{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T11:47:25Z","timestamp":1769168845773,"version":"3.49.0"},"reference-count":59,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,2]],"date-time":"2021-08-02T00:00:00Z","timestamp":1627862400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11975009;11975009"],"award-info":[{"award-number":["11975009;11975009"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A diagonalization scheme for the shell model mean-field plus isovector pairing Hamiltonian in the O(5) tensor product basis of the quasi-spin SU\u039b(2) \u2297 SUI(2) chain is proposed. The advantage of the diagonalization scheme lies in the fact that not only can the isospin-conserved, charge-independent isovector pairing interaction be analyzed, but also the isospin symmetry breaking cases. More importantly, the number operator of the np-pairs can be realized in this neutron and proton quasi-spin basis, with which the np-pair occupation number and its fluctuation at the J = 0+ ground state of the model can be evaluated. As examples of the application, binding energies and low-lying J = 0+ excited states of the even\u2013even and odd\u2013odd N\u223cZ ds-shell nuclei are fit in the model with the charge-independent approximation, from which the neutron\u2013proton pairing contribution to the binding energy in the ds-shell nuclei is estimated. It is observed that the decrease in the double binding-energy difference for the odd\u2013odd nuclei is mainly due to the symmetry energy and Wigner energy contribution to the binding energy that alter the pairing staggering patten. The np-pair amplitudes in the np-pair stripping or picking-up process of these N = Z nuclei are also calculated.<\/jats:p>","DOI":"10.3390\/sym13081405","type":"journal-article","created":{"date-parts":[[2021,8,2]],"date-time":"2021-08-02T08:44:11Z","timestamp":1627893851000},"page":"1405","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["np-Pair Correlations in the Isovector Pairing Model"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5118-1719","authenticated-orcid":false,"given":"Feng","family":"Pan","sequence":"first","affiliation":[{"name":"Department of Physics, Liaoning Normal University, Dalian 116029, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9239-024X","authenticated-orcid":false,"given":"Yingwen","family":"He","sequence":"additional","affiliation":[{"name":"Department of Physics, Liaoning Normal University, Dalian 116029, China"}]},{"given":"Lianrong","family":"Dai","sequence":"additional","affiliation":[{"name":"Department of Physics, School of Science, Huzhou University, Huzhou 313000, China"}]},{"given":"Chong","family":"Qi","sequence":"additional","affiliation":[{"name":"Department of Physics, KTH Royal Institute of Technology, 10691 Stockholm, Sweden"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3568-8223","authenticated-orcid":false,"given":"Jerry P.","family":"Draayer","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/0029-5582(64)90658-3","article-title":"Treatment of neutron-proton correlations","volume":"60","author":"Goswami","year":"1964","journal-title":"Nucl. 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