Evolution of collectivity in the $N=100$ isotones near ${}^{170}\mathrm{Yb}$

An experiment using the electronic $\gamma -\gamma$ fast-timing technique was performed to measure lifetimes of the yrast states in ${}^{170}\mathrm{Yb}$. The lifetime of the yrast $2^{+}$ state was determined using the slope method. The value of $\tau =2.33\left(3\right)$ ns is in good agreement with the lifetimes measured using other techniques. The lifetimes of the first $4^{+}$ and $6^{+}$ states are determined using the generalized centroid difference method. The derived $B\left(E2\right)$ values are compared to calculations done using the confined beta soft model and show good agreement with the experimental values. These calculations were extended to the isotonic chain $N=100$ around ${}^{170}\mathrm{Yb}$ and show a good quantitative description of the collectivity observed along it.

Figure 1

Form of the potential $\nu \left(\beta \right)$ for (a) X(5), (b) CBS, and (c) rigid rotor.

Figure 2

(a) Partial level scheme of the ground-state band of ${}^{170}\mathrm{Yb}$. (b) Single-gated LaBr spectrum. (c) Single-gated HPGe spectrum.

Figure 3

(a) HPGe-LaBr and LaBr-LaBr coincidence spectra. (b) Time-difference spectrum (see text for details). The line indicates the fit to the data used to extract the lifetime.

Figure 4

The figure indicates the basic steps for extracting the lifetime of the first excited $4^{+}$ state. (a) HPGe detector projection in HPGe-LaBr gates used to check for unwanted transitions. (b) LaBr detector projection in HPGe-LaBr gates indicating the gate used to produce the time-difference spectra and the corresponding peak-to-background ratio $\mathrm{\Pi }$ for the gate region. (c) Time-difference spectra for 293–193 keV feeder-decay combination. (d) The fitted time response of the background (dashed line), together with the PRD curve and the obtained centroid difference from (c).

Figure 5

Same as Fig. 4, but for the first excited $6^{+}$ state. The tail observed around 300 keV in (b) is coming from a peak located at 296 keV. This peak is due to coincidences with the Compton background in the LaBr gate.

Figure 6

(a) Excitation energies and (b) reduced tranistion probabilities of the ground-state-band levels as function of the spin $J$ compared to the CBS prediction. The X(5) and the rigid rotor solutions are also shown as dashed and dotted lines, respectively. Data for the first excited $2^{+},4^{+}$, and $6^{+}$ states are from this experiment and for the $8^{+}$ and ${10}^{+}$ states from Ref. [25].

Figure 7

The excitation energies of the ground-band states for the isotonic chain from ${}^{168}\mathrm{Er}$ to ${}^{176}\mathrm{Os}$ normalized to the $2^{+}$ state energy. The values of the parameter $r_{\beta }$, controlling the energies within the CBS model for the different isotones, are also indicated. Data are taken from Refs. [21, 30, 31, 32, 33]. The inset shows the $R_{4/2}$ value dependence on $r_{\beta }$.

Figure 8

CBS wave function densities for the first excited $0^{+}$ and ${10}^{+}$ states in ${}^{168}\mathrm{Er}$ and ${}^{176}\mathrm{Os}$.

Figure 9

Evolution of the reduced transition probabilities for the yrast states up to spin 10 within the isotonic chain from ${}^{168}\mathrm{Er}$ to ${}^{176}\mathrm{Os}$. The values of the parameter ${\beta }_M$ are 0.45, 0.44, 0.43, 0.37, and 0.41, respectively. Data for ${}^{172}\mathrm{Hf}$ are taken from Ref. [34], for the $2^{+}$ state in ${}^{174}\mathrm{W}$ from Ref. [35] and all the rest from Nuclear Data Sheets [21, 30, 31, 32, 33].