Multiple triaxial bands in ${}^{138}\mathrm{Nd}$

High-spin states in ${}^{138}\mathrm{Nd}$ were investigated by using the ${}^{48}\mathrm{Ca}+{}^{94}\mathrm{Zr}$ reaction and $\gamma$-ray coincidences were acquired with the GASP spectrometer. A rich level scheme was developed including 14 new bands of quadrupole transitions at very high spins. Linking transitions connecting 11 high-spin bands to low-energy states have been observed. Calculations based on the cranked Nilsson–Strutinsky formalism have been used to assign configurations to the observed bands. The main result of these calculations is that all 14 bands exhibit a stable triaxial deformation up to the highest observed spins, giving strong support to the existence of a triaxial minimum with normal deformation and positive asymmetry parameter in nuclei with a few holes in the $N=82$ shell closure.

Figure 1

Partial level scheme of ${}^{138}\mathrm{Nd}$ showing the high-spin bands.

Figure 2

Doubly gated sum spectra for the bands T1–T3 in ${}^{138}\mathrm{Nd}$. The gates were set on selected transitions of each band. The transitions marked with asterisks represent the members of the band.

Figure 3

The same as Fig. 2, but for bands T4–T6 in ${}^{138}\mathrm{Nd}$.

Figure 4

The same as Fig. 2, but for bands T7–T11 in ${}^{138}\mathrm{Nd}$. The peaks marked with “#” are contaminants from other nuclei.

Figure 5

The same as Fig. 2, but for bands T12–T14 in ${}^{138}\mathrm{Nd}$.

Figure 6

The energy of the observed and linked to low-lying states high-spin bands in ${}^{138}\mathrm{Nd}$ are drawn relative to a rotating liquid drop energy. In addition, the HD band [22] is drawn at an arbitrary excitation energy and with tentative spin values. Full lines are used for positive-parity states and dashed lines for negative-parity states; closed symbols are used for the signature $\alpha =0$ and open symbols for $\alpha =1$. Dotted lines are used for the bands T5 and T6 which are drawn with two alternative spin values specified in the legend.

Figure 7

The spin values $I$ of the observed high-spin bands in ${}^{138}\mathrm{Nd}$ vs transition energy $E_{\gamma }$. For bands T5 and T6, where two spin values are suggested, only the lower values are used, with the “band-head spin” specified in the legend. The unlinked bands T12–T14 (and HD) are included with tentative spin values.

Figure 8

Calculated potential-energy surfaces with $(\pi ,\alpha )=(-,0)$ for ${}^{138}\mathrm{Nd}$. The contour-line separation is 0.25 MeV.

Figure 9

Single-neutron orbitals at no rotation and with $A=150$ Nilsson parameters drawn first as a function of ${\varepsilon }_2$ at prolate shape $\left(\gamma =0^{\circ }\right)$, then as function of $\gamma$ at a fixed quadrupole deformation ${\varepsilon }_2=0.2$, and finally at oblate shape $\left(\gamma ={60}^{\circ }\right)$ as function of decreasing ${\varepsilon }_2$ back to spherical shape. Full (dashed) lines are used for positive-parity (negative-parity) orbitals. Colors are used to make an approximate distinction between orbitals of high-$j$ and low-$j$ character, respectively. Note the interaction between the $n_z=0,N=4$ orbitals on the prolate side $\left(\gamma \approx 0^{\circ }\mathrm{to}{20}^{\circ }\right)$ and the interaction between the $n_z=0,h_{11/2}$ orbitals on the oblate side $\left(\gamma \approx {40}^{\circ }\mathrm{to}{60}^{\circ }\right)$ leading to the triaxial $N=78$ gap.

Figure 10

Energies relative to a standard rotating liquid drop reference calculated for configurations with negative parity and four high-$j$ particles, i.e., two or three protons in $h_{11/2}$ and two or one neutrons excited above $N=82$. The labeling of the configurations is explained in the text. With an odd number of $h_{11/2}$ neutron holes, two signature degenerate bands are formed which are shown by the same color and symbols. Configurations assigned to the observed bands are shown by thicker lines and larger symbols. The negative-parity yrast lines of both signatures at triaxial shape for $\gamma >0^{\circ }$ are shown by dotted lines. Note that the observed bands are generally predicted to be rather high above yrast in most of their observed spin range.

Figure 11

Calculated configurations at triaxial shape $({\varepsilon }_2,\gamma )\approx (0.27,{35}^{\circ })$ for 16 different parity-signature combinations are drawn relative to the rotating liquid drop energy. The left and right panels are for positive and negative parity, respectively. The energy differences between the CNS and CNSB results, interpreted as pairing corrections, are shown in panels (c) and (f). The magenta lines denote the average pairing corrections.

Figure 12

The observed bands T1, T2, T3, and T4 in ${}^{138}\mathrm{Nd}$ are shown relative to a rotating liquid drop reference in the upper panel, with the calculated configurations assigned to these bands shown relative to the same reference in the middle panel. Aligned states are encircled. In the calculated bands, an average pairing energy (see Fig. 11) is added. The lower panel shows the difference between calculations and experiment. Full (open) lines are used for positive (negative) parity and closed (open) symbols for signature $\alpha =0(\alpha =1)$.

Figure 13

Calculated shape trajectories for the configurations assigned to the bands T1, T3, T4, and T8.

Figure 14

Same as Fig. 12 for the bands T5 and T6 with two different spin values and corresponding assignments for the two bands.

Figure 15

Same as Fig. 12 but for the bands T7 and T8. The two observed bands are drawn with their preferred parities, but possible assignments are also presented for the two bands having opposite parity.

Figure 16

Same as Fig. 12 but for the observed bands T9, T10, and T11. In addition to our preferred assignments, two more possible configurations are shown in the middle panel.