Rotational properties of the superheavy nucleus ${}^{256}$Rf and its neighboring even-even nuclei in a particle-number-conserving cranked shell model

The ground state band was recently observed in the superheavy nucleus ${}^{256}$Rf. We study the rotational properties of ${}^{256}$Rf and its neighboring even-even nuclei by using a cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method in which the blocking effects are taken into account exactly. The kinematic and dynamic moments of inertia of the ground state bands in these nuclei are well reproduced by the theory. The spin of the lowest observed state in ${}^{256}$Rf is determined by comparing the experimental kinematic moments of inertia with the PNC-CSM calculations and agrees with previous spin assignment. The effects of the high order deformation ${\varepsilon }_6$ on the angular momentum alignments and dynamic moments of inertia in these nuclei are discussed.

Figure 1

The cranked Nilsson levels near the Fermi surface of ${}^{256}$Rf (a) for protons and (b) for 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 deformation parameters ${\varepsilon }_2=0.255$ and ${\varepsilon }_4=0.025$.

Figure 2

The comparison of experimental kinematic MOI's of the GSB in ${}^{256}$Rf with the PNC-CSM calculations. The red up-triangles, black solid circles, and blue down-triangles denote the experimental MOI's extracted by assigning the 161 keV transition as $8^{+}\to 6^{+}$, $6^{+}\to 4^{+}$, and $4^{+}\to 2^{+}$, respectively. The data are taken from Ref. [15].

Figure 3

The experimental (solid circles) and calculated kinematic MOI's $J^{\left(1\right)}$ with (solid black lines) and without (dotted blue lines) pairing correlations for ${}^{256}$Rf and the neighboring even-even nuclei ${}^{250}$Fm [44] and ${}^{252,254}$No [45, 46].

Figure 4

The experimental (solid circles) and calculated (solid black lines) dynamic MOI's $J^{\left(2\right)}$ for ${}^{256}$Rf and the neighboring even-even nuclei ${}^{250}$Fm [44] and ${}^{252,254}$No [45, 46]. The red lines are the results when the high-order deformation parameter ${\varepsilon }_6$ is considered in the PNC-CSM calculation. ${\varepsilon }_6$ for ${}^{250}$Fm, ${}^{252,254}$No, and ${}^{256}$Rf are 0.044, 0.040, 0.042, and 0.038, respectively, which are taken from Ref. [27].

Figure 5

Contribution of each proton and neutron major shell to the angular momentum alignment $\langle \Psi \left|J_x\right|\Psi \rangle$ for the GSB in ${}^{256}$Rf. The left (right) part is the result without (with) ${\varepsilon }_6$ deformation. The diagonal ${\sum }_{\mu }{j}_x\left(\mu \right)$ calculated from Eq. (8) and off-diagonal parts ${\sum }_{\mu <\nu }{j}_x\left(\mu \nu \right)$ from Eq. (9) for the proton $N=6$ and neutron $N=7$ shells are shown by dashed lines.

Figure 6

The single particle levels near the Fermi surface of ${}^{256}$Rf as a function of ${\varepsilon }_6$ deformation. The deformation parameters ${\varepsilon }_2=0.255$ and ${\varepsilon }_4=0.025$. The proton and neutron intruder orbital are denoted by blue and red lines, respectively.