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Register a new userSystematic study of $^{9,10,11}$Li with the tensor and pairing correlations
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We make a systematic study of Li isotopes (A=9,10,11) in the tensor optimized shell model for 9Li and treat the additional valence neutrons in the cluster model approach by taking into account the Pauli-blocking effect caused by the tensor and pairing correlations. We describe the tensor correlations in 9Li fully in the tensor-optimized shell model, where the variation of the size parameters of the single particle orbits is essential for getting strong tensor correlations. We have shown in our previous study that in $^{10,11}$Li the tensor and pairing correlations in 9Li are Pauli-blocked by additional valence neutrons, which make the p-shell configurations pushed up in energy. As a result, the $s^2$ valence neutron component increases to reveal the halo structure of 11Li and the inversion phenomenon of the single particle spectrum in 10Li arises. Following the previous study, we demonstrate the reliability of our framework by performing a detailed systematic analysis of the structures of $^{9,10,11}$Li, such as the charge radius, the spatial correlation of halo neutrons of 11Li and the electromagnetic properties of Li isotopes. The detailed effects of the Pauli-blocking on the spectroscopic properties of $^{10,11}$Li are also discussed. It is found that the blocking acts strongly for the 11Li ground state rather than for 10Li and for the dipole excited states of 11Li, which is mainly caused by the interplay between the tensor correlation in 9Li and the halo neutrons. The results obtained in these analyses clearly show that the inert core assumption of 9Li is not realistic to explain the anomalous structures observed in $^{10,11}$Li. For the dipole excitation spectrum of 11Li, the effect of the final state interactions is discussed in terms of the dipole strength function.
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Rotational and deformation dependence of isovector and isoscalar pairing correlations at finite temperature are studied in an exactly solvable cranked deformed shell model Hamiltonian. It is shown that isovector pairing correlations, as expected, decrease with increasing deformation and the isoscalar pairing correlations remain constant at temperature, T=0. However, it is observed that at finite temperature both isovector and isoscalar pairing correlations are enhanced with increasing deformation, which contradict the mean-field predictions. It is also demonstrated that the pair correlations, which are quenched at T=0 and high rotational frequency re-appear at finite temperature. The changes in the individual multipole pairing fields as a function of rotation and deformation are analyzed in detail.
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High-spin rotational bands in rare-earth Er ($Z=68$), Tm ($Z=69$) and Yb ($Z=70$) isotopes are investigated by three different nuclear models. These are (i) the cranked relativistic Hartree-Bogoliubov (CRHB) approach with approximate particle number projection by means of the Lipkin-Nogami (LN) method, (ii) the cranking covariant density functional theory (CDFT) with pairing correlations treated by a shell-model-like approach (SLAP) or the so called particle-number conserving (PNC) method, and (iii) cranked shell model (CSM) based on the Nilsson potential with pairing correlations treated by the PNC method. A detailed comparison between these three models in the description of the ground state rotational bands of even-even Er and Yb isotopes is performed. The similarities and differences between these models in the description of the moments of inertia, the features of band crossings, equilibrium deformations and pairing energies of even-even nuclei under study are discussed. These quantities are considered as a function of rotational frequency and proton and neutron numbers. The changes in the properties of the first band crossings with increasing neutron number in this mass region are investigated. On average, a comparable accuracy of the description of available experimental data is achieved in these models. However, the differences between model predictions become larger above the first band crossings. Because of time-consuming nature of numerical calculations in the CDFT-based models, a systematic study of the rotational properties of both ground state and excited state bands in odd-mass Tm nuclei is carried out only by the PNC-SCM. With few exceptions, the rotational properties of experimental 1-quasiparticle and 3-quasiparticle bands in $^{165,167,169,171}$Tm are reproduced reasonably well.
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