Structure of nnn/ppp three quasiparticle quadruplets in odd-A nuclei

Abstract

In the present article, we have explored the nuclear structure of 9 three quasiparticle (3qp) quadruplets arising from the coupling of like particles (nnn/ppp) observed in odd-A ¹⁷⁹Hf, ^175,181Ta, ^177,179,183W, ¹⁸³Re, and ¹⁸⁵Os nuclides and also confirmed the configuration assignment to 3qp quadruplets observed in ^175,177Ta and ¹⁷⁹W nuclides. To accomplish these objectives, we adopted a revised version of semi-empirical model formulation that includes all the necessary physical interactions namely the pairing among nucleons, rotation of even-even core, rotor-particle, particle–particle coupling, irrotational contributions arising from valence nucleons, and residual interactions. These interactions can affect the magnitude of bandhead energies as well as the ordering among different members of given 3qp quadruplet. We obtained an excellent agreement among calculated bandhead energies and corresponding experimental data for all the nine 3qp quadruplets which indicates the versatility and applicability of the present model formulation. Notably, the average deviation in the present model calculations is 110.2 keV, a substantial improvement (> 50%) as compared to the earlier model, which yielded a deviation of 230.3 keV. Inspired from the success of present model calculations, we predicted the bandhead energies of 27 unobserved members of these quadruplets. The validity and reliability of present model calculations are also supported by the fact that the energy ordering among different members of a given 3qp quadruplet satisfies the generalized GM rules except 5/2[402]_π ⊗ 7/2[404]_π ⊗ 9/2[514]_π 3qp configuration observed in ¹⁷⁵Ta and ¹⁸¹Ta nuclides. The observed violation of generalized GM rules in 5/2[402]_π ⊗ 7/2[404]_π ⊗ 9/2[514]_π configuration in both nuclides (¹⁷⁵Ta and ¹⁸¹Ta) is attributed to the rotational perturbation that especially affects the locations of high-K members of a given 3qp quadruplets and in the present case above said rotational perturbation reverse the energy ordering of K^π = 11/2⁻ and K^π = 21/2⁻ bandheads. We also demonstrated the application of the present semi-empirical model calculations in the configuration assignment to 3qp states observed in odd-A nuclei. We confirmed the configuration assignments of energy states at 1551.7 keV, 1522.9 keV, and 1632.0 keV observed in ¹⁷⁵Ta, ¹⁷⁷Ta, and ¹⁷⁹W nuclides, respectively, as K^π = 17/2⁺: 7/2[404]_π ⊗ 9/2[514]_π ⊗ 1/2[541]_π, K^π = 17/2⁺:9/2[514]_π ⊗ 1/2[521]_ν ⊗ 7/2[633]_ν and K^π = 21/2⁺: 9/2[624]_ν ⊗ 7/2[514]_ν ⊗ 5/2[512]_ν 3qp configurations from various probable configurations suggested in literature due to lack of experimental evidence.