{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/70200"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/70200","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Accurate Quantum Mechanical Decoupling Approximations for Molecular Scattering Theory","abstract":"Recent work is reviewed on the theory of angular momentum decoupling approximations in inelastic molecular scattering theory. It is shown that the failure of these approximations is more extensive than previously believed, particularly for completely state-selected m-transitions. A new method is presented for systematically improving these approximations, which recouples the approximate solutions to first-order using the generalized distorted wave Born approximation. As an illustration of the generality of this new recoupling technique, formulae are derived for the corrections to the centrifugal decoupling, the energy sudden and the infinite-order sudden approximations. Completely state-selected differential and integral cross sections are computed under the centrifugal decoupling approximation and its first-order distorted wave correction for Ne + HD scattering at a total energy of 31.5 meV. Five choices of the partial wave decoupling parameter (including the three known ones) are studied. The numerical results show that with the partial wave parameter chosen to be the arithmetic mean of the initial and final l-quantum numbers, the corrected centrifugal decoupling approximation gives significantly more accurate inelastic differential and integral state-selected cross sections than its uncorrected counterpart.","abstract_html":"Recent work is reviewed on the theory of angular momentum decoupling approximations in inelastic molecular scattering theory. It is shown that the failure of these approximations is more extensive than previously believed, particularly for completely state-selected m-transitions. A new method is presented for systematically improving these approximations, which recouples the approximate solutions to first-order using the generalized distorted wave Born approximation. As an illustration of the generality of this new recoupling technique, formulae are derived for the corrections to the centrifugal decoupling, the energy sudden and the infinite-order sudden approximations. Completely state-selected differential and integral cross sections are computed under the centrifugal decoupling approximation and its first-order distorted wave correction for Ne + HD scattering at a total energy of 31.5 meV. Five choices of the partial wave decoupling parameter (including the three known ones) are studied. The numerical results show that with the partial wave parameter chosen to be the arithmetic mean of the initial and final l-quantum numbers, the corrected centrifugal decoupling approximation gives significantly more accurate inelastic differential and integral state-selected cross sections than its uncorrected counterpart.","abstract_has_math":false,"creators":["Mclenithan, Kelly Daniel"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Chemistry","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-15T23:17:47Z","date_published":"2014-12-15T23:17:47Z","updated_at":"2026-07-22T22:26:02Z","subjects":["Chemistry, Physical"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8302933"],"render_values":[{"text":"(UMI)AAI8302933","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/70200","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Mclenithan, Kelly Daniel"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-15T23:17:47Z","10000-01-01","1982"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Chemistry"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Chemistry, Physical"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/70200","(UMI)AAI8302933"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Recent work is reviewed on the theory of angular momentum decoupling approximations in inelastic molecular scattering theory. It is shown that the failure of these approximations is more extensive than previously believed, particularly for completely state-selected m-transitions. A new method is presented for systematically improving these approximations, which recouples the approximate solutions to first-order using the generalized distorted wave Born approximation. As an illustration of the generality of this new recoupling technique, formulae are derived for the corrections to the centrifugal decoupling, the energy sudden and the infinite-order sudden approximations. Completely state-selected differential and integral cross sections are computed under the centrifugal decoupling approximation and its first-order distorted wave correction for Ne + HD scattering at a total energy of 31.5 meV. Five choices of the partial wave decoupling parameter (including the three known ones) are studied. The numerical results show that with the partial wave parameter chosen to be the arithmetic mean of the initial and final l-quantum numbers, the corrected centrifugal decoupling approximation gives significantly more accurate inelastic differential and integral state-selected cross sections than its uncorrected counterpart.","Made available in DSpace on 2014-12-15T23:17:47Z (GMT). No. of bitstreams: 1 8302933.pdf: 23218920 bytes, checksum: e0e11c95a59d4c8ef1323b4422ccbed9 (MD5) Previous issue date: 1982","Embargo set by: Seth Robbins for item 70366 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","822 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1982."]},{"key":"dc:title","label":"Title","values":["Accurate Quantum Mechanical Decoupling Approximations for Molecular Scattering Theory"]}]}],"canonical_facts":{"dc:creator":["Mclenithan, Kelly Daniel"],"dc:date":["2014-12-15T23:17:47Z","10000-01-01","1982"],"dc:description":["Recent work is reviewed on the theory of angular momentum decoupling approximations in inelastic molecular scattering theory. It is shown that the failure of these approximations is more extensive than previously believed, particularly for completely state-selected m-transitions. A new method is presented for systematically improving these approximations, which recouples the approximate solutions to first-order using the generalized distorted wave Born approximation. As an illustration of the generality of this new recoupling technique, formulae are derived for the corrections to the centrifugal decoupling, the energy sudden and the infinite-order sudden approximations. Completely state-selected differential and integral cross sections are computed under the centrifugal decoupling approximation and its first-order distorted wave correction for Ne + HD scattering at a total energy of 31.5 meV. Five choices of the partial wave decoupling parameter (including the three known ones) are studied. The numerical results show that with the partial wave parameter chosen to be the arithmetic mean of the initial and final l-quantum numbers, the corrected centrifugal decoupling approximation gives significantly more accurate inelastic differential and integral state-selected cross sections than its uncorrected counterpart.","Made available in DSpace on 2014-12-15T23:17:47Z (GMT). No. of bitstreams: 1 8302933.pdf: 23218920 bytes, checksum: e0e11c95a59d4c8ef1323b4422ccbed9 (MD5) Previous issue date: 1982","Embargo set by: Seth Robbins for item 70366 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","822 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1982."],"dc:identifier":["http://hdl.handle.net/2142/70200","(UMI)AAI8302933"],"dc:subject":["Chemistry, Physical"],"dc:title":["Accurate Quantum Mechanical Decoupling Approximations for Molecular Scattering Theory"],"dc:type":["text"],"thesis:degree_discipline":["Chemistry"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:02Z"}