High-resolution study of ${}^{166}\mathrm{Er}$ with the ($p, t$) reaction

Excited states in the deformed nucleus ${}^{166}\mathrm{Er}$ have been studied with high-energy resolution in the ($p,t$) reaction, with the Munich Q3D spectrograph. 143 states have been observed up to 4 MeV excitation, and spin and parity has been proposed for about 100 states, based on a DWBA analysis of their angular distributions, out of which 11 are excited $0^{+}$ states, and 39 $2^{+}$ states. The excitation pattern of these states (especially the $0^{+}$ ones) in ${}^{166}\mathrm{Er}$ is compared to that in ${}^{168}\mathrm{Er}$. Calculations were carried out with the $spdf$-IBM model, which gives a reasonable agreement with the observed number of $0^{+}$ states in ${}^{166}\mathrm{Er}$ and their excitation in the ($p,t$) reaction. The $2n$-transfer intensity pattern for the $0^{+}$ states in the ${}^{166}\mathrm{Er}(t,p){}^{168}\mathrm{Er}$ reaction is also reasonably predicted. However, the $spdf$-IBM calculations do not explain the differences between ${}^{166}\mathrm{Er}$ and ${}^{168}\mathrm{Er}$, in the ($p,t$) transfer distribution of the $0^{+}$ states. The understanding of these differences, which appear to be related to a structure change at the $N=98$ deformed subshell closure, remains as an important issue of future, more elaborated model calculations.

Figure 1

Spectra measured at an angle ${\theta }_L={10}^{\circ }$ for the ${}^{168}\mathrm{Er}(p,t){}^{166}\mathrm{Er}$ reaction at 25.0 MeV. The three spectra shown have been measured for three different magnetic field settings of the Q3D spectrograph, and integrated charges of (a) 2.8, (b) 4.7, and (c) 10.1 mC, respectively. Peak labels represent excitation energies in keV. The states assigned as $0^{+}$ are marked.

Figure 2

Angular distributions of states assigned as $0^{+}$. The curves are DWBA calculations normalized to the data (see text). The angular distribution observed for the 1458 keV peak (lowest right side graph) is well described by a one-step DWBA calculation for a $2^{-}$ transfer, as required by the ${\left(2\right)}^{-}$ state known at 1458 keV [16, 22, 27, 29, 45], therefore the known 1460 keV $0^{+}$ state [16, 32] has a negligible population in our reaction. For the states with excitation energy given within parentheses the $L=0$ assignment is tentative because of the smaller number of points.

Figure 3

Angular distributions of $2^{+}$ states. The level at 1527 keV was seen in the spectra collected with both the first and second magnetic setting (there is a small region of overlap between the two settings). The open and filled symbols are the cross sections calculated for the spectra of the two settings, respectively. In all the other cases, the states have been seen at only one magnetic setting and only full symbols are given. The continuous (red) curves represent DWBA (one-step process) calculations normalized to the experimental data, while the dashed (blue) curves are coupled-channel calculations (see text).

Figure 4

Transferred $L$ values, other than 0 or 2, assigned to excited states in ${}^{166}\mathrm{Er}$. The continuous (red) curves are one-step DWBA calculations normalized to the data, and the dashed (blue) curves are coupled-channel calculations (see text). The peaks with excitation energies of 1663 and 2241 correspond to unresolved doublets with known spin/parity, as shown both in this figure and in Table 3.

Figure 5

Partial low-lying level scheme of ${}^{166}\mathrm{Er}$. The width of the horizontal lines is proportional with the ($p,t$) transfer strength, while the width of the arrows is proportional to the reduced transition probabilities. The dashed lines represent states, which were not seen in the present study. The nature of the $0^{+}$ states as deduced from all available experimental data is also shown.

Figure 6

Relative cross sections for $0^{+}$ states of Er isotopes, populated in the ($p,t$) and ($t,p$) reactions. Graphs (a) and (b): summed strength for the excited $0^{+}$ states known up to about 2.5 MeV, normalized to that of the $\text{gs}\to \text{gs}$ transition taken as 100 in the ($t,p$) and ($p,t$) reactions, respectively. Graph (c) shows the evolution of the excitation energy of some selected states. The lower four graphs show relative strengths for individual states, observed for ${}^{166}\mathrm{Er}$ in the (d) ($p,t$) and (f) ($t,p$) reactions, and for ${}^{168}\mathrm{Er}$, graphs (e) and (g), respectively. Experimental data are from: ${}^{160}\mathrm{Er}$ from ($p,t$): Ref. [35]; ${}^{162}\mathrm{Er}$ from ($p,t$): [34]; ${}^{164}\mathrm{Er}$ from ($p,t$): [34, 36]; ${}^{166}\mathrm{Er}$ from ($p,t$): Ref. [32] (intensities that fit those found in this work); ${}^{166}\mathrm{Er}$ from ($t,p$): [32]; ${}^{168}\mathrm{Er}$ from ($p,t$): [4]; ${}^{168}\mathrm{Er}$ from ($t,p$): [33]; ${}^{172}\mathrm{Er}$ from ($t,p$) [52]. The $\times$ symbols and dashed red line in graph (a) show the values for the ($t,p$) intensities in the isotonic Dy isotopes [53], while those in black are the corresponding values for Er isotopes; in panel (b), the summed transfer intensities are given in black, while in blue there are the intensities for the $0_2^{+}$ state; the empty circle for ${}^{168}\mathrm{Er}$ in graph (b) includes the two states just above 2.5 MeV; in (c) the black squares, green stars, empty circles, red crosses, and blue diamonds correspond to the $2_1^{+}, 2_2^{+}, 0_2^{+}, 0_3^{+}$, and $0_4^{+}$ states, respectively; the vertical dashed lines in (a)–(c) at mass 166 mark the $N=98$ subshell closure; in panel (d), the arrows correspond to known $0^{+}$ states, which were not observed in the present experiment. Note: the ($t,p$) reaction intensities correspond to cross sections measured at one angle [32, 33, 52].

Figure 7

Cumulative two-neutron transfer strengths in the ($p,t$) reaction. The arrows indicate the position of the pairing energies in the two nuclei.

Figure 8

Comparison between experimental and $spdf$-IBM calculated energy levels up to about 4 MeV in ${}^{166}\mathrm{Er}$. Besides the $0^{+}$ states, which are all shown (with both firm and tentative assignment, see Table 1) only the first two $2^{+}$ states, first two $1^{-}$ states (red dash-dotted line), and the first $2^{-}$ state (blue dotted line), respectively, are also displayed. The transfer intensities in the ($p,t$) reaction for the $0^{+}$ states and the $B\left(E2\right)$ electromagnetic transition probabilities (arrows) between the lowest levels are also indicated, the width of the arrows being proportional with the reduced strength. The calculated levels drawn with a dashed line have a two-octupole character.

Figure 9

Experimental and $spdf$-IBM calculated $2n$-transfer intensities in the ($p,t$) reaction to $0^{+}$ states, both for individual levels and cumulated strength in ${}^{166}\mathrm{Er}$ [(a)–(c)] and ${}^{168}\mathrm{Er}$ [(d)–(f)].

Figure 10

Experimental and $spdf$-IBM calculations of $2n$-transfer strengths for ($t,p$) reaction leading to $0^{+}$ excited states of ${}^{168}\mathrm{Er}$. The transfer intensities are given in percent, relative to the $\mathrm{gs}\to \mathrm{gs}$ transition.