{"id":203784,"date":"2025-01-15T04:17:15","date_gmt":"2025-01-15T10:17:15","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2025\/01\/direct-measurement-of-three-different-deformations-near-the-ground-state-in-an-atomic-nucleus"},"modified":"2025-01-15T04:17:15","modified_gmt":"2025-01-15T10:17:15","slug":"direct-measurement-of-three-different-deformations-near-the-ground-state-in-an-atomic-nucleus","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2025\/01\/direct-measurement-of-three-different-deformations-near-the-ground-state-in-an-atomic-nucleus","title":{"rendered":"Direct measurement of three different deformations near the ground state in an atomic nucleus"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/direct-measurement-of-three-different-deformations-near-the-ground-state-in-an-atomic-nucleus.jpg\"><\/a><\/p>\n<p>Since Morinaga proposed more than six decades ago that the excited \\(0_2^+\\) state in the <sup>16 <\/sup>O nucleus was deformed<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 1\" title=\"Morinaga, H. Interpretation of some of the excited states of 4n self-conjugate nuclei. Phys. Rev. 101254&ndash;258 (1956).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR1\" id=\"ref-link-section-d85232007e1398\">1<\/a><\/sup>, a large body of experimental evidence has been collected to demonstrate that atomic nuclei can possess different shapes<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 2\" title=\"Garrett, P. E., Zieli\u0144ska, M. & Cl\u00e9ment, E. An experimental view on shape coexistence in nuclei. Prog. Part. Nucl. Phys. 124, 103931 (2022).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR2\" id=\"ref-link-section-d85232007e1402\">2<\/a><\/sup>. Apart from the lightest elements, shape coexistence has been suggested to be present in all nuclei<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 3\" title=\"Heyde, K. & Wood, J. L. Nuclear shapes: from earliest ideas to multiple shape coexisting structures. Phys. Scr. 91, 083008 (2016).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR3\" id=\"ref-link-section-d85232007e1406\">3<\/a><\/sup> and the competition of different configurations can result in several different shapes within the same nucleus<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 4\" title=\"Heyde, K. & Wood, J. L. Shape coexistence in atomic nuclei. Rev. Mod. Phys. 83, 1467&ndash;1521 (2011).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR4\" id=\"ref-link-section-d85232007e1411\">4<\/a><\/sup>. Nevertheless, coexistence of three or more total energy minima near the ground state have been predicted to occur in only few regions in the chart of nuclei<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 5\" title=\"M\u00f6ller, P., Sierk, A. J., Bengtsson, R., Sagawa, H. & Ichikawa, T. Global calculation of nuclear shape isomers. Phys. Rev. Lett. 103, 212501 (2009).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR5\" id=\"ref-link-section-d85232007e1415\">5<\/a><\/sup>, but direct experimental proof remained to be obtained. A notable example to date is the <sup>186 <\/sup>Pb<sub>104<\/sub> nucleus, where the three lowest-energy states are 0<sup>+<\/sup> states, each assigned with a different shape \u2013 namely spherical, prolate and oblate<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 6\" title=\"Andreyev, A. N. et al. A triplet of differently shaped spin-zero states in the atomic nucleus 186Pb. Nature 405430&ndash;433 (2000).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR6\" id=\"ref-link-section-d85232007e1425\">6<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 7\" title=\"Ojala, J. et al. Reassigning the shapes of the 0+ states in the 186Pb nucleus. Commun. Phys. 5,213 (2022).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR7\" id=\"ref-link-section-d85232007e1428\">7<\/a><\/sup>. The <sup>186 <\/sup>Pb nucleus lies at the heart of the neutron-deficient Pb region, which has been a subject for numerous theoretical and experimental investigations<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 3\" title=\"Heyde, K. & Wood, J. L. Nuclear shapes: from earliest ideas to multiple shape coexisting structures. Phys. Scr. 91, 083008 (2016).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR3\" id=\"ref-link-section-d85232007e1435\">3<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Julin, R., Grahn, T., Pakarinen, J. & Rahkila, P. In-beam spectroscopic studies of shape coexistence and collectivity in the neutron-deficient Z \u2248 82 nuclei. J. Phys. G Nucl. Part. Phys. 43, 024004 (2016).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR8\" id=\"ref-link-section-d85232007e1438\">8<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Julin, R., Helariutta, K. & Muikku, M. Intruder states in very neutron-deficient Hg, Pb and Po nuclei. J. Phys. G Nucl. Part. Phys. 27, R109 (2001).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR9\" id=\"ref-link-section-d85232007e1438_1\">9<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Egido, J. L., Robledo, L. M. & Rodr\u00edguez-Guzm\u00e1n, R. R. Unveiling the origin of shape coexistence in lead isotopes. Phys. Rev. Lett. 93, 082502 (2004).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR10\" id=\"ref-link-section-d85232007e1438_2\">10<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 11\" title=\"Bender, M., Bonche, P., Duguet, T. & Heenen, P.-H. Configuration mixing of angular momentum projected self-consistent mean-field states for neutron-deficient Pb isotopes. Phys. Rev. C 69, 064303 (2004).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR11\" id=\"ref-link-section-d85232007e1441\">11<\/a><\/sup>. Within the mean-field picture, the total energy curve along the quadrupole deformation shows spherical, prolate and oblate minima close in energy. These minima are related to the spherical <i>Z<\/i> = 82 shell gap, and prolate and oblate deformed gaps in the proton and neutron Nilsson orbitals, respectively. From a shell model perspective, the deformed minima (noted as \\(\\pi (h_9\/2<sup>4<\/sup>)\\) for prolate and \\(\\pi (h_9\/2<sup>2<\/sup>)\\) for oblate in the present work) are expected to have a complex spherical multiparticle-multihole configuration both for protons and neutrons<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Egido, J. L., Robledo, L. M. & Rodr\u00edguez-Guzm\u00e1n, R. R. Unveiling the origin of shape coexistence in lead isotopes. Phys. Rev. Lett. 93, 082502 (2004).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR10\" id=\"ref-link-section-d85232007e1546\">10<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Bender, M., Bonche, P., Duguet, T. & Heenen, P.-H. Configuration mixing of angular momentum projected self-consistent mean-field states for neutron-deficient Pb isotopes. Phys. Rev. C 69, 064303 (2004).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR11\" id=\"ref-link-section-d85232007e1546_1\">11<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 12\" title=\"Bonatsos, D., Karakatsanis, K. E., Martinou, A., Mertzimekis, T. J. & Minkov, N. Islands of shape coexistence from single-particle spectra in covariant density functional theory. Phys. Rev. C 106, 044323 (2022).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR12\" id=\"ref-link-section-d85232007e1549\">12<\/a><\/sup>. Similar competition of different configurations is present in neighbouring isotopes around the <i>N<\/i> = 104 midshell<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 13\" title=\"Heyde, K. et al. A shell-model description of 0+ intruder states in even-even nuclei. Nucl. Phys. A 466189&ndash;226 (1987).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR13\" id=\"ref-link-section-d85232007e1557\">13<\/a><\/sup>. In <sup>188 <\/sup>Pb, in addition to low-lying deformed bands associated with predominantly prolate and oblate shapes<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Heese, J. et al. Evidence for low-lying prolate bands in 188Pb and 186Pb. Phys. Lett. B 302390&ndash;395 (1993).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR14\" id=\"ref-link-section-d85232007e1563\">14<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Dracoulis, G. D. et al. Spectroscopy of $188\\atop{82}Pb_106$$188 82 Pb 106 : evidence for shape coexistence. Phys. Rev. C 69, 054318 (2004).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR15\" id=\"ref-link-section-d85232007e1563_1\">15<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 16\" title=\"Papadakis, P. et al. Direct observation of E0ions in 188Pb through in-beam spectroscopy. Phys. Lett. B 858, 139048 (2024).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR16\" id=\"ref-link-section-d85232007e1566\">16<\/a><\/sup>, three isomeric states assigned with different shapes<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 17\" title=\"Dracoulis, G. D. et al. Spherical and deformed isomers in 188Pb. Phys. Rev. C 60, 014303 (1999).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR17\" id=\"ref-link-section-d85232007e1570\">17<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 18\" title=\"Dracoulis, G. D. et al. Isomer bands, E0ions, and mixing due to shape coexistence in $188\\atop{82}$$188 82 Pb106. Phys. Rev. C 67, 051301 (2003).\" href=\"https:\/\/www.nature.com\/articles\/s42005-024-01928-8#ref-CR18\" id=\"ref-link-section-d85232007e1573\">18<\/a><\/sup> have been proposed.<\/p>\n<p>Intruding structures built on different configurations have also been observed in nuclei in the region around <sup>186 <\/sup>Pb. In fact, the shape staggering of Hg isotopes observed in an isotopic shift experiment was a groundbreaking discovery in the 1970\u2019s<sup>19<\/sup> that triggered multiple investigations into shape coexistence. Laser spectroscopic measurements have examined the onset of ground-state deformation also in the even-mass Po and Pt isotopes<sup>20,21<\/sup>. Since the neutron-deficient Pb isotopes are spherical in their ground states<sup>22,23,24<\/sup>, the onset of deformation in the Pb isotopes can be assessed by investigating the \\(2_1^+\\) states. It is proposed that the heaviest Pb nucleus exhibiting collectivity associated with deformation is <sup>194 <\/sup>Pb<sup>25<\/sup>, whereas in heavier Pb isotopes the underlying configurations of the lowest excited states arise from single-nucleon excitations in the seniority scheme leading to a spherical interpretation<sup>26<\/sup>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Since Morinaga proposed more than six decades ago that the excited \\(0_2^+\\) state in the 16 O nucleus was deformed1, a large body of experimental evidence has been collected to demonstrate that atomic nuclei can possess different shapes2. Apart from the lightest elements, shape coexistence has been suggested to be present in all nuclei3 and [\u2026]<\/p>\n","protected":false},"author":427,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1497],"tags":[],"class_list":["post-203784","post","type-post","status-publish","format-standard","hentry","category-energy"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/203784","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/427"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=203784"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/203784\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=203784"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=203784"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=203784"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}