Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)




The alpha particle model presupposes the nucleus to be composed of alpha particles bound by harmonic forces in some equilibrium configuration. These alpha particles may not retain their identity but may exchange like nucleons. This model receives additional support in that alpha nuclei have higher binding energies than neighboring nuclei. Nearly 90% of the total nuclear binding energy is accounted for in the alpha particles. A more objectionable defect arises in the requirement that the amplitudes of vibration be as large as the nucleus itself. This precludes consideration of the alpha particles as distinct entities. The alpha particle model further presumes that the lower excited states arise form excitations of the 3N-3 rotational and vibrational degrees of freedom. With reasonable assumptions, results very nearly in agreement with experiment were obtained. The availability of more recent and complete experimental data prompted a calculation of the lower lying energy levels in this paper. The body-centered octahedron (Oh), the body-centered tetragonal bipyramid (D4h), the distorted body-centered tetragonal bipyramid (D2d), the pentagonal bipyramid (D5h), the one-face centered distorted octahedron (C3v), the one-face centered distorted trigonal prism (D3h) and the body-centered trigonal anti-prism (D3d) are the proposed structures for Si. Finally, the nuclear dimensions and normal vibrations were examined to see whether the values implied in each assignment were reasonable.

Library of Congress Subject Headings

Group theory


Includes bibliographical references



Number of Pages



South Dakota State University