Systematic investigation of the high-$K$ isomers and the high-spin rotational bands in the neutron-rich Nd and Sm isotopes by a particle-number conserving method

The rotational properties of the neutron-rich Nd and Sm isotopes with mass number $A\approx 150$ are systematically investigated by using the cranked shell model with pairing correlations treated by a particle-number conserving method, in which the Pauli blocking effects are taken into account exactly. The two-quasiparticle states in even-even Nd and Sm isotopes with excitation energies lower than 2.5 MeV are systematically calculated. The available data can be well reproduced and some possible two- and four-quasiparticle isomers are also suggested for future experiments. The experimentally observed rotational frequency variations of moments of inertia for the even-even and odd-$A$ nuclei are reproduced very well by the calculations. The effects of high-order deformation ${\varepsilon }_6$ on the two-quasiparticle excitation energies and moments of inertia of the ground-state bands in even-even Nd and Sm isotopes are analyzed in detail. By analyzing the occupation probability $n_{\mu }$ of each cranked Nilsson orbitals near the Fermi surface and the contribution of each major shell to the angular-momentum alignments, the alignment mechanism in these nuclei is understood clearly.

Figure 1

Comparison between the experimental (black solid circles) and calculated (red open circles) neutron odd-even difference $P_n$ for Nd (upper panel) and Sm (lower panel) isotopes. The experimental binding energies are taken from Ref. [60].

Figure 2

The cranked Nilsson levels near the Fermi surface of ${}^{156}\mathrm{Sm}$ for (a) protons and (b) neutrons. The positive (negative) parity levels are denoted by blue (red) lines. The signature $\alpha =+1/2$ ($\alpha =-1/2$) levels are denoted by solid (dotted) lines. The Nilsson parameters ($\kappa$ and $\mu$) are taken as the traditional values [55]. The deformation parameters ${\varepsilon }_2=0.258$, ${\varepsilon }_4=-0.053$, and ${\varepsilon }_6=0.038$ are taken from Ref. [57]. In addition, the neutron orbital $\nu 5/2^{+}\left[642\right]$ is shifted upwards slightly by $0.07\hslash {\omega }_0$ to reproduce the experimental level sequence.

Figure 3

Experimental (solid circles) and calculated (solid black lines) kinematic MOIs $J^{\left(1\right)}$ for the GSBs in even-even Nd and Sm isotopes from $N=92$ to $N=100$. The data are taken from Refs. [12, 16, 22]. The calculated results without high-order deformation ${\varepsilon }_6$ are also shown as red lines.

Figure 4

Occupation probability $n_{\mu }$ of each orbital $\mu$ (including both $\alpha =\pm 1/2$) near the Fermi surface for the GSBs in Nd isotopes. The top and bottom rows are for protons and neutrons, respectively. The positive-parity (negative-parity) levels are denoted by blue solid (red dotted) lines. The Nilsson levels far above the Fermi surface ($n_{\mu }\sim 0$) and far below ($n_{\mu }\sim 2$) are not shown.

Figure 5

Contribution of each proton (upper panel) and neutron (lower panel) major shell to the angular-momentum alignment $J_x$ for the GSBs in Nd isotones. The diagonal ${\sum }_{\mu }{j}_x\left(\mu \right)$ and off-diagonal parts ${\sum }_{\mu <\nu }{j}_x\left(\mu \nu \right)$ in Eq. (8) from the proton $N=5$ and neutron $N=6$ shells are shown by dotted lines.

Figure 6

The experimental and calculated MOIs of two-qp bands in Nd and Sm isotopes. The experimental MOIs are denoted by full black circles (signature $\alpha =0$) and open circles (signature $\alpha =1$), respectively. The calculated MOIs by the PNC-CSM are denoted by black solid lines (signature $\alpha =0$) and red dotted lines (signature $\alpha =1$), respectively. The data are taken from Refs. [16, 19, 21]. ${\nu }^2{5}^{-}$ and ${\pi }^2{5}^{-}$ denote ${\nu }^{2}5/2^{-}\left[523\right]\otimes 5/2^{+}\left[642\right]$ and ${\pi }^{2}5/2^{+}\left[413\right]\otimes 5/2^{-}\left[532\right]$, respectively.

Figure 7

The experimental and calculated kinematic MOIs $J^{\left(1\right)}$ of the GSBs for odd-$A$ Nd and Sm isotopes. The data are taken from Refs. [17, 58, 59]. The experimental MOIs are denoted by full squares (signature $\alpha =+1/2$) and open squares (signature $\alpha =-1/2$), respectively. The MOIs calculated by the PNC-CSM are denoted by solid lines (signature $\alpha =+1/2$) and dotted lines (signature $\alpha =-1/2$), respectively.

Figure 8

Similar as Fig. 7, but for the excited one-qp bands in odd-$A$ Nd and Sm isotopes. The data are taken from Refs. [14, 17, 18, 59].