First lifetime investigations of $N>82$ iodine isotopes: The quest for collectivity

We report on spectroscopic information and lifetime measurements in the neutron-rich ${}^{135,137,139}\mathrm{I}$ isotopes. This is the first lifetime data on iodine isotopes beyond $N=82$. Excited states were populated in fast neutron-induced fission of ${}^{238}\mathrm{U}$ at the ALTO facility of IJCLab with the LICORNE neutron source and detected using the hybrid $\nu$-ball spectrometer. The level schemes of the ${}^{135,137,139}\mathrm{I}$ isotopes are revised in terms of excited states with up to maximum spin-parity of $(33/2^{+})$, populated for the first time in fast neutron-induced fission. We provide first results on the lifetimes of the $(9/2_1^{+})$ and $(13/2_1^{+})$ states in ${}^{137}\mathrm{I}$ and ${}^{139}\mathrm{I}$, and the $(17/2_1^{+})$ state in ${}^{137}\mathrm{I}$. In addition, we give upper lifetime limits for the $(11/2_1^{+})$ states in ${}^{135-139}\mathrm{I}$, the $(15/2_1^{+})$ state in ${}^{137}\mathrm{I}$, the $(17/2_1^{+})$ state in ${}^{139}\mathrm{I}$, and reexamine the $(29/2_1^{+})$ state in ${}^{137}\mathrm{I}$. The isomeric data in ${}^{135}\mathrm{I}$ are reinvestigated, such as the previously known $(15/2_1^{+})$ and $(23/2_1^{-})$ isomers with $T_{1/2}$ of 1.64(14) and 4.6(7) ns, respectively, as obtained in this work. The new spectroscopic information is compared to that from spontaneous or thermal-neutron induced fission and discussed in the context of large scale shell-model (LSSM) calculations for the region beyond ${}^{132}\mathrm{Sn}$, indicating the behavior of collectivity for the three valence-proton iodine chain with $N=82,84,86$.

Figure 1

(a) Schematic representation of the experimental setup. The neutrons are produced in the ${}^7\mathrm{Li}(p,n){}^7\mathrm{Be}$ reaction and are focused on the ${}^{238}\mathrm{U}$ target to induce fission. The $\gamma$ rays are detected by the $\nu$-ball array consisting of 20 ${\mathrm{LaBr}}_3\left(\mathrm{Ce}\right)$ detectors (ring 1), 24 HPGe Clover detectors (rings 2 and 3), and ten HPGe Phase-I detectors (ring 4). Adapted from Ref. [32]. (b) HPGe (red) and ${\mathrm{LaBr}}_3$(Ce) (blue) efficiency curves. The data points were obtained using a ${}^{152}\mathrm{Eu}$ source and corrected for self-absorption effects. For details see text.

Figure 2

HPGe singles spectrum labeled with contaminants (“c”) and transitions from different fission fragments. The inset shows an energy projection with different multiplicity conditions $M$.

Figure 3

Level schemes for the ${}^{135,137,139}\mathrm{I}$ isotopes as observed in this work. The arrow widths correspond to the relative $\gamma$-ray intensities. Where applicable, states are labeled with their lifetime as measured in this work.

Figure 4

HPGe energy projections after gating on ground state transitions in (a) ${}^{137}\mathrm{I}$ and (b) ${}^{139}\mathrm{I}$ as labeled. Transitions from the isotopes of interest are indicated by their respective energy, while those from the background (inelastic neutron scattering or fission binary partners) are labeled with “c”.

Figure 5

Lifetime measurement of the $(15/2^{+})$ state in ${}^{135}\mathrm{I}$. (a) HPGe (red) and ${\mathrm{LaBr}}_3$(Ce) (blue) energy spectra gated on the 1134 keV $(11/2^{+})\to 7/2^{+}$ transition. (b) Background-subtracted ${\mathrm{LaBr}}_3$(Ce) time distribution for the sum of the 288 and 1134 keV transitions. The spectrum is fitted with a prompt Gaussian (blue) convoluted with an exponential decay curve plus a constant background, resulting in the full fit function (red).

Figure 6

HPGe (red) and ${\mathrm{LaBr}}_3$(Ce) (blue) energy spectra after a HPGe sum or single gates and an additional ${\mathrm{LaBr}}_3$(Ce) gate for transitions in (a) ${}^{137}\mathrm{I}$ and (b) ${}^{139}\mathrm{I}$ isotopes. The respective gates are labeled. Time difference spectra for the $(9/2^{+})$ state in (c) ${}^{137}\mathrm{I}$ and (d) ${}^{139}\mathrm{I}$ nuclei. The lifetimes result from a convolution fit (red) of a prompt Gaussian (blue) and an exponential decay plus constant background. The shaded area indicate the uncertainty bands from variation of parameters and fit regions.

Figure 7

Time difference spectra for the measured (a), (b) $(13/2^{+})$ and (c) $(17/2^{+})$ states in ${}^{137}\mathrm{I}$, and (d) the $(13/2^{+})$ state in ${}^{139}\mathrm{I}$. Respective HPGe gates (to select the cascade of interest) and the ${\mathrm{LaBr}}_3$(Ce) time differences ($\mathrm{\Delta }T$) are labeled. Each spectrum is fitted with a convolution of a prompt Gaussian (blue) and an exponential decay plus constant background (black). Shaded areas represent parameter fluctuations in the fits.

Figure 8

Energy of excited states as a function of mass number for ${}^{135,137,139}\mathrm{I}$. Experimental values are taken from the evaluated nuclear data sheets [19, 24, 25] and are shown with filled squares. The identification of $(13/2^{+})$ state in $A=135$ is tentative. Theoretical values from the present shell-model calculations are shown with empty squares (SM-I) and empty triangles (SM-II). Solid and dashed lines are drawn to guide the eye. Each sequence is labeled with spin and parity.

Figure 9

Occupations for the most prominent proton or neutron-proton configurations, respectively, in the ${}^{135}\mathrm{I}$ (a), the ${}^{137}\mathrm{I}$ (b,c), and the ${}^{139}\mathrm{I}$ (d), (e) isotopes as calculated by the shell-model using the N3LOP and the Kuo-Herling (KH) shell-model interactions. See text for details.

Figure 10

Comparison of experimental and theoretical (SM-I and SM-II) excitation energies for the ${}^{135,137,139}\mathrm{I}$ isotopes. See text for details.

Figure 11

Reduced transition probabilities given as (a) $B(M1;J_i\to J_i-1)$ and (b) $B(E2;J_i\to J_i-2)$. Experimental values are shown as filled squares and theoretical values from shell-model calculations as empty symbols. Solid lines for experimental values are drawn to guide the eye. All experimental values are determined in this work. The notation for the theoretical values is given in Table 2.

Figure 12

$E2$ reduced transition probabilities of yrast transitions for neutron-rich tellurium and iodine isotopes beyond $N=82$. The data for ${}^{134,136,138}\mathrm{Te}$ are taken from Ref. [28] and the results for the iodine isotopes are determined in this work.