readily observable in such spectra because they create new recurrences, and because at a bifurcation, observed recurrences are especially strong. We predicted the sequence of bifurcations, and the energies at which each would occur, in a paper published early in 1994. Recently, experimental measurements carried out at M.I.T. have confirmed these predictions.;Near a bifurcation, the original form of closed-orbit theory diverges, since a bifurcation is correlated with a focus of classical orbits. An improved closed-orbit theory is derived by using the uniform semiclassical approximation, and by extending the wave function from the real three dimensional space into a four dimensional space. In this extended space, the orbits of the electron near the nucleus are straight lines. These lines are arranged so that they form a cusped caustic, and furthermore they form cylindrical foci in two independent planes in the four-dimensional space. We derive a formula for the wave function associated with this cylindrically focused cusp, and make a new prediction of the behavior of the recurrence spectrum near a bifurcation. These predictions are compared with new experimental results. We find that the improved form of closed orbit theory accurately accounts for experimental measurements both globally and locally.
© The Author
Gao, Jing, "Photoabsorption spectra of hydrogen and alkali atoms in electric fields" (1994). Dissertations, Theses, and Masters Projects. Paper 1539623858.