\"When the Kirkwood superposition approximation for the triplet distribution function is used in the Born-Green equation for the pair distribution function of a liquid, the fourth virial coefficient is given incorrectly. In view of this, two suggestions for improving the approximation have been investigated. A suggestion, due to G.H.A. Cole, that better results could be obtained by using a second-order integro-differential equation of the Born-Green type with the superposition approximation used for both the triplet and quadruplet distribution functions has been investigated, and results for a hard-sphere model show that this method gives considerably less reliable results than those obtained by simply using the superposition approximation in the first- order Born-Green equation. A second approach, due to Ryuzo Abe, based on an expansion of the potential of the mean force in a series involving powers of the density, was found to give exact results when used in the Born-Green equation\"--Abstract, page ii.
","abstract_html":"<p>"When the Kirkwood superposition approximation for the triplet distribution function is used in the Born-Green equation for the pair distribution function of a liquid, the fourth virial coefficient is given incorrectly. In view of this, two suggestions for improving the approximation have been investigated. A suggestion, due to G.H.A. Cole, that better results could be obtained by using a second-order integro-differential equation of the Born-Green type with the superposition approximation used for both the triplet and quadruplet distribution functions has been investigated, and results for a hard-sphere model show that this method gives considerably less reliable results than those obtained by simply using the superposition approximation in the first- order Born-Green equation. A second approach, due to Ryuzo Abe, based on an expansion of the potential of the mean force in a series involving powers of the density, was found to give exact results when used in the Born-Green equation"--Abstract, page ii.</p>","abstract_has_math":false,"creators":["Cochran, Russell V., Jr."],"institution":"University of Missouri at Rolla","degree_name":"Ph. D. in Physics","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-02-10T08:00:00Z","date_published":"2016-02-10T08:00:00Z","updated_at":"2026-07-24T03:19:54Z","subjects":["Physics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsmine.mst.edu/doctoral_dissertations/467","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Cochran, Russell V., Jr."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-02-10T08:00:00Z"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D. in Physics"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Missouri at Rolla"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Physics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsmine.mst.edu/doctoral_dissertations/467"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["\"When the Kirkwood superposition approximation for the triplet distribution function is used in the Born-Green equation for the pair distribution function of a liquid, the fourth virial coefficient is given incorrectly. In view of this, two suggestions for improving the approximation have been investigated. A suggestion, due to G.H.A. Cole, that better results could be obtained by using a second-order integro-differential equation of the Born-Green type with the superposition approximation used for both the triplet and quadruplet distribution functions has been investigated, and results for a hard-sphere model show that this method gives considerably less reliable results than those obtained by simply using the superposition approximation in the first- order Born-Green equation. A second approach, due to Ryuzo Abe, based on an expansion of the potential of the mean force in a series involving powers of the density, was found to give exact results when used in the Born-Green equation\"--Abstract, page ii.
"]},{"key":"dc:title","label":"Title","values":["On the Kirkwood superposition approximation"]}]}],"canonical_facts":{"dc:creator":["Cochran, Russell V., Jr."],"dc:date.available":["2016-02-10T08:00:00Z"],"dc:description.abstract":["\"When the Kirkwood superposition approximation for the triplet distribution function is used in the Born-Green equation for the pair distribution function of a liquid, the fourth virial coefficient is given incorrectly. In view of this, two suggestions for improving the approximation have been investigated. A suggestion, due to G.H.A. Cole, that better results could be obtained by using a second-order integro-differential equation of the Born-Green type with the superposition approximation used for both the triplet and quadruplet distribution functions has been investigated, and results for a hard-sphere model show that this method gives considerably less reliable results than those obtained by simply using the superposition approximation in the first- order Born-Green equation. A second approach, due to Ryuzo Abe, based on an expansion of the potential of the mean force in a series involving powers of the density, was found to give exact results when used in the Born-Green equation\"--Abstract, page ii.
"],"dc:identifier":["https://scholarsmine.mst.edu/doctoral_dissertations/467"],"dc:subject":["Physics"],"dc:title":["On the Kirkwood superposition approximation"],"dc:type":["Dissertation - Open Access"],"thesis:degree_name":["Ph. D. in Physics"],"thesis:institution_name":["University of Missouri at Rolla"]},"updated_at":"2026-07-24T03:19:54Z"}