Cranked self-consistent mean-field description of the triaxially deformed rotational bands in ${}^{138}\mathrm{Nd}$

Background: Compared to the axially deformed nuclei, triaxially deformed ones are relatively scarce. This is mainly due to the difficulties in the identification of experimental signatures pertaining to the triaxial degree of freedom. In the nucleus ${}^{138}\mathrm{Nd}$, a number of rotational bands have been observed to have medium or high spin values. They have been interpreted in the macroscopic-microscopic method, to be based on triaxial minima. In particular, for a few configurations, the calculations suggested that a reorientation of the rotational axis may have occurred along the rotational bands.

Purpose: The present work aims at a quantitative description of the experimentally observed bands in ${}^{138}\mathrm{Nd}$, using the cranked self-consistent Skyrme-Hartree-Fock (SHF) method or cranked nuclear density functional theory (DFT). Such a study, which is still missing, will provide alternative interpretations of the structure of the bands and hence, shed new light on the triaxiality issue in connection with experimental data.

Methods: The rotational bands are described using cranked self-consistent mean-field method with SLy4 and SkM* Skyrme energy density functionals (EDFs). For SLy4 EDF, the time-odd pieces are included using Landau parameters (denoted with ${\mathrm{SLy}4}_{\mathrm{L}}$). For SkM* EDF, the local gauge invariance argument has been used to determine the time-odd components of the mean field.

Results: The survey of different configurations near Fermi surface of ${}^{138}\mathrm{Nd}$ results in 12 lowest configurations, at both positive- and negative-$\gamma$ deformations. These are calculated to be the energetically lowest configurations. The results show that, for both EDFs, the rotational states based on positive-$\gamma$ minimum, which is at $\gamma \approx {35}^{\circ }$, are lower than the respective configurations with negative-$\gamma$ deformation. The general trends of the spin-versus-$\omega$ curve, and the energy-versus-spin curve reproduce well those of the experimental data. Further, for the observed bands T1–T8, the calculated results using ${\mathrm{SLy}4}_{\mathrm{L}}$ allows the configurations of the observed bands to be assigned. The calculations predict transitional quadrupole moments, which can be used to compare with future experimental data.

Conclusions: The current cranked self-consistent mean-field calculations of the near-yrast high-spin rotational bands in ${}^{138}\mathrm{Nd}$ reproduce well the experimental data. The results suggest that the experimentally observed bands can be assigned to the calculated bands with various configurations at the positive-$\gamma$ deformation. The predictions of the current calculations are complementary to that of the well-known macroscopic-microscopic calculations, both of which await future experiment to verify.

Figure 1

Single-particle Routhians from cranked SHF calculations with ${\mathrm{SLy}4}_{\mathrm{L}}$ EDF for ${}_{60}{}^{138}\mathrm{Nd}_{78}$. The configuration is pg01 in Table 1. The quadrupole moments for rotational frequencies between $0.4–0.8$ MeV are $(Q_{20},Q_{22})\approx (10.0,5.3)\mathrm{b}$. The levels with positive and negative parities are indicated by black and light gray lines, respectively. The levels with $+i$ and $-i$ signatures are indicated by solid and dashed lines, respectively. One could find the order of the level within its $(\pi ,\rho )$ block at the beginning and the end of each line.

Figure 2

Total Routhian surfaces for ${}^{138}\mathrm{Nd}$ for configuration pg01 in Table 1. Calculations are performed with (a) Skyrme EDF ${\mathrm{SLy}4}_{\mathrm{L}}$, and (b) SkM* at a rotational frequency of 0.6 MeV. Contour lines are 0.4 MeV apart in energy.

Figure 3

The total angular momenta as a function of rotational frequency for different configurations at positive-$\gamma$ values as a function of rotational frequency calculated with ${\mathrm{SLy}4}_{\mathrm{L}}$ and SkM* EDFs. The solid, dashed, dotted, and dotted-dashed lines denote states with $(\pi ,\rho )=(+,0),(+,+1),(-,0),$ and $(-,+1)$, respectively.

Figure 4

The total angular momenta for different configurations at negative $\gamma$ values as a function of rotational frequency calculated with ${\mathrm{SLy}4}_{\mathrm{L}}$ and SkM* EDFs.

Figure 5

Total energies for different configurations at positive $\gamma$ values. Results are calculated with ${\mathrm{SLy}4}_{\mathrm{L}}$ and SkM* EDFs.

Figure 6

Same as Fig. 5, except that the curves correspond to the configurations with negative $\gamma$ values.

Figure 7

Experimental angular momenta as a function of rotational frequency (a) for t1-t8 bands from Ref. [19]. The $\hslash \omega$ values for $E\left(I\right)$ values are evaluated as $\frac{1}{2}{E}_{\gamma }(I+1\to I-1)$. The calculated values (b) are extracted from Figs. 3 and 4. The proposed configuration assignment of the current work for the experimental data are indicated by labeling the respective calculated curve with the same type of markers. See text for the case of t3 and t4 bands.

Figure 8

Total energies as a function of angular momenta extracted from experimental data [16, 19, 29], compared with the ${\mathrm{SLy}4}_{\mathrm{L}}$ shown in Fig. 5. The energy values are plotted with respect to the energy of the ${22}^{+}$ state of T7. The calculated values (b) are extracted from Figs. 5 and 6.