Date of Award
Doctor of Philosophy (PhD)
Gary E. Copeland
James L. Cox
Robert L. Ake
In calculating the radiative recombination cross sections for interstellar H II regions usually only the electric dipole term in the expansion of the interaction Hamiltonian is kept. However, conditions present in these regions permit recombination into highly excited states and the "effective size" of the atom is not much less than the wavelength of the emitted photon. These physical conditions do not meet the requirements for making the dipole approximation. A higher order approximation is to keep an additional term in the expansion of the Hamiltonian, and, therefore, to include contributions of quadrupole transitions in the calculation of the partial recombination cross sections. The dipole and quadrupole transition strengths in closed analytical form are calculated using the Coulomb wave functions because results for any electron energy and for recombination into any angular momentum state of hydrogen are needed.
Several interesting effects are found. First, the transition probabilities are maximum for recombination into specific intermediate angular momentum states at low energies (w < 2eV) and where the free state angular momentum is greater than that of the bound state. Further, that specific intermediate angular momentum state depends on the kinetic energy of the free electron. This behavior is in contrast to the "normal" behavior of the transition strengths where recombination into s states is greatest and decreases with increasing angular momentum. Second, the quadrupole matrix elements vanish for certain velocities of the free electron. This leads to minima in the corresponding quadrupole cross sections when plotted as a function of the free electron's kinetic energy. Finally, the partial cross sections for highly excited states are greater than previously calculated because of the additional effects of the quadrupole transitions.
Fazio, Patricia M..
"Partial Radiative Recombination Cross Sections for Excited States of Hydrogen"
(1984). Doctor of Philosophy (PhD), dissertation, Physics, Old Dominion University, DOI: 10.25777/he2g-0a53