{"id":151,"date":"2015-10-02T23:07:45","date_gmt":"2015-10-02T20:07:45","guid":{"rendered":"http:\/\/magneticmoments.info\/wp\/?p=151"},"modified":"2015-10-02T23:08:49","modified_gmt":"2015-10-02T20:08:49","slug":"paper-the-energy-weighted-sum-rule-and-the-nuclear-radius","status":"publish","type":"post","link":"https:\/\/magneticmoments.info\/wp\/?p=151","title":{"rendered":"[paper] The energy-weighted sum rule and the nuclear radius"},"content":{"rendered":"<p><em> The energy-weighted sum rule and the nuclear radius<\/em><\/p>\n<p>Hans Peter Schr\u00f6der<\/p>\n<p>doi: <a href=\"http:\/\/dx.doi.org\/10.1140\/epja\/i2015-15109-9\">10.1140\/epja\/i2015-15109-9<\/a><\/p>\n<p>The energy-weighted integrated cross-section for photon absorption &#8211;known as sum rule \u03c3\u22121 &#8212; is under certain conditions proportional to the mean square nuclear radius (Levinger, Bethe (Phys. Rev. 78, 115 (1950))). Due to the energy weight factor the low-energy absorption components are emphasized and the dipole transitions in the region of giant resonances contribute enhanced at \u03c3\u22121 . Thus, the cross-section of the full interaction can be replaced in good approximation by the dipole cross-section. Under these aspects, we have calculated \u03c3\u22121 and the radii of various gg-nuclei. For our purpose, we have chosen a simple shell model where the integrals can be solved analytically, and the contributions of uncorrelated functions and correlation corrections can be shown explicitly. The mean square radius as a function of \u03c3\u22121 differs by a factor of 1.5\/0.87 from the previous result of Levinger and Kent (Phys. Rev. 95, 418 (1954)) without correlation corrections. Plotting the function of the correlation corrections g(A) and the uncorrelated function f(A) as a ratio it shows that g(A)\/f(A) tends towards a limit. Finally, our results for the radii of gg-nuclei are in good agreement with recent experiments (I. Angeli, K.P. Marinova, At. Data Nucl. Data Tables 99, 69 (2013)).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The energy-weighted sum rule and the nuclear radius Hans Peter Schr\u00f6der doi: 10.1140\/epja\/i2015-15109-9 The energy-weighted integrated cross-section for photon absorption &#8211;known as sum rule \u03c3\u22121 &#8212; is under certain conditions proportional to the mean square nuclear radius (Levinger, Bethe (Phys.&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[206,4],"tags":[166,5],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p6YIb0-2r","jetpack-related-posts":[{"id":249,"url":"https:\/\/magneticmoments.info\/wp\/?p=249","url_meta":{"origin":151,"position":0},"title":"[paper] In-gas-cell laser spectroscopy of the magnetic dipole moment of the N\u2248126 isotope 199Pt","date":"Jul 11, 2017","format":false,"excerpt":"In-gas-cell laser spectroscopy of the magnetic dipole moment of the N\u2248126 isotope 199Pt Y. 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Both charge and matter radii are\u2026","rel":"","context":"In &quot;radii&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/magneticmoments.info\/wp\/index.php?rest_route=\/wp\/v2\/posts\/151"}],"collection":[{"href":"https:\/\/magneticmoments.info\/wp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magneticmoments.info\/wp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magneticmoments.info\/wp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/magneticmoments.info\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=151"}],"version-history":[{"count":1,"href":"https:\/\/magneticmoments.info\/wp\/index.php?rest_route=\/wp\/v2\/posts\/151\/revisions"}],"predecessor-version":[{"id":152,"href":"https:\/\/magneticmoments.info\/wp\/index.php?rest_route=\/wp\/v2\/posts\/151\/revisions\/152"}],"wp:attachment":[{"href":"https:\/\/magneticmoments.info\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=151"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magneticmoments.info\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=151"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magneticmoments.info\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=151"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}