Prompt-delayed $\gamma$-ray spectroscopy of neutron-rich ${}^{119,121}\mathrm{In}$ isotopes

Background: The $Z=50$ shell closure, near $N=82$, is unique in the sense that it is the only shell closure with the spin-orbit partner orbitals, $\pi g_{9/2}$ and $\pi g_{7/2}$, enclosing the magic gap. The interaction of the proton hole/particle in the above-mentioned orbitals with neutrons in the $\nu h_{11/2}$ orbital is an important prerequisite to the understanding of the nuclear structure near $N=82$ and the $\nu \pi$ interaction.

Purpose: To explore the structural similarity between the high-spin isomeric states in In ($Z=49$), Sn ($Z=50$), and Sb ($Z=51$) isotopes from a microscopic point of view. In addition, to understand the role of a proton hole or particle in the spin-orbit partner orbitals, $\pi g_{9/2}$ and $\pi g_{7/2}$, respectively, with neutron holes in the $\nu h_{11/2}$ orbital on these aforementioned isomers.

Methods: The fusion and transfer induced fission reaction ${}^9\mathrm{Be}({}^{238}\mathrm{U}, f)$ with 6.2 MeV/u beam energy, using a unique setup consisting of AGATA, $\mathrm{VAMOS}++$, and EXOGAM detectors, was used to populate through the fission process and study the neutron-rich ${}^{119,121}\mathrm{In}$ isotopes. This setup enabled the prompt-delayed $\gamma$-ray spectroscopy of isotopes in the time range of $100\mathrm{ns}–200\mu \mathrm{s}$.

Results: In the odd-$A{}^{119,121}\mathrm{In}$ isotopes, indications of a short half-life $19/2^{-}$ isomeric state, in addition to the previously known $25/2^{+}$ isomeric state, were observed from the present data. Further, new prompt transitions above the $25/2^{+}$ isomer in ${}^{121}\mathrm{In}$ were identified along with reevaluation of its half-life.

Conclusions: The experimental data were compared with the theoretical results obtained in the framework of large-scale shell-model calculations in a restricted model space. The $\langle \pi g_{9/2}\nu h_{11/2};I\left|\widehat{\mathcal{H}}\right|\pi g_{9/2}\nu h_{11/2};I\rangle$ two-body matrix elements of residual interaction were modified to explain the excitation energies and the $B\left(E2\right)$ transition probabilities in the neutron-rich In isotopes. The (i) decreasing trend of $E(29/2^{+})–E(25/2^{+})$ in odd-In (with dominant configuration $\pi g_{9/2}^{-1}\nu h_{11/2}^{-2}$ and maximum aligned spin of $29/2^{+}$) and (ii) increasing trend of $E(27/2^{+})-E(23/2^{+})$ in odd-Sb (with dominant configuration $\pi g_{7/2}^{+1}\nu h_{11/2}^{-2}$ and maximum aligned spin of $27/2^{+}$) with increasing neutron number could be understood as a consequence of hole-hole and particle-hole interactions, respectively.

Figure 1

The level scheme of ${}^{119}\mathrm{In}$. The widths of the arrows represent the intensities of the transitions. The newly identified and the previously known isomeric states are indicated by a thick red and black line, respectively. The previously known half-life but remeasured in this work and consistent with the previous work is marked by a red dashed box.

Figure 2

$A$- and $Z$-gated $\gamma$-ray spectrum for ${}^{119}\mathrm{In}$: (a) The tracked Doppler corrected prompt singles $\gamma$-ray (${\gamma }_P$) spectrum with the new $\gamma$-ray transitions marked with asterisk. (b) Tracked Doppler corrected prompt ${\gamma }_P\text{−}{\gamma }_P$ coincidence spectrum with sum gate on the 145, 207, and 289 keV $\gamma$-ray transitions. (c) Tracked Doppler corrected prompt ${\gamma }_P\text{−}{\gamma }_P$ coincidence spectrum with gate on the 928 keV $\gamma$ ray. (d) The delayed singles $\gamma$-ray (${\gamma }_D$) spectra for $t_{\mathrm{decay}}<3\mu \mathrm{s}$. (e) Tracked Doppler corrected ${\gamma }_P$ in coincidence with ${\gamma }_D=152$ and 218 keV $\gamma$ rays (for $t_{\mathrm{decay}}<3\mu \mathrm{s}$). The inset shows the tracked Doppler corrected prompt ${\gamma }_P\text{−}{\gamma }_P$ coincidence spectrum with gate on the 336 keV $\gamma$ ray.

Figure 3

Decay curves along with the fits for the different transitions in ${}^{119}\mathrm{In}$: (a) 152 keV and (b) sum of 1204 and 928 keV transitions.

Figure 4

The level scheme of ${}^{121}\mathrm{In}$. The widths of the arrows represent the intensities of the transitions. The newly identified transitions are shown in red. The newly identified and the previously known isomeric states are indicated by a thick red and black line, respectively. The newly redetermined half-life is marked by a red box. The $X$ and $Y$ energies refer, respectively, to the energies of the unobserved $(17/2^{-})\to (15/2^{-})$ and $(19/2^{-})\to (17/2^{-})$ transitions as reported in Ref. [12]. Because of these unobserved transitions, excitation energies of levels above the $15/2^{-}$ level are not determined.

Figure 5

$A$- and $Z$-gated $\gamma$-ray spectra for ${}^{121}\mathrm{In}$: (a) The tracked Doppler corrected prompt singles $\gamma$-ray (${\gamma }_P$) spectrum with the new $\gamma$-ray transitions marked with asterisk. (b) Tracked Doppler corrected prompt ${\gamma }_P\text{−}{\gamma }_P$ coincidence spectrum with sum gate on the 110, 169, and 361 keV $\gamma$-ray transitions. (c) Tracked Doppler corrected prompt ${\gamma }_P\text{−}{\gamma }_P$ coincidence spectrum with gate on the 953 keV $\gamma$ ray. (d) The delayed singles $\gamma$-ray (${\gamma }_D$) spectra for $t_{\mathrm{decay}}<30\mu \mathrm{s}$. The inset in (d) shows the decay curve along with the fit for the 99 keV transition. (e) Tracked Doppler corrected ${\gamma }_P$ in coincidence with ${\gamma }_D=214$ keV $\gamma$ ray (for $t_{\mathrm{decay}}<30\mu \mathrm{s}$). The inset shows the tracked Doppler corrected prompt ${\gamma }_P\text{−}{\gamma }_P$ coincidence spectrum with gate on the 352 keV $\gamma$ ray.

Figure 6

Decay curves along with the fits for the different transitions in ${}^{121}\mathrm{In}$: (a) 99 keV, (b) 214 keV, (c) 953 keV, and (d) 1181 keV transitions.

Figure 7

(a) Comparison of the experimental (Expt.) level schemes with those obtained from shell model calculations using the interaction (SM) in the present work for both positive- and negative-parity states in ${}^{119,121}\mathrm{In}$. The different states with the same spin are joined by dotted lines. (b) The experimental $B\left(E2\right)$ values for $25/2^{+}\to 21/2^{+}$ in odd-$A{}^{119,121}\mathrm{In}$ from the previous work (Ref. [12]) and the present work are shown by the black square and red triangle, respectively. The shell model (SM) calculations from Ref. [26] and the present work are shown by green dashed and red solid lines, respectively, for ${}^{119–129}\mathrm{In}$ isotopes.

Figure 8

Evolution of the calculated (SM) energies and the probabilities for the neutron angular momentum and neutron seniority for the, spin-orbit partners of In and Sb isotopes. (a) Energies of $21/2^{+}$ (black), $25/2^{+}$ (red), and $29/2^{+}$ (blue) states in $Z=49{}^{119–129}\mathrm{In}$ isotopes; (b) Energies of the $19/2^{+}$ (black), $23/2^{+}$ (red), and $27/2^{+}$ (blue) level in $Z=51{}^{121–131}\mathrm{Sb}$ isotopes. The evolution of the ${10}^{+}$ states in $Z=50{}^{120–130}\mathrm{Sn}$ isotopes are also shown in green in these panels. The probability of the neutron angular momentum, $P(I_{\nu }=8^{+}$ and ${10}^{+})$ for the (c) $29/2^{+}$ (blue filled), $25/2^{+}$ levels (red hatched filled) in In; and (d) for the $27/2^{+}$ (blue filled), $23/2^{+}$ (red filled and hatched) states in Sb isotopes. The occupancy of the $\nu h_{11/2}$ orbital for each level is also shown on top of each bar in these panels. The probability of the neutron seniority, $P({\upsilon }_{\nu }=2$ and 4) for the (e) $29/2^{+}$ (blue), $25/2^{+}$ states (red) in In; and (f) $27/2^{+}$ (blue filled and hatched), $23/2^{+}$ (red filled hatched) states in Sb isotopes.