Nuclear pairing reduction due to rotation and blocking

X. Wu (吴熙), Z. H. Zhang (张振华), J. Y. Zeng (曾谨言), and Y. A. Lei (雷奕安)

Phys. Rev. C 83, 034323 – Published 29 March 2011

Abstract

Nuclear pairing gaps of normally deformed and superdeformed nuclei are investigated using the particle-number-conserving (PNC) formalism for the cranked shell model, in which the blocking effects are treated exactly. Both rotational frequency $ω$ dependence and seniority (number of unpaired particles) $ν$ dependence of the pairing gap $Δ̃$ are investigated. For the ground-state bands of even-even nuclei, PNC calculations show that, in general, $Δ̃$ decreases with increasing $ω$ , but the $ω$ dependence is much weaker than that calculated by the number-projected Hartree-Fock-Bogolyubov approach. For the multiquasiparticle bands (seniority $ν > 2$ ), the pairing gaps stay almost $ω$ independent. As a function of the seniority $ν$ , the bandhead pairing gaps $Δ̃ (ν, ω = 0)$ decrease slowly with increasing $ν$ . Even for the highest seniority $ν$ bands identified so far, $Δ̃ (ν, ω = 0)$ remains greater than $70 %$ of $Δ̃ (ν = 0, ω = 0)$ .

Received 2 June 2010

DOI:https://doi.org/10.1103/PhysRevC.83.034323

Authors & Affiliations

X. Wu (吴熙)^1,2, Z. H. Zhang (张振华)^1,3, J. Y. Zeng (曾谨言)¹, and Y. A. Lei (雷奕安)^1,*

¹State Key Lab of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China
²School of Computing, University of Southern Mississippi, Hattiesburg, Mississippi 39401, USA
³Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China

^*yalei@pku.edu.cn

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Vol. 83, Iss. 3 — March 2011

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Figure 1
The MOIs and pairing gaps $Δ̃$ for the ground-state bands of ${}^{168}{Yb}$ and ${}^{168}{Hf}$ . (a) The experimental MOIs [30, 31] are denoted by the solid circle $•$ , and the calculated MOIs by the PNC method are denoted by solid lines. The Nilsson parameters ( $κ, μ$ ) and deformation ( $ɛ_{2}, ɛ_{4}$ ) are taken from [32, 33]. The monopole and quadrupole pairing strengths for protons and neutrons are adopted to reproduce the odd-even differences in nuclear binding energies, $G_{n} = 0.30$ , $G_{2 n} = 0.010$ , $G_{p} = 0.29$ for ${}^{168}{Yb}$ ; $G_{n} = 0.39$ , $G_{p} = 0.35$ for ${}^{168}{Hf}$ . (b) The PNC calculated pairing gaps for protons (neutrons) are denoted by solid (dashed) lines.Reuse & Permissions
Figure 2
MOIs of four low-lying seniority $ν = 1$ bands in ${}^{177}{Ta}$ . The experimental MOIs [38] are denoted by $•$ $(α = 1 / 2)$ and $ˆ$ $(α = - 1 / 2)$ , respectively. The calculated MOIs by the PNC method are denoted by solid lines ( $α = 1 / 2$ ) and dotted lines ( $α = - 1 / 2$ ), respectively. The Nilsson parameters ( $κ, μ$ ) in [32] are slightly adjusted to reproduce the bandhead energies of the 1-qp bands. For protons, $κ_{4} = 0.060$ ( $N = 4$ ), $κ_{5} = 0.061$ ( $N = 5$ ), $μ_{4} = 0.55$ , and $μ_{5} = 0.69$ . For neutrons, $κ_{5} = 0.066$ , $κ_{6} = 0.058$ , $μ_{5} = 0.49$ , and $μ_{6} = 0.40$ . The deformation parameters ( $ɛ_{2}, ɛ_{4}$ ) $=$ (0.24, 0.04) are from [33], i.e., an average of the neighboring even-even Hf and W isotopes. The effective pairing interaction strengths for both protons and neutrons, $G_{n} = 0.26$ MeV, $G_{p} = 0.26$ MeV, are determined by the experimental odd-even differences in nuclear binding energies.Reuse & Permissions
Figure 3
The proton pairing gaps ${Δ̃}_{p}$ for the $ν_{p} = 1, 3$ bands in ${}^{177}{Ta}$ (dotted lines) and $ν_{p} = 0, 2, 4$ configurations in ${}^{178}W$ (solid lines). ${}^{177}{Ta}$ : $ν_{p} = 1$ band (gsb), $π 7 / 2^{+} [404]$ ; $ν_{p} = 3$ , $K^{π} = 17 / 2^{+}$ band at 1523 keV [38], $π^{3} 17 / 2^{+} (7 / 2^{+} [404] \otimes 9 / 2^{-} [514] \otimes 1 / 2^{-} [541])$ . ${}^{178}W$ : gsb, $ν_{p} = 0$ , $K^{π} = 0^{+}$ ; $ν_{p} = 2$ configuration $π^{2} 8^{-} (7 / 2^{+} [404] \otimes 9 / 2^{-} [514])$ in $K^{π} = 15^{+}$ ( $π^{2} 8^{-} \otimes ν^{2} 7^{-}$ ) band at 3653 keV; $ν_{p} = 4$ configuration $π^{4} 11^{-} (7 / 2^{+} [404] \otimes 5 / 2^{+} [402] \otimes 9 / 2^{-} [514] \otimes 1 / 2^{-} [541])$ in $K^{π} = 18^{+}$ ( $π^{4} 11^{-} \otimes ν^{2} 7^{-}$ ) band at 4878 keV [37, 39].Reuse & Permissions
Figure 4
The MOIs and pairing gaps of the gsb of ${}^{238}U$ and ${}^{253}{No}$ . (a) The experimental MOIs [40, 41] are denoted by $•$ ( $α = 0, 1 / 2$ ) and $ˆ$ ( $α = - 1 / 2$ ). The calculated MOIs by the PNC method are denoted by solid lines ( $α = 0, 1 / 2$ ) and dotted lines ( $α = - 1 / 2$ ). The Nilsson parameters ( $κ, μ$ ) are taken from [32] for both ${}^{238}U$ and ${}^{253}{No}$ . Deformations ( $ɛ_{2}, ɛ_{4}) = (0.21, - 0.04)$ of ${}^{238}U$ are taken from [33]. For ${}^{253}{No}$ , the quadrupole deformation parameters for the neighbor even-even nuclei are deduced as $β_{2} = 0.28 \pm 0.02$ from the experiment [42]. Here we choose $ɛ_{2} = 0.26$ and $ɛ_{4} = 0.01$ in our calculation for ${}^{253}{No}$ . To reproduce the experimental odd-even difference in binding energies and the $ω$ dependence of MOIs, it seems that a small amount of quadrupole pairing interaction is necessary, i.e., $G_{n} = 0.29$ MeV, $G_{2 n} = 0.015$ MeV, $G_{p} = 0.32$ MeV, $G_{2 p} = 0.040$ MeV for ${}^{238}U$ ; $G_{n} = 0.22$ MeV, $G_{2 n} = 0.010$ MeV, $G_{p} = 0.26$ MeV, $G_{2 p} = 0.010$ MeV for ${}^{253}{No}$ . (b) The PNC calculated pairing gaps ${Δ̃}_{p}$ ’s ( ${Δ̃}_{n}$ ’s) for the ground-state bands of ${}^{238}U$ and ${}^{253}{No}$ are denoted by solid (dashed) lines.Reuse & Permissions
Figure 5
The pairing gaps of the SD bands in Hg isotopes calculated by the PNC formalism. The Nilsson level schemes are taken from [50]. ${}^{193}{Hg}$ (1): 1-quasineutron SD band, $ν 5 / 2^{-} [512], α = - 1 / 2$ ; ${}^{193}{Hg}$ (2b): 1-quasineutron SD band, $ν 9 / 2^{+} [624], α = 1 / 2$ . ${}^{194}{Hg}$ (1): quasivacuum SD band ( $α = 0$ ); ${}^{194}{Hg}$ (2): 2-quasineutron SD band $ν^{2} 7^{-} (5 / 2^{-} [512] \otimes 9 / 2^{+} [624]), α = 0$ .Reuse & Permissions

Physical Review C

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