Tilted precession bands in ${}^{135}\mathrm{Nd}$

Two new excited bands built on the $\pi h_{11/2}$ configuration have been identified in ${}^{135}\mathrm{Nd}$ in addition to the known $\pi h_{11/2}$ band. The energy spectra of the excited bands and the available electromagnetic transition probabilities are in good agreement with theoretical results obtained using quasiparticle-plus-triaxial-rotor model calculations. The properties of the bands identify them as tilted precession bands instead of wobbling bands. Our results give a new insight into the interpretation of the low-lying bands in odd-$A$ mass nuclei, and can stimulate future studies to address the nuclear triaxiality.

Figure 1

(a) and (b) illustrate rotational bands and the angular momentum generation, respectively, in odd-mass triaxial nuclei with $\mathrm{\Delta }I=1$ nature and $\mathrm{\Omega }=9/2$. (c) and (d) represent such bands with $\mathrm{\Delta }I=2$ nature. The $\mathrm{\Delta }I=1$ bands are labeled by $\left[K_{\perp }\right]$, while the $\mathrm{\Delta }I=2$ bands by $[I-I_{\perp }]$. The symbols $\parallel$ and $\perp$ denote projections along the intermediate axis (the axis with largest MoI) and orthogonal to it (on the long or short axis), respectively. For more information see text.

Figure 2

Schematic illustration of the trajectory of the total angular momentum for transverse coupling of the angular momenta of the valence nucleon and the core. The total angular momentum trajectory is the intersection of the angular momentum sphere (in blue) and the energy ellipsoid (in red). (a)–(c) correspond to the yrast $\mathrm{\Delta }I=1$ band as the spin $I$ increases due to rotation mainly along the intermediate axis. (d)–(f) correspond to the yrast $\mathrm{\Delta }I=2$ band as the spin $I$ increases due to rotation mainly along the long (or short) axis.

Figure 3

Partial level scheme of ${}^{135}\mathrm{Nd}$ relevant for the present work. Known (new) levels and transitions are drawn with black (red) colors, respectively.

Figure 4

Spectra for the bands TiP1 and TiP2 of ${}^{135}\mathrm{Nd}$ showing the newly identified transitions (in red color). The peaks marked with an asterisk are contaminants from ${}^{136}\mathrm{Nd}$.

Figure 5

Polarization spectra measured for the 727-keV, 518-keV ($13/2^{-}\to 11/2^{-}$), and 618-keV transitions in which the perpendicular ($C_V$) and parallel ($C_h$) spectra are marked with blue and red colors, respectively.

Figure 6

Angular distribution figures for the 518-, 618-, and 567-keV interconnecting transitions between the bands TiP1 and D1, and for the 410-keV transition of band TiP1. The angular distributions of the 518-, 618-, 567-, and 410-keV transitions were obtained by gating on the 694-, 594-, 709-, and 518-keV transitions, respectively.

Figure 7

Sketch of the TiP bands, based on the $h_{11/2}$ orbitals with projections on the long nuclear axis of ${\mathrm{\Omega }}_l=9/2$ (left), and ${\mathrm{\Omega }}_l=11/2$ (right), for a Fermi level closer to the ${\mathrm{\Omega }}_l=9/2$ orbital. Each TiP band is labeled with [${\mathrm{\Omega }}_l$, $K_l$].

Figure 8

Calculated excitation energies for the D1 and the TiP bands in ${}^{135}\mathrm{Nd}$ in comparison with experimental data.

Figure 9

Contributions of the basis wave functions labeled with their $h_{11/2}$ singe-particle orbitals and projections $K_l$ on the long axis for the states with $I=9/2$ to 27/2 of D1 band in ${}^{135}\mathrm{Nd}$. The color corresponds to $K_l$, as shown in the legend.

Figure 10

The same as Fig. 9, but for band TiP1.

Figure 11

The same as Fig. 9, but for band TiP2.

Figure 12

Comparison of the experimental and calculated $B(M1,I\to I-1)/B{\left(E2\right)}_{\mathrm{in}}$ and $B(E2,I\to I-1)/B{\left(E2\right)}_{\mathrm{in}}$ ratios for the intraband transitions of band D1 and for the transitions between bands TiP1 and D1.

Figure 13

(a)–(c) show a schematic illustration of the precession of the total angular momentum for: (a) even-even nuclei with no odd nucleon ($j=0$) or with odd nucleon aligned along the intermediate axis ($j\parallel R$); (b) odd-mass nuclei with an odd nucleon aligned along the short or long nuclear axis, ($j\perp R$), where $j$ is frozen, and (c) odd-mass nuclei as in (b) but where the odd nucleon is free. (d) and (g) illustrate the excitation energies of the TiP and wobbling bands, respectively, for an angular momentum coupling as shown in (a). (e), and (h) show the excitation energies corresponding to a coupling as shown in (b). (f), and (i) illustrate the reduced transition probabilities $B{(\sigma L,I\to I-1)}_{\mathrm{out}}$, where $\sigma$ stands for $M$ (or $E$) and $L$ stands for 1 (or 2) for transitions linking two consecutive bands, for instance $b_2$ to $b_1$ for TiP bands or $n=2$ to $n=1$ for wobbling bands. The green double arrows in (g)–(i) highlight the expected phonon quantization.

Figure 14

Calculated energies of the negative-parity quasiparticle orbitals $E$(QP), and single-particle orbitals $E$(SP), near the Fermi level of ${}^{135}\mathrm{Nd}$.

Figure 15

The calculated excitation energies of the $h_{11/2}$ negative-parity bands in ${}^{135}\mathrm{Nd}$ where the pairing is excluded.