A group theoretic approach to Layzer's 1/2 expansion method is explored. In part this builds on earlier work of Wulfman(2), of Moshinsky et al(l4), and of Sinanoglu, Herrick(lS), and Kellman (16) on second row atoms.
I investigate atoms with electrons in the 3s-3p-3d shell and find:
1. Wulfman's constant of motion accurately predicts configuration mixing for systems with two to eight electrons in the 3s-3p subshell.
2. The same constant of motion accurately predicts configuration mixing for systems with two electrons in the 3s-3p-3d shell.
3. It accurately predicts configuration mixing in systems of high angular momentum L and of high spin angular momentum S containing three electrons in the 3s-3p-3d shell, but gives less accurate results when L and S are both small.
I also show how effective nuclear charges may be calculated by a group theoretical approach. In addition I explore several new methods for expressing electron repulsion operators in terms of operators of the 80(4,2) dynamical group of one - electron atoms.
","abstract_html":"<p>A group theoretic approach to Layzer's 1/2 expansion method is explored. In part this builds on earlier work of Wulfman(2), of Moshinsky et al(l4), and of Sinanoglu, Herrick(lS), and Kellman (16) on second row atoms.</p> <p>I investigate atoms with electrons in the 3s-3p-3d shell and find:</p> <p>1. Wulfman's constant of motion accurately predicts configuration mixing for systems with two to eight electrons in the 3s-3p subshell.</p> <p>2. The same constant of motion accurately predicts configuration mixing for systems with two electrons in the 3s-3p-3d shell.</p> <p>3. It accurately predicts configuration mixing in systems of high angular momentum L and of high spin angular momentum S containing three electrons in the 3s-3p-3d shell, but gives less accurate results when L and S are both small.</p> <p>I also show how effective nuclear charges may be calculated by a group theoretical approach. In addition I explore several new methods for expressing electron repulsion operators in terms of operators of the 80(4,2) dynamical group of one - electron atoms.</p>","abstract_has_math":false,"creators":["Ho, Yanfang"],"institution":null,"degree_name":"Master of Science (M.S.)","degree_level":"Thesis","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Carl E. Wulfman"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1985,"date_issued":"1985-01-01T08:00:00Z","date_published":"1985-01-01T08:00:00Z","updated_at":"2026-07-24T05:36:28Z","subjects":["Atoms Mathematical models","Atomic structure","Quantum theory","Lie groups","Mathematical physics","Physical Sciences and Mathematics"],"languages":[],"rights":[],"rights_urls":["http://rightsstatements.org/vocab/NKC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://scholarlycommons.pacific.edu/uop_etds/487","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Carl E. Wulfman"]},{"key":"dc:creator","label":"Author","values":["Ho, Yanfang"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2018-06-29T09:06:23Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Atoms Mathematical models","Atomic structure","Quantum theory","Lie groups","Mathematical physics","Physical Sciences and Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["http://rightsstatements.org/vocab/NKC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarlycommons.pacific.edu/uop_etds/487"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A group theoretic approach to Layzer's 1/2 expansion method is explored. In part this builds on earlier work of Wulfman(2), of Moshinsky et al(l4), and of Sinanoglu, Herrick(lS), and Kellman (16) on second row atoms.
I investigate atoms with electrons in the 3s-3p-3d shell and find:
1. Wulfman's constant of motion accurately predicts configuration mixing for systems with two to eight electrons in the 3s-3p subshell.
2. The same constant of motion accurately predicts configuration mixing for systems with two electrons in the 3s-3p-3d shell.
3. It accurately predicts configuration mixing in systems of high angular momentum L and of high spin angular momentum S containing three electrons in the 3s-3p-3d shell, but gives less accurate results when L and S are both small.
I also show how effective nuclear charges may be calculated by a group theoretical approach. In addition I explore several new methods for expressing electron repulsion operators in terms of operators of the 80(4,2) dynamical group of one - electron atoms.
"]},{"key":"dc:source","label":"Dc Source","values":["120"]},{"key":"dc:title","label":"Title","values":["Group theoretical analysis of in-shell interaction in atoms"]}]}],"canonical_facts":{"dc:contributor":["Carl E. Wulfman"],"dc:creator":["Ho, Yanfang"],"dc:date.available":["2018-06-29T09:06:23Z"],"dc:description.abstract":["A group theoretic approach to Layzer's 1/2 expansion method is explored. In part this builds on earlier work of Wulfman(2), of Moshinsky et al(l4), and of Sinanoglu, Herrick(lS), and Kellman (16) on second row atoms.
I investigate atoms with electrons in the 3s-3p-3d shell and find:
1. Wulfman's constant of motion accurately predicts configuration mixing for systems with two to eight electrons in the 3s-3p subshell.
2. The same constant of motion accurately predicts configuration mixing for systems with two electrons in the 3s-3p-3d shell.
3. It accurately predicts configuration mixing in systems of high angular momentum L and of high spin angular momentum S containing three electrons in the 3s-3p-3d shell, but gives less accurate results when L and S are both small.
I also show how effective nuclear charges may be calculated by a group theoretical approach. In addition I explore several new methods for expressing electron repulsion operators in terms of operators of the 80(4,2) dynamical group of one - electron atoms.
"],"dc:identifier":["https://scholarlycommons.pacific.edu/uop_etds/487"],"dc:rights":["http://rightsstatements.org/vocab/NKC/1.0/"],"dc:source":["120"],"dc:subject":["Atoms Mathematical models","Atomic structure","Quantum theory","Lie groups","Mathematical physics","Physical Sciences and Mathematics"],"dc:title":["Group theoretical analysis of in-shell interaction in atoms"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science (M.S.)"]},"updated_at":"2026-07-24T05:36:28Z"}