Three beta-decaying states in 128 In and 130 In resolved for the ﬁrst time using Penning-trap techniques

Isomeric states in 128 In and 130 In have been studied with the JYFLTRAP Penning trap at the IGISOL facility. By employing state-of-the-art ion manipulation techniques, three diﬀerent beta-decaying states in 128 In and 130 In have been separated and their masses measured. JYFLTRAP was also used to select the ions of interest for identiﬁcation at a post-trap decay spectroscopy station. A new beta-decaying high-spin isomer feeding the 15 − isomer in 128 Sn has been discovered in 128 In at 1797 . 6(20) keV. Shell-model calculations employing a CD-Bonn potential re-normalized with the perturbative G-matrix approach suggest this new isomer to be a 16 + spin-trap isomer. In 130 In, the lowest-lying (10 − ) isomeric state at 58 . 6(82) keV was resolved for the ﬁrst time using the phase-imaging ion cyclotron resonance technique. The energy diﬀerence between the 10 − and 1 − states in 130 In, stemming from parallel/antiparallel coupling of ( π 0 g − 1 9 / 2 ) ⊗ ( ν 0 h − 1 11 / 2 ), has been found to be around 200 keV lower than predicted by the shell model. Precise information on the energies of the excited states determined in this work is crucial for producing new improved eﬀective interactions for the nuclear shell model description of nuclei near 132 Sn.

r-process [5] traversing through the N = 82 isotones and forming its second abundance peak at A ≈ 130. Nuclear masses are key inputs for calculating the r-process abundances, with the nuclei in the 132 Sn region being one of the most impactful in this respect [6]. Recently, many de- 10 cay spectroscopy experiments have been performed in the A ≈ 130 region [7,8,9,10,11,12,13], and given evidence e.g. for a reduction of the Z = 40 proton subshell gap when approaching N = 82 [7,12]. Despite these advances, excitation energies for many long-living beta-decaying iso-15 meric states have remained unknown although they can provide crucial information on the nucleon-nucleon interactions close to 132 Sn and play a role in the r-process [14,15]. Low-lying isomeric states can be thermally populated in astrophysical environments and change the ef-20 fective half-life of a nucleus, therefore affecting the final r-process abundance pattern.
Isomers have a different spin, shape, or structure compared to the lower-lying states in the nucleus (see e.g. [16]), hindering their de-excitation and prolonging 25 the lifetimes. High-spin isomers in odd-odd nuclei, such as 128 In studied in this work, cannot be populated via the ground-state beta decay of their even-even parent nucleus. The fission yields of high-spin isomers can also be lower than for the ground states, making it possible to miss re-30 lated beta decays or even the existence of such isomers. For example the isomeric yield fraction of the (21/2 − ) isomer in 127 In has been measured to be less than 30 % in proton-induced fission on uranium [17]. In this work, we employ state-of-the-art Penning-trap techniques to study topes [21,22]. Recently, several indium isotopes were measured with the TITAN Penning trap [23] but some isomeric states were not fully resolved.
For even-A nuclei the high-spin states of 122,124,126 In have been recently studied using the nuclear shell model 55 [24]. A good agreement between the shell-model calculations and the experiment was found using the effective interaction jj45pna. On the other hand, restrictions to the model space had to be used for the lighter isotopes which needed to be compensated by re-adjusting the ef-60 fective charges of the nucleons. As computational power increases, calculations in the full relevant model space become possible. Information on the spins, parities, energies, and reduced transition probabilities are vital for fitting new effective interactions for these previously computationally problematic model spaces. The present paper is a step towards understanding the properties of nuclei southwest of 132 Sn.
In this work, we have studied long-living beta-decaying states in 128 In and 130 In by applying state-of-the-art ion-70 trapping methods to measure their masses and decay properties. The neutron-rich indium isotopes were produced with a 30-MeV proton beam impinging into a uranium target at the Ion Guide Isotope Separator On-Line (IGISOL) facility [25]. The fission fragments were thermalized in he-75 lium gas, extracted from the IGISOL gas cell and guided towards the high-vacuum region of the mass separator using a sextupole ion guide [26]. Most of the fragments end up as singly-charged ions, which were accelerated to 30 keV, and mass-separated with a dipole magnet. The 80 continuous A/q beam was cooled and bunched employing the radiofrequency quadrupole cooler and buncher (RFQ) [27] before injecting into the JYFLTRAP double Penning trap mass spectrometer [28]. A dedicated post-trap spectroscopy setup was prepared after JYFLTRAP to iden-85 tify the states whose masses had been studied. The isomerically purified ion bunches from JYFLTRAP were implanted into a movable mylar tape surrounded by a scintillator detector, two 70 % coaxial and a broad-energy range Ge detector.

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At JYFLTRAP, the ions were first cooled and purified using the buffer-gas cooling technique [30] in the first trap. This method allows the cleaning of ions from isobaric contaminants. To resolve the isomeric states from each other and from the ground state an additional purifi-95 cation step employing a Ramsey dipolar cleaning [31] pattern with two 5-ms excitation fringes, separated by either 40 ms ( 128 In m2 and 130 In) or 90 ms ( 128 In and 128 In m1 ) waiting time in between, was applied in the second trap. This was further followed by a cooling period in the first 100 trap before the actual mass measurements in the second trap. The time-of-flight ion cyclotron resonance (TOF-ICR) [32,33] technique was used to determine the ion's cyclotron frequency ν c = qB/(2πm), where q and m are the charge and the mass of the ion and B is the magnetic 105 field strength. The measurements were performed using time-separated oscillatory fields [29,34] with 25 ms (On) -  In, respectively. The use of isobaric references had the benefit that possible systematic uncertainties due to imperfections in the trap cancel out [36]. Time-dependent 115 fluctuations in the magnetic field strength [37] were also taken into account in the analysis. Count-rate class analysis [38] was performed to account for ion-ion interactions in the trap. For the final result, a weighted mean and its inner and outer errors [39] were calculated, and the larger of the errors was adopted. The results from the TOF-ICR measurements are summarized in Table 1 and noted with a .
For 128 In, it is interesting to compare the results with clean samples of 128 In + states obtained at JYFLTRAP, to the combined ground state and isomer measurements performed with 128 In 13+ ions using the TITAN Penning trap at TRIUMF [23]. Whereas the masses for 128 In m1 agree well between the two measurements, the groundstate mass determined from the two-state fit on 128 In 13+

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[23] is 20(10) keV higher than the seven times more precise JYFLTRAP value. As a result, the excitation energy obtained at TITAN is 23(13) keV lower than the JYFLTRAP value (see Table 1).
For 130 In, the TOF-ICR measurement was not able to 135 resolve the 1 (−) ground state from the (10 − ) isomeric state lying at 50 (50) keV [40]. The TOF-ICR resonances collected with 400 ms and 600 ms excitation times showed a similar production ratio between the (5 + ) isomer and the lower-mass state. This suggests that the lower-mass state 140 was the (10 − ) level which has a similar half-life to the (5 + ) isomeric state (see Table 1) whereas the 1 (−) ground state has a much shorter half-life of 290(20) ms [40]. This is consistent with the non-observation of the most prominent gamma lines from the beta decay of the 1 (−) state in 145 the collected beta-gated gamma-ray spectra for the studied lower-mass state. We conclude that the (10 − ) and (5 + ) isomers in 130 In were measured with the TOF-ICR technique, however, the result for the (10 − ) state might still contain a small contribution from the weakly produced 150 ground state.
To resolve all three states in 130 In, a phase-imaging ion cyclotron resonance (PI-ICR) technique [42,43,44] was employed at JYFLTRAP. The cyclotron frequency was determined based on the phase difference after a phase 155 accumulation time t acc . With the PI-ICR technique, all three short-living, beta-decaying states were resolved with a high resolving power R = φ/∆φ ≈ 4.5 × 10 6 , where φ is the accumulated total cyclotron phase and ∆φ is the angular size (FWHM) of the cyclotron spot (see Fig. 1 160 (b)). The 130 In m2 isomer was measured using 133 Cs (∆ = −88070.931(8) keV [35]) as a reference (t acc = 250 ms), and the other two states were measured against 130 In m2 with t acc =320 ms. The data analysis followed otherwise the same procedures as described for TOF-ICR measure-165 ments. The PI-ICR frequency ratio results are highlighted with b in Table 1.
The shorter-living ground state of 130 In was the least populated in the PI-ICR spectra and supports the conclusion that the lower-mass state in the TOF-ICR mea-170 surements was predominantly the (10 − ) state. The massexcess values determined from the TOF-ICR and PI-ICR measurements of 130 In m1 and 130 In m2 agree with each other (see Table 1 A new isomeric state in 128 In at an excitation energy of 1797.6(20) keV was discovered in this work. The yield for this new isomer was similar to the first isomeric state in 185 128 In, and both had trap cycles of around 0.75 s. Therefore, it is estimated that the new isomeric state 128 In m2 has to have a half-life longer than 0.3 s. Since the state was previously unknown, a pure beam of 128 In m2 was prepared with the trap, and implanted on a tape which was 190 moved after every 1000 seconds (≈ 17 mins). For comparison, a spectrum employing only first-trap purification not sufficient to resolve the three states, was also collected. Figure 2 shows the two beta-gated gamma-ray spectra obtained with these settings.

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Most of the observed beta-delayed gamma transitions from the new 128 In m2 and their intensities match with the transitions observed from the 15 − isomer with T 1/2 = 220(30) ns in 128 Sn in Refs. [45,46]. Therefore, the new isomeric state in 128 In has to populate the (15 − ) isomer 200 in 128 Sn either directly or indirectly. We also observe two gamma transitions (1280 keV and 1779 keV) not observed in [45,46]. Of these, the strong 1779 keV transition has an intensity similar to the 15 − → 13 − transition, suggesting it feeds the 15 − isomer. The 1779 keV transition has 205 been already observed in [19] where it was not assigned because it was not coincident with other gamma transitions within the used time window of 2-20 ns. Therefore, coincidences between the transitions above and below the 15 − state with a half-life of 220(30) ns could not have been 210 observed in Ref. [19]. In this work, the statistics was too low to firmly confirm coincidences between the 1779 keV and lower-lying gamma transitions. Further studies to establish the level scheme above the 15 − isomeric state are needed. The resulting level scheme for 128 Sn is shown on 215 the left in Fig. 3.
To further investigate the studied states and the new high-spin isomer in 128 In, shell-model calculations were performed in a valence space consisting of the proton orbitals 1p 3/2 , 0f 5/2 , 1p 1/2 , and 0g 9/2 , and the neutron or-220 bitals 0g 7/2 , 1d 5/2 , 1d 3/2 , 2s 1/2 , and 0h 11/2 using the shell model code NuShellX@MSU [48] with the effective interaction jj45pna [49]. The interaction jj45pna is a CD-Bonn potential re-normalized with the perturbative G-matrix approach. Interestingly, the calculations predict that the 225 first isomeric state in 128 In would be 10 − (see Fig. 4), similar to 130 In, but in disagreement with literature suggesting it is (8 − ) [41]. The earlier (8 − ) assignment is based on the systematics of odd-odd In isotopes and on the observed beta-decay branching ratio of 14(12) % and 230 log f t = 5.8 to the (7 − ) isomeric state in 128 Sn [19,41], supporting an allowed beta decay. The observed feeding in Ref. [19] might be explained by missed transitions from Table 1: Isomeric states in 128 In and 130 In studied in this work together with their spins, parities J π , and half-lives T 1/2 from literature [40,41]. The frequency ratios r = ν c,ref /νc determined using the TOF-ICR ( a ) and PI-ICR ( b ) techniques in this work, corresponding mass-excess values ∆ and excitation energies Ex are tabulated and compared to the literature values from [23, 40,35]. The reference nuclides have been listed for each measurement. The TOF-ICR measurement of 130 In m1 (marked with c ) was done as an admixture with the ground state, and hence the PI-ICR value is recommended.  and their relative intensities. The conversion coefficients α from the BrIcc calculator [47] were used to obtain the total intensity Itot = (1 + α)Iγ . This mainly concerns the 119.5-keV (α = 0.848(12)) and 207.5-keV (α = 0.1226(18)) E2 transitions since for the others, α < 0.01. Due to the used coincidence gate of 1.5 µs, the γ transitions following the 10 + (T 1/2 = 3 µs) and 7 − (T 1/2 = 6.5(5) s) states were strongly suppressed (marked with * ). For comparison, intensities obtained within 1.5 µs after the 128 Sn implantation in Ref. [45] are given, renormalized to the 119-keV transition. In (including all three states, in black) and to the new high spin isomer 128 In m2 at 1.8 MeV, which was additionally purified with the Ramsey cleaning method (in red). The peaks tabulated in Table 2 are shown with an asterisk (*). The strong 1779-keV transition is shown in the inset.
higher-lying levels, such as the ones fed by the beta decay of the (16 + ) isomer. In this work, the intensity of the 235 1055-keV transition is greatly enhanced when all isomeric states are present in the beam, allowing also the (10 − ) assignment for 128 In m1 in agreement with the shell model. The excitation energy determined here for this first isomeric state in 128 In, 285.1(25) keV, is significantly higher 240 than recently obtained at TITAN (262(13) keV [23]) but still lower than the theoretical prediction (452 keV).
According to the shell-model calculations, the new highspin isomer in 128 In is 16 + since no other spin-trap states are located at around 2 MeV (see Fig. 4). The 16 + 245 state consists 92 % of the configuration (π0g 9/2 ) −1 ⊗ (ν1d −1 3/2 0h −2 11/2 ). The 16 + assignment is further supported by the systematics of high-spin isomers in the N = 79 isotones 129 Sn, 130 Sb and 131 Te (see Fig. 5). They all have cay from the 16 + isomer to the 15 + state would convert the 0g 9/2 proton hole into 0g 7/2 neutron hole, in agreement with an allowed beta decay. The calculated 16 + state in 128 Sn is 99.5 % (ν0h 11/2 ) −4 and so not likely to be fed in this beta decay. Although the observed 1280 keV transi- Figure 4: Experimental level scheme of 128 In based on this work and [50] (left). The lowest excited states for each spin-parity were calculated with the shell model using the effective interaction jj45pna [49] (right). The calculated excitation spectrum contains also many other states with the same spin-parities but they are too numerous to be presented in this figure. In fact, the 16 + -state is the 71st state in 128 In.
with other gamma transitions as reported in [19]) and originates from a (15 + ) level directly fed in the beta decay of 128 In m2 . This would place the new (15 + ) state at 5878 keV. The right of Fig. 3 shows that the shell model predicts the 15 + and 16 + states at somewhat lower energies.

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However, the next 15 + and 16 + states are calculated at energies greater than 7.2 MeV. For 130 In (see Fig. 6), the shell model predicts a lowlying isomeric 10 − state but at 264 keV. This is around 200 keV higher than the experimental value of 58.6(82) keV.

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The 10 − isomeric state has the (π0g −1 9/2 ) ⊗ (ν0h −1 11/2 ) configuration which is also the largest component for the 1 − ground state with ≈ 80% contribution. The other two significant contributions to the ground state come from the configurations (π1p −1 3/2 ) ⊗ (ν1d −1 5/2 ), ≈ 8 %, and 290 (π1p −1 1/2 ) ⊗ (ν2s −1 1/2 ), ≈ 6 %. The shell-model calculations predict 3 + and 5 + states at 457 keV and 550 keV. The excitation energy for the (5 + ) isomer, 385.5(50) keV, falls below the observed (3 + ) state at 388.3(2) keV [53, 54]. Although the (5 + ) state is around 200 keV lower than pre-295 dicted, the experimental and theoretical spectra are in a relatively good agreement indicating that the current theoretical understanding of this mass region is reasonable. Therefore, one can expect that the theoretical predictions, such as the spin-parity of the new 128 In isomer, are reli-  (452 keV). In 130 In, the energy difference for the (10 − ) and 1 (−) states, stemming from parallel/antiparallel coupling of (π0g −1 9/2 ) ⊗ (ν0h −1 11/2 ) has been found to be 58.6(82) keV, which is around 200 keV lower than predicted by the shell model. Precise information on the energies of excited 325 states determined in this work is crucial for producing new improved effective interactions for the nuclear shell model description of nuclei near 132 Sn. Here we have demonstrated that such previously challenging isomeric states can be studied, or even new isomers discovered, using a   [50], compared with the shell-model calculations using the effective interaction jj45pna [49]. The calculated level scheme contains only the lowest excited states for each spin-parity. There are also many other states with the same spinparities but they are too numerous to be presented in this figure. cellence Programme 2012-2017 (Nuclear and Accelerator Based Physics Research at JYFL) and projects No.