Lifetime of the $4^+_1$ state of $^{132}$Te

TL;DR

The study addresses the question of whether the $4^+_1$ state in $^{132}$Te exhibits genuine quadrupole collectivity or remains dominated by seniority-type configurations near the $N=82$ shell closure. It employs a direct lifetime measurement via recoil-distance Doppler-shift (RDDS) using the two-neutron transfer population $^{130}$Te($^{18}$O,$^{16}$O)$^{132}$Te$^*$, with a Bateman-equation-based analysis to correct for feeding from higher-lying states. The results yield $\tau(4_1^+) = 13.4(14)\,\text{ps}$ and $B(E2;4^+_1\rightarrow2^+_1) = 9.3(10)\,\text{W.u.}$, which agree with shell-model predictions (SN100PN) and contradict earlier fast-timing values. The findings indicate emerging but not fully developed collectivity in $^{132}$Te, with a proton-dominated $s=2$ seniority component and modest $s=4$ admixtures, highlighting the coexistence of competing configurations near closed shells.

Abstract

The evolution of the collectivity of tellurium isotopes from mid-shell towards $N=82$ is currently based mainly on properties of the first excited $2^+$ states. To extend structural information in this isotopic chain, in particular with respect to the balance of microscopic, seniority-type and collective excitations, electric quadrupole transition strengths from $4^+$ states need to be considered. An experiment was performed to determine the $4_1^+$ lifetime of $^{132}$Te via the recoil-distance Doppler-shift method at the University of Cologne tandem accelerator. The isotope of interest was populated in the two neutron-transfer reaction $^{130}$Te($^{18}$O,$^{16}$O)$^{132}$Te$^*$. The $E2$ decay transition strength has been determined to be $B(E2; 4^+_1\rightarrow 2^+_1) = 9.3(10)\, \text{W.u.}$ and compares favourably to shell model calculations.

Figures (7)

• Figure 1: The evolution of the $B(E2; 2^+_1\rightarrow 0^+_1)$ values (upper panel) in the tellurium isotopes follows a clear trend, declining from $N=72$ towards the shell closure at $N=82$. A similar trend cannot be seen for the $B(E2; 4^+_1\rightarrow 2^+_1)$ values due to the insufficient number of precision data (lower panel). Weighted averages of the $B(E2; 2_1^+\rightarrow0_1^+)$ values were taken from the Nuclear Data Sheets $A=126$--$130,134$A126A128A130A134. For ^132Te the $B(E2; 2_1^+\rightarrow0_1^+)$ value from Danchev et al.Danchev was used. The $B(E2; 4_1^+\rightarrow2_1^+)$ values are taken from Kumar et al.Kumar, Prill et al.prill and Refs. Saxena024316STOKSTAD1967507A134.
• Figure 2: The observed $\gamma$-ray energy spectrum is shown with applied particle-coincidence condition as displayed in the inset of Fig. \ref{['fig:spectrum_697']}. The spectrum is summed over all detectors and all distance settings. Therefore, some transitions show Doppler-shifted behaviour and appear as triple-peak structures. The peaks of the most prominent transitions are marked. The $4_1^+\to2_1^+$ transition of ^132Te contributes the most to the peak marked by the bracket. The contamination of the $2_2^+\to2_1^+$ transition of ^132Te is visible in the enlarged spectrum depicted in Fig. \ref{['fig:spectrum_697']}. The possible contamination by the $4_3^+\to4_1^+$ transition of ^130Te is discussed in section \ref{['sec:data_analysis']}. Spectroscopic information is taken from A130A131A132A133.
• Figure 3: Comparison of $\gamma$-ray energy spectra at backward ($142$°) and forward ($45$°) angles summed over all distances. A coincidence condition was applied on the two-neutron transfer, i.e. the peak at high particle energies (blue area in the inset) with a background condition marked by the hatched area (shown in the inset). Both spectra are shown in an interval around the $4_1^+\rightarrow2_1^+$ transition at $696.7\,$keV with its Doppler-shifted components at $688.4$ keV and $704.2$ keV. In the backward spectrum the contaminant at $681.3\,$keV originating from the $2_2^+\rightarrow2_1^+$ transition is clearly visible. In the forward spectrum the contaminant is suspected to be located at $698.4\,$keV between the unshifted and the shifted component of the $4_1^+\rightarrow2_1^+$ transition. The deviation in events between forward and backward direction arises from the asymmetric detector setup with one HPGe more mounted at forward than at backward angles.
• Figure 4: Level scheme of the five observed excited states of ^132Te and their transitions that were populated in the experiment. Information on energy (keV), spin and parity quantum numbers is taken from Refs. A132 and Biswas.
• Figure 5: The fit of the Bateman equations to the intensity ratios at the backward (top) and forward (bottom) angle of the decay curve defined in Eq. \ref{['eq:decay_curve']} is shown. The lifetime of the $4^+_1$ state of ^132Te is extracted from the fits because it is the only free fit parameter. The uncertainties introduced by varying peak widths and positions are not reflected in the depicted uncertainty bars but in the resulting values of the lifetime.