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Register a new userRotational Properties of the Odd-$Z$ Transfermium Nucleus $^{255}$Lr by a Particle-number-conserving Method in the Cranked Shell Model
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Experimentally observed ground state band based on the $1/2^{-}[521]$ Nilsson state and the first exited band based on the $7/2^{-}[514]$ Nilsson state in the odd-$Z$ nucleus $^{255}$Lr are studied by the cranked shell model (CSM) with the paring correlations treated by the particle-number-conserving (PNC) method. This is the first time the detailed theoretical investigations being performed on these rotational bands. Both the experimental kinematic and dynamic moment of inertia ($mathcal{J}^{(1)}$ and $mathcal{J}^{(2)}$) versus rotational frequency are reproduced quite well by the PNC-CSM calculations. By comparing the theoretical kinematic moment of inertia $mathcal{J}^{(1)}$ with the experimental ones extracted from different spin assignments, the spin $17/2^{-}rightarrow13/2^{-}$ is assigned to the lowest-lying $196.6(5)$ keV transition of the $1/2^{-}[521]$ band, and $15/2^{-}rightarrow11/2^{-}$ to the $189(1)$ keV transition of the $7/2^{-}[514]$ band, respectively. The proton $N=7$ major shell is included in the calculations. The intruder of the high$-j$ low$-Omega$ orbitals $1j_{15/2}$ $ (1/2^{-}[770])$ at the high spin leads to the band-crossing at $hbaromegaapprox0.20$ ($hbaromegaapprox0.25$) MeV for the $7/2^{-}[514]$ $alpha=-1/2$ ($alpha=+1/2$) band, and at $hbaromegaapprox0.175$ MeV for the $1/2^{-}[521]$ $alpha=-1/2$ band, respectively. Further investigations show that the band-crossing frequencies are quadrupole deformation dependent.
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The particle-number conserving (PNC) method in the framework of cranked shell model (CSM) is developed to deal with the reflection-asymmetric nuclear system by applying the $S_x$ symmetry. Based on an octupole-deformed Nilsson potential, the alternating-parity bands in element{236,238}{U} and element{238,240}{Pu} are investigated. The experimental kinematic moments of inertia (MoI) and the angular momentum alignments of all studied bands are reproduced well in the PNC-CSM calculations. The striking difference of rotational behaviors between U and Pu isotopes can be linked to the strength of octupole correlations. The upbendings of the alternating-parity bands inelement{236,238}{U} are due to the alignments of pairs of nucleons occupying $ u g_{9/2}$, $pi f_{7/2}$ orbitals and $ u j_{15/2}$, $pi i_{13/2}$ high-$j$ intruder orbitals. Particularly, the interference terms of nucleon occupying the octupole-correlation pairs of $ u^2 j_{15/2} g_{9/2}$ and of $pi^2 i_{13/2} f_{7/2}$ give a very important contribution to the suddenly gained alignments.
The recently observed two and four-quasiparticle high-spin rotational bands in the odd-odd nuclei $^{166, 168, 170, 172}$Re are investigated using the cranked shell model with pairing correlations treated by a particle-number conserving method. The experimental moments of inertia and alignments can be reproduced well by the present calculation if appropriate bandhead spins and configurations are assigned for these bands, which in turn confirms their spin and configuration assignments. It is found that the bandhead spins of those two rotational bands observed in $^{166}$Re~[Li {it et al.}, Phys. Rev. C 92 014310 (2015)] should be both increased by $2hbar$ to get in consistent with the systematics of the experimental and calculated moments of inertia for the same configurations in $^{168, 170, 172}$Re. The variations of the backbendings/upbendings with increasing neutron number in these nuclei are investigated. The level crossing mechanism is well understood by analysing the variations of the occupation probabilities of the single-particle states close to the Fermi surface and their contributions to the angular momentum alignment with rotational frequency. In addition, the influence of the deformation driving effects of the proton $1/2^-[541]$ ($h_{9/2}$) orbtial on the level crossing in $^{172}$Re is also discussed.
The newly observed isomer and ground-state band in the odd-Z neutron-rich rare-earth nucleus $^{163}$Eu are investigated by using the cranked shell model (CSM) with pairing treated by the particle-number conserving (PNC) method. This is the first time detailed theoretical investigations are performed of the observed $964(1)$ keV isomer and ground-state rotational band in $^{163}$Eu. The experimental data are reproduced very well by the theoretical results. The configuration of the $964(1)$ keV isomer is assigned as the three-particle state $frac{13}{2}^{-}( ufrac{7}{2}^{+}[633]otimes ufrac{1}{2}^{-}[521]otimespifrac{5}{2}^{+}[413]$). More low-lying multi-particle states are predicted in $^{163}$Eu. Due to its significant effect on the nuclear mean field, the high-order $varepsilon_{6}$ deformation plays an important role in the energy and configuration assignment of the multi-particle states. Compared to its neighboring even-even nuclei $^{162}$Sm and $^{164}$Gd, there is a $10%sim15%$ increase of $J^{(1)}$ of the one-particle ground-state band in $^{163}$Eu. This is explained by the pairing reduction due to the blocking of the nucleon on the proton $pifrac{5}{2}^{+}$[413] orbital in $^{163}$Eu.
A cranked shell model approach for the description of rotational bands in $Napprox Z$ nuclei is formulated. The isovector neutron-proton pairing is taken into account explicitly. The concept of spontaneous breaking and subsequent restoration of the isospin symmetry turns out to be crucial. The general rules to construct the near yrast-spectra for rotating nuclei are presented. For the model case of particles in a j-shell, it is shown that excitation spectra and the alignment processes are well described as compared to the exact shell model calculation. Realistic cranked shell model calculations are able to describe the experimental spectra of $^{72,73}$Kr and $^{74}$Rb isotopes.
We calculate the isospin-mixing parameter for several Tz=-1, Tz=0 and Tz=1 nuclei from Mg to Sn in the particle-number conserving Higher Tamm-Dancoff approach taking into account the pairing correlations. In particular we investigate the role of the Coulomb interaction and the |Tz|=1 pairing correlations. To do so the HTDA approach is implemented with the SIII Skyrme effective nucleon-nucleon interaction in the mean-field channel and a delta interaction in the pairing channel. We conclude from this investigation that the pairing correlations bring a large contribution to isospin-symmetry breaking, whereas the Coulomb interaction turns out to play a less important role. Moreover we find that the isospin-mixing parameters for Tz=-1 and Tz=1 nuclei are comparable while they are about twice as large for Tz=0 nuclei (between 3% and 6%, including doubly magic nuclei).
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