Diverse collective excitations in ${}^{159}\mathbf{Er}$ up to high spin

A spectroscopic investigation of the $\gamma$ decays from excited states in ${}^{159}\mathrm{Er}$ has been performed to study the changing structural properties exhibited as ultrahigh spins ($I>60\hslash$) are approached. The nucleus of ${}^{159}\mathrm{Er}$ was populated by the reaction ${}^{116}\mathrm{Cd}{(}^{48}\mathrm{Ca},5n\gamma )$ at a beam energy of 215 MeV, and the resulting $\gamma$ decays were studied using the Gammasphere spectrometer. New rotational bands and extensions to existing sequences were observed, which are discussed in terms of the cranked shell model, revealing a diverse range of quasiparticle configurations. At spins around $50\hslash$, there is evidence for a change from dominant prolate collective motion at the yrast line to oblate non-collective structures via the mechanism of band termination. A possible strongly deformed triaxial band occurs at these high spins, which indicates collectivity beyond $50\hslash$. The high-spin data are interpreted within the framework of cranked Nilsson-Strutinsky calculations.

Figure 1

Partial-level scheme for ${}^{159}\mathrm{Er}$ constructed from the present paper; see Fig. 2 for the remainder of the scheme. Transition energies and the excitation energy of the band heads are given to the nearest keV. The width of the arrows represents the relative intensity of the transitions with the unshaded regions attributed to internal conversion. Spin assignments and excitation energy of the band labeled TSD 1 are based on comparisons with results from CNS calculations; see text as well as Ref. [20].

Figure 2

Partial-level scheme for ${}^{159}\mathrm{Er}$ constructed from the present paper for the strongly coupled bands; see Fig. 1 for the remainder of the scheme. Transition energies and the excitation energy of the band heads are given to the nearest keV. The width of the arrows represents the relative intensity of the transitions with the unshaded regions attributed to internal conversion.

Figure 3

Background-subtracted $\gamma$-ray spectra from the $E_{\gamma }^4$ hypercube produced with (a) a sum of triple gates set on the yrast band, (b) a sum of triple gates set on the 830–1153(1154)-keV transitions in coincidence with the 1342-keV transition, and (c) a sum of triple gates set on the 830–1232-keV transitions (excluding the 1153- to 1154-keV transitions) in coincidence with the 1276-keV transition.

Figure 4

Background-subtracted $\gamma$-ray spectra from the $E_{\gamma }^4$ hypercube produced with (a) a sum of triple gates set on band 1 above the $47/2^{+}$ state to the ($87/2^{+}$) state and a sum of triple gates set on band 2 up to the ($93/2^{-}$) state in coincidence with (b) the 1209-keV transition and (c) the 1292-keV transition. Photopeaks that correspond to linking transitions are labeled with triangles, and photopeaks within the yrast band are labeled with diamonds.

Figure 5

Background-subtracted $\gamma$-ray spectra from the $E_{\gamma }^4$ hypercube produced with (a) a sum of triple gates set on transitions in band 3 to display the low- and high-spin parts of this sequence and (b) a sum of triple gates set on band 5. Photopeaks that correspond to linking transitions are labeled with triangles, photopeaks within the yrast band are labeled with diamonds, and photopeaks labeled with crosses correspond to transitions within band 2.

Figure 6

Background-subtracted $\gamma$-ray spectra from the $E_{\gamma }^4$ hypercube produced with a sum of triple gates set on band 3 from the decay of the $39/2^{-}$ state to the $79/2^{-}$ state in coincidence with (a) the 1209-keV transitions and (b) the 1222-keV transition. Photopeaks that correspond to linking transitions are labeled with triangles.

Figure 7

Background-subtracted $\gamma$-ray spectra from the $E_{\gamma }^4$ hypercube produced with a sum of triple gates set on (a) band 4, from the decay of the $33/2^{-}$ state to the $57/2^{-}$ state, in coincidence with the 1046-keV transition, and (b) band 10, from the decay of the $59/2^{-}$ state to the ($91/2^{-}$) state. Photopeaks that correspond to linking transitions are labeled with triangles, photopeaks that correspond to transitions within the yrast band are labeled with diamonds, and photopeaks labeled with asterisks correspond to transitions within band 3.

Figure 8

Background-subtracted $\gamma$-ray spectra from the $E_{\gamma }^4$ hypercube for the $\gamma$ band, produced with a sum of triple gates set on (a) the 438-, 497-, 549-, and 610-keV transitions and (b) the transitions that correspond to the decay of the $21/2^{+}$ state to the $61/2^{+}$ state. Photopeaks that correspond to linking transitions are labeled with triangles, photopeaks that correspond to transitions within the yrast band are labeled with diamonds, and the photopeak labeled with an asterisk corresponds to a transition within band 1.

Figure 9

Background-subtracted $\gamma$-ray spectrum from the $E_{\gamma }^4$ hypercube for bands 6 and 7 produced with a sum of triple gates set on the interband transitions. (a) shows the energy range between 100 and 700 keV, (b) shows the energy range between 700 and 1300 keV, and (c) shows the energy range between 1300 and 1900 keV. Photopeaks that correspond to linking transitions are labeled with triangles, photopeaks that correspond to transitions within the yrast band are labeled with diamonds, photopeaks labeled with asterisks correspond to transitions within bands 1 and 2, and photopeaks labeled with squares correspond to the interband transitions between bands 6 and 7.

Figure 10

Background-subtracted $\gamma$-ray spectra from the $E_{\gamma }^4$ hypercube for bands 6 and 7 produced with a sum of triple gates set on the interband transitions from 130 to 327 keV and (a) the 1072-, 1125-, and 1196-keV transitions from band 6 and (b) the 1109-keV transition from band 7. Photopeaks that correspond to linking transitions are labeled with triangles.

Figure 11

Background-subtracted $\gamma$-ray spectra from the $E_{\gamma }^4$ hypercube for bands 8 and 9. (a) was produced with a triple gate set on the 249- and 272-keV transitions from the decay of bands 6 and 7 and the 215-keV transitions from band 9, and (b) was produced by a sum of triple gates set on all of the interband transitions between bands 8 and 9 in coincidence with the 984-keV transition of band 9. Photopeaks that correspond to linking transitions are labeled with triangles, photopeaks that correspond to transitions within the yrast band are labeled with diamonds, photopeaks labeled with asterisks in (b) correspond to the interband transitions between bands 8 and 9, and photopeaks labeled with squares in (b) correspond to transitions from bands 6 and 7.

Figure 12

The results of the CSM calculations for ${}^{159}\mathrm{Er}$ (a) neutrons and (b) protons. The deformation parameters used were ${\beta }_2=0.235,{\beta }_4=0.046$, and $\gamma =0.0^{\circ }$ and with pair gaps ${\Delta }_n=1.00\mathrm{MeV}$ and ${\Delta }_p=1.13\mathrm{MeV}$. The quasiparticle labeling is given in Table . Solid lines (red) show levels with parity and signature $(\pi ,\alpha )=(+,+1/2)$; dotted lines (red) show ($+,-1/2$) levels; dashed lines (blue) show ($-,-1/2$) levels; dot-dashed lines (blue) show ($-,+1/2$) levels.

Figure 13

(a) The aligned angular momentum (alignment) as a function of rotational frequency for the yrast band and its high-spin parallel sequence labeled ${(+,+1/2)}_2$, band 1 and branching above ($87/2^{+}$), labeled ${(+,-1/2)}_2$, and the $\gamma$ band. (b) Energy relative to a rotating liquid drop as a function of spin for these bands.

Figure 14

Systematics for the $2^{+},3^{+},4^{+},5^{+}$, and $6^{+}$ states of the bands based on $\gamma$-vibrational excitations for ${}^{156}\mathrm{Er}$ [46], ${}^{157}\mathrm{Er}$ [3], ${}^{158}\mathrm{Er}$ [22], ${}^{159}\mathrm{Er},{}^{160}\mathrm{Er}$ [47], and ${}^{162}\mathrm{Er}$ [48]. Also included are the values for the yrast $2^{+}$ and $4^{+}$ states. The energies and spins of the bands observed in the odd-$A$ isotopes are given relative to the lowest-lying state of the yrast band with $13/2^{+}$.

Figure 15

The aligned angular momentum (alignment) as a function of rotational frequency for band 2 with (a) band 3 and its high-spin parallel sequence labeled ${(-,-1/2)}_2$ and (b) bands 4 and 10.

Figure 16

(a) The aligned angular momentum (alignment) as a function of rotational frequency for bands 2 and 5. (b) Energy relative to a rotating liquid drop as a function of spin for bands 2, 3 [with its high-spin parallel sequence ${(-,-1/2)}_2$], 4, 5, and 10.

Figure 17

(a) The aligned angular momentum (alignment) as a function of rotational frequency for the strongly coupled bands. (b) Energy relative to a rotating liquid drop as a function of spin for these bands. See text for further details.

Figure 18

Calculated energy as a function of the shape of the nuclear potential. The potential is specified by using the quadrupole deformation parameter ${\varepsilon }_2$ and the triaxiality parameter $\gamma$. The energy surfaces are drawn for the $(+,+1/2)\pi {\left(h_{11/2}\right)}^4\nu {\left(i_{13/2}\right)}^3$ configuration of ${}^{159}\mathrm{Er}$ at spins 85/2, 89/2, 97/2, 101/2, 105/2, and 109/2. Contour lines are separated by 0.25 MeV, and the $\gamma$ plane is marked at ${15}^{\circ }$ intervals. Dark regions represent low energy.

Figure 19

Sloping Fermi surface diagrams for protons and neutrons at the deformation specified in the figure, which is typical for the terminating configurations in ${}^{159}\mathrm{Er}$. The orbitals are labeled by subshells, but some of these subshells are strongly mixed so that, for example, the neutron $h_{9/2}{f}_{7/2}$ or the proton $g_{7/2}{d}_{5/2}$ orbitals are treated as one entity. In the fully aligned proton ${16}^{+}$ state and neutron $69/2^{+}$ state, all orbitals below the sloping Fermi surfaces drawn by thick lines are occupied. Then, how favored lower spin-aligned states can be formed if one neutron is moved to an antialigned orbital and how higher spin favored states are formed when one proton is excited across the $Z=64$ gap are indicated by arrows. With the present $A=150$ parameters [51], the $m=\pm 1/2$ and $m=\pm 3/2$ states of the proton $h_{11/2}$ subshell and those labeled $d_{3/2}$ are very close to degenerate. Therefore, the $d_{3/2}$ states are drawn at a somewhat higher energy to make the figure easier to read.

Figure 20

Experimental and calculated energies relative to a rotating liquid drop as a function of spin for the near-yrast bands above $30\hslash$. (a) and (b) are positive-parity states. (d) and (e) are negative-parity states. The energy difference between the experimental states and the associated calculated states assigned by theory is presented in (c) and (f) for the positive- and negative-parity states, respectively. The calculated configurations are labeled in the standard way by the number of $h_{11/2}$ protons and $i_{13/2}$ neutrons but, in addition, by the number of $d_{3/2}{s}_{1/2}$ protons in parentheses. Positive-parity states are connected by solid lines, and negative-parity states are connected by broken lines. Solid symbols correspond to ($\alpha =+1/2$), and open symbols correspond to ($\alpha =-1/2$). Aligned states are marked with large open circles. Suggested band crossings are indicated by thin dashed lines. Note that the differences in panel (f) are obtained when the negative-parity bands 2 and 3 are compared with configurations that are calculated a few hundred keV above yrast; see text for details.