Effects of one valence proton on seniority and angular momentum of neutrons in neutron-rich ${}_{51}{}^{122–131}\mathrm{Sb}$ isotopes

Background: Levels fulfilling the seniority scheme and relevant isomers are commonly observed features in semimagic nuclei; for example, in Sn isotopes ($Z=50$). Seniority isomers in Sn, with dominantly pure neutron configurations, directly probe the underlying neutron-neutron ($\nu \nu$) interaction. Furthermore, an addition of a valence proton particle or hole, through neutron-proton ($\nu \pi$) interaction, affects the neutron seniority as well as the angular momentum.

Purpose: Benchmark the reproducibility of the experimental observables, like the excitation energies ($E_X$) and the reduced electric-quadrupole transition probabilities $\left[B\right(E2\left)\right]$, with the results obtained from shell-model interactions for neutron-rich Sn and Sb isotopes with $N<82$. Study the sensitivity of the aforementioned experimental observables to the model interaction components. Furthermore, explore from a microscopic point of view the structural similarity between the isomers in Sn and Sb, and thus the importance of the valence proton.

Methods: The neutron-rich ${}^{122}{}_{–}{}^{131}\mathrm{Sb}$ isotopes were produced as fission fragments in the reaction ${}^9\mathrm{Be}\left({}^{238}\mathrm{U}, f\right)$ with 6.2 MeV/u beam energy. A unique setup, consisting of AGATA, VAMOS++, and EXOGAM detectors, was used which enabled the prompt-delayed $\gamma$-ray spectroscopy of fission fragments in the time range of 100 ns to $200\mu \mathrm{s}$.

Results: New isomers and prompt and delayed transitions were established in the even-$A$ ${}^{122}{}_{–}{}^{130}\mathrm{Sb}$ isotopes. In the odd-$A$ ${}^{123}{}_{–}{}^{131}\mathrm{Sb}$ isotopes, new prompt and delayed $\gamma$-ray transitions were identified, in addition to the confirmation of the previously known isomers. The half-lives of the isomeric states and the $B\left(E2\right)$ transition probabilities of the observed transitions depopulating these isomers were extracted.

Conclusions: The experimental data was compared with the theoretical results obtained in the framework of large-scale shell-model (LSSM) calculations in a restricted model space. Modifications of several components of the shell-model interaction were introduced to obtain a consistent agreement with the excitation energies and the $B\left(E2\right)$ transition probabilities in neutron-rich Sn and Sb isotopes. The isomeric configurations in Sn and Sb were found to be relatively pure. Furthermore, the calculations revealed that the presence of a single valence proton, mainly in the $g_{7/2}$ orbital in Sb isotopes, leads to significant mixing (due to the $\nu \pi$ interaction) of (i) the neutron seniorities (${\upsilon }_{\nu }$) and (ii) the neutron angular momentum ($I_{\nu }$). The above features have a weak impact on the excitation energies, but have an important impact on the $B\left(E2\right)$ transition probabilities. In addition, a constancy of the relative excitation energies irrespective of neutron seniority and neutron number in Sn and Sb was observed.

Figure 1

The level schemes of ${}^{122}{}_{–}{}^{131}\mathrm{Sb}$. The newly observed $\gamma$-ray transitions above and below the isomer are indicated in red and blue, respectively. The width of the arrows represent the intensity of the transitions. The isomeric states are indicated by a thick line. The previously known half-lives but remeasured in this work have been underlined by a red line, whereas the newly measured half-lives have been marked with a red box. The half-lives not measured in this work are also shown.

Figure 2

$A\text{−}$ and $Z$-gated $\gamma$-ray spectrum for ${}^{122}\mathrm{Sb}$: The tracked Doppler-corrected prompt singles $\gamma$-ray (${\gamma }_P$) spectrum. The newly identified $\gamma$ rays are marked with an asterisk.

Figure 3

$A$- and $Z$-gated $\gamma$-ray spectra for ${}^{123}\mathrm{Sb}$: (a) The tracked Doppler-corrected prompt $\gamma$-ray (${\gamma }_P$) spectrum with the new $\gamma$-ray transitions marked with asterisk. (b), (c) The delayed $\gamma$-ray (${\gamma }_D$) spectra for $0<t_{\mathrm{decay}}<2\mu \mathrm{s}$ and $6<t_{\mathrm{decay}}<100\mu \mathrm{s}$, respectively. The insets in panels (b) and (c) show the decay curves along with the fits for the 200 and $128+442+956$ keV transitions, respectively. (d) ${\gamma }_P$ in coincidence with any ${\gamma }_D$ for $6<t_{\mathrm{decay}}<100\mu \mathrm{s}$.

Figure 4

$A$- and $Z$-gated $\gamma$-ray spectra for ${}^{124}\mathrm{Sb}$: (a) The tracked Doppler-corrected prompt $\gamma$-ray (${\gamma }_P$) singles spectrum. (b) The prompt $\gamma \text{−}\gamma$ (${\gamma }_P\text{−}{\gamma }_P$) spectrum with gate on 1068 keV transition. The newly identified prompt transitions are marked with an asterisk.

Figure 5

$A$- and $Z$-gated $\gamma$-ray spectra for ${}^{125}\mathrm{Sb}$: (a) The tracked Doppler-corrected prompt singles $\gamma$-ray (${\gamma }_P$) spectrum with the new $\gamma$-ray transitions marked with asterisk. The inset shows the tracked Doppler-corrected prompt ${\gamma }_P\text{−}{\gamma }_P$ coincidence spectrum with gate on the newly observed 658 keV $\gamma$-ray. (b), (c) The delayed singles $\gamma$-ray (${\gamma }_D$) spectra for $0<t_{\mathrm{decay}}<3\mu \mathrm{s}$ and $5<t_{\mathrm{decay}}<60\mu \mathrm{s}$, respectively. The insets in panels (b) and (c) shows the delayed ${\gamma }_D\text{−}{\gamma }_D$ coincidence spectra with gate on 146 and 141 keV $\gamma$ rays, respectively. (d) Tracked Doppler-corrected ${\gamma }_P$ in coincidence with ${\gamma }_D=146\mathrm{keV}\gamma$-ray (for $0<t_{\mathrm{decay}}<3\mu \mathrm{s}$). The inset shows the decay curve along with the fit for the 146 keV transition. (e) ${\gamma }_P$ in coincidence with the ${\gamma }_D=141\mathrm{keV}\gamma$-ray (for $5<t_{\mathrm{decay}}<60\mu \mathrm{s}$). The inset shows the decay curve along with the fit for the 141 keV transition.

Figure 6

$A$- and $Z$-gated $\gamma$-ray spectra for ${}^{126}\mathrm{Sb}$: (a) Tracked Doppler-corrected prompt $\gamma$-ray singles spectrum (${\gamma }_P$). The inset shows the tracked Doppler-corrected ${\gamma }_P\text{−}{\gamma }_P$ coincidence spectrum with sum gate on ${\gamma }_P\mathrm{s}$; namely, the 353, 443, and 961 keV transitions. The newly identified prompt $\gamma$ rays are marked with an asterisk. (b) The delayed singles $\gamma$-ray spectrum (${\gamma }_D$) for $0<t_{\mathrm{decay}}<4\mu \mathrm{s}$. The newly identified delayed $\gamma$ rays are marked with a hash. The inset shows the tracked Doppler-corrected ${\gamma }_P\text{−}{\gamma }_P$ coincidence spectrum with gate on the newly identified 491 keV prompt $\gamma$ ray. (c), (d) The decay curve along with the fit for the delayed 121 and 645 keV transitions, respectively.

Figure 7

$A$- and $Z$-gated $\gamma$-ray spectra for ${}^{127}\mathrm{Sb}$: (a) The tracked Doppler-corrected prompt singles $\gamma$-ray (${\gamma }_P$) spectrum with the new $\gamma$-ray transitions marked with asterisk. The inset shows the prompt ${\gamma }_P\text{−}{\gamma }_P$ coincidence spectrum with a sum gate on ${\gamma }_P$; namely, 387, 392, 539, and 613 keV $\gamma$ rays. (b), (c) The delayed singles $\gamma$-ray (${\gamma }_D$) spectra for $0<t_{\mathrm{decay}}<4\mu \mathrm{s}$ and $10<t_{\mathrm{decay}}<100\mu \mathrm{s}$, respectively. The insets in panels (b) and (c) show the delayed ${\gamma }_D\text{−}{\gamma }_D$ coincidence spectra with the gate on 247 and 1115 keV $\gamma$ rays. (d) Tracked Doppler-corrected ${\gamma }_P$ in coincidence with the sum gate of the ${\gamma }_D$; namely, 85, 120, 131, 144, 247, 852, 956, and 1096 keV $\gamma$ rays (for $0<t_{\mathrm{decay}}<4\mu \mathrm{s}$). The inset shows the decay curve along with the fit for the 131 keV transition. (e) Tracked Doppler-corrected ${\gamma }_P$ in coincidence with the ${\gamma }_D=1115\mathrm{keV}\gamma$-ray (for $10<t_{\mathrm{decay}}<100\mu \mathrm{s}$). The inset shows the decay curve along with the fit for the 825 keV transition.

Figure 8

$A$- and $Z$-gated $\gamma$-ray spectra for ${}^{128}\mathrm{Sb}$: (a) Tracked Doppler-corrected Prompt singles $\gamma$-ray spectrum (${\gamma }_P$). The newly identified prompt and delayed $\gamma$ rays are marked with an asterisk and hash, respectively. The inset shows the ${\gamma }_P\text{−}{\gamma }_P$ coincidence spectrum with sum gate on the ${\gamma }_P$'s, namely the 264, 364 and 414 keV transitions. (b) The delayed singles $\gamma$-ray spectrum (${\gamma }_D$) for $0<t_{\mathrm{decay}}<4\mu \mathrm{s}$. The newly identified delayed $\gamma$ rays are marked with hash. The inset shows the ${\gamma }_D\text{−}{\gamma }_D$ coincidence spectrum with gate on the delayed 773 keV $\gamma$-ray. (c) The ${\gamma }_P$ in coincidence with any delayed $\gamma$-ray for $0<t_{\mathrm{decay}}<4\mu \mathrm{s}$. Again, the newly identified prompt transitions are marked with an asterisk. The inset shows the ${\gamma }_P\text{−}{\gamma }_P$ coincidence spectrum with sum gate on many ${\gamma }_P$'s, namely the 541 and 1195 keV transitions. Panels (d) and (e) show the decay curves along with the fits for the delayed 153 and 773 keV transitions, respectively.

Figure 9

$A$- and $Z$-gated $\gamma$-ray spectra for ${}^{129}\mathrm{Sb}$: (a) The tracked Doppler-corrected prompt singles $\gamma$-ray (${\gamma }_P$) spectrum with the new $\gamma$-ray transitions marked with an asterisk. The inset shows the tracked Doppler-corrected prompt ${\gamma }_P\text{−}{\gamma }_P$ coincidence spectrum with gate on the newly identified 1078 keV transition. (b), (c) The delayed singles $\gamma$-ray (${\gamma }_D$) spectra for $0<t_{\mathrm{decay}}<4\mu \mathrm{s}$ and $5<t_{\mathrm{decay}}<10\mu \mathrm{s}$, respectively. The insets in panels (b) and (c) show the decay curves along with the fits for the 189 and 732 keV transitions, respectively. (d) Tracked Doppler-corrected ${\gamma }_P$ in coincidence with the sum gate of the ${\gamma }_D\mathrm{s}$; namely, 98, 189, 234, and 755 keV delayed transitions (for $0<t_{\mathrm{decay}}<4\mu \mathrm{s}$).

Figure 10

$A$- and $Z$-gated $\gamma$-ray spectra for ${}^{130}\mathrm{Sb}$: (a) Tracked Doppler-corrected prompt singles $\gamma$-ray spectrum (${\gamma }_P$). The newly identified prompt $\gamma$ rays are marked with an asterisk. The inset shows the tracked Doppler-corrected ${\gamma }_P\text{−}{\gamma }_P$ coincidence spectrum with gate on the newly identified 822 keV prompt $\gamma$-ray. (b) The delayed singles $\gamma$-ray spectrum (${\gamma }_D$) for $0<t_{\mathrm{decay}}<5\mu \mathrm{s}$. The inset shows the ${\gamma }_D\text{−}{\gamma }_D$ coincidence spectrum with gate on the delayed 365 keV $\gamma$ ray. (c) The tracked Doppler-corrected ${\gamma }_P$ in coincidence with the delayed $\gamma$ rays = 365 and 1143 keV transitions, for $0<t_{\mathrm{decay}}<5\mu \mathrm{s}$. The newly identified prompt transitions are marked with an asterisk. The inset shows the decay curve along with the two-component fit for the delayed 365 keV transition.

Figure 11

$A$- and $Z$-gated $\gamma$-ray spectra for ${}^{131}\mathrm{Sb}$: The tracked Doppler-corrected prompt singles $\gamma$-ray (${\gamma }_P$) spectrum with the new $\gamma$-ray transitions marked with asterisk. The inset shows the tracked Doppler-corrected prompt ${\gamma }_P\text{−}{\gamma }_P$ coincidence spectrum with gate on the newly identified 1756 keV transition. (b), (c) The delayed singles $\gamma$-ray (${\gamma }_D$) spectra for $0<t_{\mathrm{decay}}<3\mu \mathrm{s}$ and $5<t_{\mathrm{decay}}<150\mu \mathrm{s}$, respectively. The insets in panels (b) and (c) show the decay curves along with the fits for the 344 and 450 keV transitions, respectively. (d) Tracked Doppler-corrected ${\gamma }_P$ in coincidence with the sum gate of the ${\gamma }_D$; namely, 96, 344, and 382 keV delayed transitions (for $0<t_{\mathrm{decay}}<3\mu \mathrm{s}$).

Figure 12

Evolution of the experimental (Expt.) energy differences, as a function of mass number, in Sn (open symbols) (a) $E\left(2^{+}\right)-E\left(0^{+}\right)$ (red squares), $E(15/2^{-})-E(11/2^{-})$ (black circle), and in Sb (shaded symbols) (b) $E(11/2^{+})-E(7/2^{+})$ (red squares), $E\left({10}^{-}\right)-E\left(8^{-}\right)$ (black circle). The filled symbol is the newly observed state from the present experiment.

Figure 13

Evolution of the experimental (Expt.) (a) $5^{-}$ (black triangle down), $6^{-}$ (green diamond), $7^{-}$ (red triangle up), $8^{+}$ (blue circle), ${10}^{+}$ (violet square), $23/2^{+}$ (brown x), and $19/2^{+}$ (orange star) states in ${}^{118}{}_{–}{}^{130}\mathrm{Sn}$ (open symbols), and (b) $15/2^{-}$ (black triangle down), $17/2^{-}$ (green diamond), $19/2^{-}$ (red triangle up), $19/2^{+}$ (blue circle), $23/2^{+}$ (violet square), ${13}^{+}$ (brown x), and ${11}^{+}$ (orange star) states in ${}^{123}{}_{–}{}^{131}\mathrm{Sb}$ (shaded symbols) with mass number, A. The filled symbols are the newly observed states from the present experiment.

Figure 14

(a) Comparison of the experimental (Expt.) level schemes with that obtained from shell model calculations using the interaction in Ref. [6] (SM1 blue) and the modified interaction in the present work (SM2 red) for both positive and negative-parity states in ${}^{127}\mathrm{Sb}$. The different states with the same spin have been joined by dotted lines to show the agreement. (b) The experimental and calculated B($E2$) values (black square) for the $23/2^{+}\to 19/2^{+}$ in odd-$A$ ${}^{123}{}_{–}{}^{131}\mathrm{Sb}$ (see text).

Figure 15

Comparison of experimental (Expt.) (shown in black) [22, 23, 24, 25, 26] and theoretical calculations [from shell model (SM2); shown in red] level schemes for odd-$A$ ${}^{121}{}_{–}{}^{131}\mathrm{Sb}$ isotopes for both positive (+ve) and negative (-ve) parities. The experimental and shell-model states of the same spin-parity have been joined with dotted lines to show the agreement.

Figure 16

Comparison of experimental (Expt.) (shown in black) [6, 35, 36, 43, 47] and theoretical calculations [from shell model (SM2); shown in red] level schemes for even-$A$ ${}^{122}{}_{–}{}^{130}\mathrm{Sb}$ isotopes for both positive (+ve) and negative (-ve) parities. The experimental and shell-model states of the same spin-parity are joined with dotted lines to show the agreement.

Figure 17

The experimental (Expt.) B($E2$) values (black squares) for the (a) ${10}^{+}\to 8^{+}$ in even-$A$ ${}^{118}{}_{–}{}^{130}\mathrm{Sn}$ [16, 21, 48], (b) $23/2^{+}\to 19/2^{+}$ in odd-$A$ ${}^{123}{}_{–}{}^{131}\mathrm{Sb}$ (see text), (c) $7^{-}\to 5^{-}$ in even-$A$ ${}^{118-126}\mathrm{Sn}$ [21], (d) $19/2^{-}\to 15/2^{-}$ transitions in odd-$A$ ${}^{123}{}_{–}{}^{131}\mathrm{Sb}$ (see text), (e) $23/2^{+}\to 19/2^{+}$ in odd-$A$ ${}^{119}{}_{–}{}^{129}\mathrm{Sn}$ [20, 21], (f) ${13}^{+}\to {11}^{+}$ in the even-$A$ ${}^{126-130}\mathrm{Sb}$ (see text), and (g) $27/2^{-}\to 23/2^{-}$ in odd-$A$ ${}^{119}{}_{–}{}^{129}\mathrm{Sn}$ isotopes [20, 21, 49]. The shell-model calculations using the full interaction SM2 (red solid line), SM2 restricted to only one broken neutron pair (green dash-dotted line) and SM2 with $e_{\pi }=0$ (purple dotted line) are also shown. The probability ratios for the (h)–(j) neutron seniority mixing $[(P\left({\upsilon }_{\nu }\right)/P({\upsilon }_{\nu }+2)]$ and (k)–(m) neutron angular-momentum mixing $[(P\left(I_{\nu }\right)/P(I_{\nu }-2)]$ and $[(P\left(I_{\nu }\right)/P(I_{\nu }-1)]$ are also shown.

Figure 18

(a) The states with different neutron seniorities at different excitation energies in even-$A$ Sn ($Z,N$) (${}^{124}\mathrm{Sn}$), odd-$A$ Sb ($Z+1,N$) (${}^{125}\mathrm{Sb}$), odd-$A$ Sn ($Z,N+1$) (${}^{125}\mathrm{Sn}$), and even-$A$ Sb ($Z+1,N+1$) (${}^{126}\mathrm{Sb}$) isotopes. The blue and red arrows represent the energy required to break the first pair of neutrons from seniority ${\upsilon }_{\nu }=n$ to ${\upsilon }_{\nu }=n+2$ ($n=0,...,4$) in even-$A$ Sn $\left[E(2^{+}\to 0^{+})\right]$ and other isotopes, respectively. (b) Plot of the energy differences between states with neutron seniority ${\upsilon }_{\nu }=n$ and ${\upsilon }_{\nu }=n+2$ ($n=0,...,4$), as shown in panel (a), for odd-$A$ and even-$A$ ${}^{119-130}\mathrm{Sn}$ and ${}^{121}{}_{–}{}^{131}\mathrm{Sb}$ nuclei.