Structure changes in ${}^{160}\mathrm{Er}$ from low to ultrahigh spin

A spectroscopic investigation of the $\gamma$ decays from excited states in ${}^{160}\mathrm{Er}$ has been performed in order to study the changing structural properties exhibited from low spin up toward ultrahigh spin ($I~60\hslash$). The nucleus ${}^{160}\mathrm{Er}$ was populated by the reaction ${}^{116}\mathrm{Cd}$(${}^{48}\mathrm{Ca}$,4$n$$\gamma$) at a beam energy of 215 MeV, and resulting $\gamma$ decays were studied using the Gammasphere spectrometer. New rotational structures and extensions to existing bands were observed, revealing a diverse range of quasiparticle configurations, which are discussed in terms of the cranked shell model. At spins around 50$\hslash$ there is evidence for oblate states close to the yrast line. Three rotational bands that have the characteristics of strongly deformed triaxial structures are observed, marking a return to collectivity at even higher spin. The high-spin data are interpreted within the framework of cranked Nilsson-Strutinsky calculations.

Figure 1

The level scheme for ${}^{160}\mathrm{Er}$ constructed from the present work. Energies are given in keV, and the width of the arrows is proportional to the relative intensity of the transitions. Spin assignments and excitation energy of the bands labeled TSD 1, 2, and 3 are based on comparisons with results from CNS calculations; see text as well as Ref. [20].

Figure 2

Background subtracted $\gamma$-ray spectra produced with sums of triple gates from the $E_{\gamma }^4$ hypercube for (a) the positive-parity yrast band, (b) band 1, and (c) band 2 in ${}^{160}\mathrm{Er}$. Photopeaks labeled with parentheses are tentative; see text for details.

Figure 3

Intensity profiles for the top of the positive-parity yrast band (a) and the negative parity bands 1 and 2 (b), relative to sums of triple coincidences set in the $E_{\gamma }^4$ hypercube up to the $I^{\pi }={42}^{+}$ state for the yrast band and the ${44}^{-}$ and ${43}^{-}$ levels for bands 1 and 2, respectively. Transitions that are not fixed in the level scheme are denoted by their energy; see text for details.

Figure 4

Background subtracted $\gamma$-ray spectra for (a) band 3 produced with a sum of triple gates, (b) band 3 produced with a double gate set on the 1045 and 1079 keV transitions, and (c) band 4 produced with a sum of triple gates involving the first four transitions up to the decay of the $I^{\pi }=({24}^{+})$ state. Photopeaks corresponding to linking transitions are labeled with triangles, photopeaks that correspond to transitions within the yrast band are labeled $♯$, photopeaks that are labeled “$*$” in (c) correspond to transitions associated with band 3 (see text for details), and photopeaks labeled with parentheses are tentative.

Figure 5

Background subtracted $\gamma$-ray spectra for (a) band 5 produced with a sum of triple gates set above its $({17}^{+})$ level, (b) band 5 produced with a sum of triple gates set below its $({17}^{+})$ level, and (c) band 6 produced with a sum of triple gates. Photopeaks corresponding to linking transitions are labeled with triangles, photopeaks that correspond to transitions within the yrast band are labeled $♯$, photopeaks labeled with parentheses are tentative, and photopeaks labeled “c” are contaminant peaks of unknown origin brought in by the gating process.

Figure 6

Background subtracted $\gamma$-ray spectra characteristic for transitions from (a) bands 7 and 8 produced with a triple gate at 221, 234, and 255 keV, (b) bands 9, 10, 11, and 12 produced with a triple gate at 175, 204, and 227 keV, and (c) bands 9, 10, 11, and 12 produced with sums of triple gates set at 444, 536, 614, and 676 keV. Photopeaks corresponding to linking transitions are labeled with triangles, photopeaks that correspond to transitions within the yrast band are labeled $♯$, and photopeaks labeled with parentheses are tentative.

Figure 7

Background subtracted $\gamma$-ray spectrum produced with a sum of triple gates set on all the transitions associated with band TSD 3 up to the 1233 keV $\gamma$ ray. Photopeaks labeled $♯$ correspond to transitions within the yrast band, the photopeak labeled with a triangle is a possible linking transition, and photopeaks labeled with parentheses are tentative.

Figure 8

The results of CSM calculations for ${}^{160}\mathrm{Er}$ (a) neutrons and (b) protons. The deformation parameters used were ${\beta }_2=0.253$, ${\beta }_4=0.040$, and $\gamma =0.0^0$, and with ${\Delta }_n$ and ${\Delta }_p=1.14$ MeV. The quasiparticle labeling is given in Table , and the legend denotes the parity and signature as $(\pi ,\alpha )$ of the orbitals.

Figure 9

(a) The aligned angular momentum (alignment) as a function of rotational frequency for the yrast band and band 5 ($K=2$). (b) Energy relative to a rotating liquid drop as a function of spin for these bands.

Figure 10

(a) The aligned angular momentum (alignment) as a function of rotational frequency for the yrast band, bands 3 and 4, and the $\beta$ band observed by Refs. [22, 40]. (b) Energy relative to a rotating liquid drop as a function of spin for these bands.

Figure 11

(a) The aligned angular momentum (alignment) as a function of rotational frequency for the yrast band and the negative parity bands 1, 2, and 6. (b) Energy relative to a rotating liquid drop as a function of spin for these bands.

Figure 12

(a) The aligned angular momentum (alignment) as a function of rotational frequency for the strongly coupled bands (bands 7–12). The yrast band and band 1 are plotted for comparison. (b) Energy relative to a rotating liquid drop as a function of spin for these bands.

Figure 13

Experimental B(M1)/B(E2) ratios as a function of spin. The solid lines represent the theoretical predictions for the proposed configurations using the geometric model [44, 45].

Figure 14

Calculated potential-energy surfaces versus quadrupole deformation ${\varepsilon }_2$ and the triaxiality parameter $\gamma$ for ${}^{160}\mathrm{Er}$ with $(\pi ,\alpha )=(-,1)$ at spins $I=31$, $41$, $51,$ and $61$ labeled (a)–(d), respectively. Contour lines are separated by 0.25 MeV, and the $\gamma$ plane marked at ${15}^{°}$ intervals. Dark regions represent low energy with absolute minima labeled with a white dot. Individual minima labeled $1$–$5$ are discussed in the text.

Figure 15

(a) Energy relative to a rotating liquid drop [34, 35] as a function of spin for the near yrast bands observed above $20\hslash$, (b) calculated excitation energies relative to a rotating liquid drop as a function of spin for the lowest energy states based on collective prolate structures (see text for details of configuration labeling), and (c) the difference between (a) and (b). Solid lines correspond to positive parity configurations and broken lines to negative parity ones. Similarly, solid symbols correspond to positive signature and open symbols to negative signature.

Figure 16

Calculated excitation energies relative to a rotating liquid drop [34, 35] as a function of spin for the lowest energy states based on collective prolate and single-particle oblate configurations; see text for details of configuration labeling. The convention style for the lines and symbols is as given in Fig. 15. The large open circles indicate oblate noncollective band terminating states.

Figure 17

Intensity profiles for the yrast, band 1 and band 2 in ${}^{160}\mathrm{Er}$, from the present work. Also plotted are the intensities in the $(+,0){}_1$ band for ${}^{158}\mathrm{Er}$ (from the data of Ref. [16]), and ${}^{156}\mathrm{Er}$ [50] and ${}^{162}\mathrm{Er}$ [49], plotted relative to their $6^{+}\to 4^{+}$ yrast transition intensity.

Figure 18

The dynamic moment of inertia $J^{(2)}$ as a function of rotational frequency for the three proposed TSD bands in ${}^{160}\mathrm{Er}$. The parentheses are associated with tentative transitions.

Figure 19

Calculated excitation energies relative to a rotating liquid drop [34, 35] as a function of spin for the lowest energy states based on collective triaxial configurations (see text for details) and prolate and single-particle oblate configurations. The convention style for the lines and symbols is as given in Fig. 15. The configuration labels 1 to 5 correspond to the minima in the PES plots of Fig. 14.