Excitation of Hydrogen Atoms by Fast Protons

Date of Award

Winter 1-1970

Document Type


Degree Name

Master of Science (MS)



Committee Director

G. S. Khandelwal

Committee Member

Ian D. Howard

Committee Member

Grayson. H. Rayborn

Call Number for Print

Special Collections LD4331.P48F57


In this thesis a theoretical study is made of excitation of hydrogenic atom by charged particles such as protons or electrons. The approximation to the cross section for an inelastic scattering process is obtained under the following radically simplifying assumptions. The projectile is represented in its initial and final state by plane waves. All distortions are neglected whether they originate in an inelastic process or an elastic deflections of the charged particle by the nucleus. The perturbation of the atomic orbits between which the projectile induces transitions is neglected. Nonrelativistic hydrogenic wave functions are used for the electronic states. In this so called Plane Wave Born Approximation (PWBA), an expression for the radial integral associated with a transition from an initial state n' ' m' to a final state nm is developed as a power series of the momentum transferred by the incident charged particle to the hydrogenic atom. Explicit expressions for the atomic form factor as a function of the momentum transfer associated with the transitions from 2s and 2p states of the hydrogen atom are obtained. Formulas for the coefficients in the series expansion are obtained for allowed transitions (2s-np,2p-ns,2p-nd) and the forbidden transitions (2s-ns,2s-nd,2s-nf,2p-np) . A comparison is made between the form factors for ls-2s and 2s-3p transitions in the neighborhood of q2 = o. Good agreement has been found between the exact and series formulas for low momentum transfer.


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