https://doi.org/10.1140/epjp/s13360-025-06585-6
Regular Article
Empirical rules for three-quasiparticle quadruplets: role of Gallagher–Moszkowski doublets
1
Department of Physics, Akal University Talwandi Sabo, 151302, Bathinda, Punjab, India
2
AINST, Amity University, 201313, Noida, India
Received:
12
April
2025
Accepted:
24
June
2025
Published online:
4
July
2025
In this article, we present an extension of well-known empirical rules proposed by Gallagher–Moszkowski for two-quasiparticle (2qp) doublets, to the more complex three-quasiparticle (3qp) quadruplets observed in odd-A nuclei. To achieve the set objective, we undertake an extensive literature review and compiled the data of 223 three-quasiparticle bands observed in the range: 63 ≤ Z ≤ 78, 88 ≤ N ≤ 112 and 153 ≤ A ≤ 187. After critical evaluation of the compiled experimental data and comparison with semi-empirical model calculations, we proposed eight generalized GM rules which determine energy ordering among various members of given three-quasiparticle quadruplets based on nnn/ppp and nnp/ppn types of 3qp configurations. The validity of proposed rules is tested for 16 nnn/ppp and nnp/ppn three-quasiparticle quadruplets. Building on the success of these rules in determining the energy ordering of three-quasiparticle quadruplets, we extended our predictions to a total of 48 nnn/ppp and nnp/ppn quadruplets. The mystery surrounding energy ordering in three-quasiparticle quadruplets has at last been unraveled. The rules proposed in the present calculations will be useful for experimentalists in determining the locations of various three-quasiparticle bandheads. Among the 223 documented three-quasiparticle rotational structures, no configuration includes all four bandheads as confirmed members of a single quadruplet, leaving this as an unresolved question for experimentalists. The role of unperturbed GM splitting energies in determining the above-said energy ordering of the members of a given quadruplet is also highlighted.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
