β-decay spectroscopy of neutron-rich 160 , 161 , 162 Sm isotopes

Neutron-rich 160,161,162Sm isotopes have been populated at the RIBF, RIKEN via β decay for the first time. β-coincident γ rays were observed in all three isotopes including γ rays from the isomeric decay of 160Sm and 162Sm. The isomers in 160Sm and 162Sm have previously been observed but have been populated via β decay for the first time. The isomeric state in 162Sm is assigned a 4− ν 7 2 [633]⊗ ν 1 2 [521] configuration based on the decay pattern. The level schemes of 160Sm and 162Sm are presented. The ground states in the parent nuclei 160Pm and 162Pm are both assigned a 6− ν 2 [633] ⊗ π 2 [532] configuration based on the population of states in the daughter nuclei. Blocked BCS calculations were performed to further investigate the spin-parities of the ground states in 160Pm, 161Pm, and 162Pm, and the isomeric state in 162Sm.


Introduction
The β decay of neutron-rich nuclei can be a useful tool to probe low-lying states in nuclei that are otherwise diffia e-mail: z.patel@surrey.ac.uk cult to populate.Here we present nuclear data on 160 Sm, 161 Sm, and 162 Sm that have been populated via β decay for the first time.These nuclei lie in the neutron-rich midshell region between the closed shells of Z = 50 and 82 and N = 82 and 126 and are expected to be among the most col-lective of nuclei.Therefore this is a good testing ground for collective models.Neutron-rich nuclei are created in the r process, which is responsible for the production of half the nuclei that exist with Z > 26 (iron).There are three major peaks in the elemental abundances at A ≈ 80, 130, and 195.These are due to the closed shells at N = 50, 82, and 126 that create "waiting" points in the r process [1].Experimental data has led to an improved understanding of these peaks [2][3][4].There is also a less pronounced peak at A ≈ 160, of which the origin is not as clear.It is thought to be due to a deformation maximum [5], however recent theories [6,7] and experimental data [8] have also suggested that a subshell gap at N = 100 may play a role.Investigation of nuclei around A = 160 may provide insight into the possible origins of this peak.The high intensity uranium beam at the RIBF, RIKEN has been utilised to populate these isotopes at the limits of known nuclei.

Experimental method
Neutron-rich 160,161,162 Pm isotopes were produced by inflight fission of a 345 A•MeV 238 U beam with an average beam intensity of 10 particle-nA incident on a 9 Be target at the RIBF.The secondary beam was passed through Bi-gRIPS and the ZeroDegree spectrometers [9,10] where the nuclei were separated according to their mass-tocharge ratio (A/q) and atomic number (Z) using time-offlight, magnetic rigidity and energy loss (TOF, Bρ, and ΔE) [11,12].
The ions were implanted into an active stopper, WAS3ABi: Wide Angle Silicon-Strip-Stopper Array for Beta and ion detection [13].This consisted of 5 DSSDs, each with 60 x 40 1-mm strips.A time window of 1 second was used to correlate an ion implantation with a βdecay particle detected in the same or neighbouring pixel.The γ rays emitted following β decay were detected using EURICA (Euroball-RIKEN Cluster Array) [14][15][16]: 84 HPGe crystals arranged in a 4π configuration at ∼ 22 cm from ion and β implantation.

Results
A γ-ray energy-time matrix was produced for each Sm nucleus by placing a particle gate on the parent Pm nucleus.Four Pm nuclei were populated: 160 Pm, 161 Pm, 162 Pm, and 163 Pm.To study the γ rays in prompt coincidence with the β decay of the parent nucleus a short time gate of < 500 ns was used.A time gate of ≥ 500 ns was used to investigate possible isomeric population following β decay.Four Pm isotopes were populated in this experiment, however the number of implanted 163 Pm ions is much lower than the A = 160-162 nuclei and no γ rays were observed following the decay of this nucleus.Prompt coincident γ rays associated with the β decay of 160 Pm, 161 Pm, and 162 Pm can be seen in Fig. 1, Fig. 3, and Fig. 4 respectively.

160 Sm
Four γ rays of 108, 162, 250, and 1128 keV known to belong to the decay of 160 Sm are seen in Fig. 1 [17,18].There is also a γ-ray peak visible at 823 keV, however, the origin of this γ ray is unknown.The 162 and 250 keV γ rays belong to the 4 + → 2 + and 6 + → 4 + transitions in the ground state band respectively.The 1128 keV γ ray is from the decay of a (5 state [18] with a half-life of 120(46) ns [17].The 108 keV γ ray originates from the (6 − ) to (5 − ) state transition [18].
The population of states in 160 Sm via the β decay of 160 Pm are shown in the level scheme in Fig. 2. The tentative assignment of a (6 − ) spin-parity to the ground state of the parent nucleus is made on the basis that the β decay populates the (6 − ) and 6 + states in 160 Sm.The intensities of the levels, measured in a 0 − 600 ns time window to include 5 half-lives of the isomeric state are shown in Tab. 1.The intensities balance through the levels within statistical uncertainties.It is likely that the β decay of 160 Pm populates the (5 − ) isomeric state directly, however there is no direct experimental evidence for this such as missing intensity, hence this transition is indicated by a dashed line in Fig. 2. Blocked BCS calculations presented in Table 3 also support a (6 − ) spin-parity assignment of the 160 Pm ground state.
Table 1.Initial level energy, E i and spin-parity, J π i of the levels of 160 Sm in this work.For each γ ray the energy, E γ , γ-ray intensity, I γ relative to the 162-keV γ-ray intensity, and final level spin, J π f , are listed.

161 Sm
Two γ rays of 104-and 242-keV energy are seen in prompt coincidence with the β decay of 161 Pm, shown in Fig.   Table 2. Initial level energy, E i and spin-parity, J π i of the levels of 162 Sm in this work.For each γ ray the energy, E γ , γ-ray intensity, I γ relative to the 775-keV γ-ray intensity, and final level spin, J π f , are listed.  16Sm is populated via β decay, shown in the β-delayed coincident γ-ray spectrum in Fig. 5.A 775-keV γ ray appears and the 257-keV γ ray is no longer visible in the delayed γ-ray spectrum which suggests the β decay populates an isomeric state of 162   2, are calculated at t = 0 using the exponential law of radioactive decay, N(t) = N 0 e (−λt) , in order to compare the intensities of the isomer-delayed γ rays to the intensities of the prompt γ rays.
The spin-parity of the ground state in the parent nucleus, 162 Pm, is assigned (6 − ) due to the decay to the (6 + ) ground band state, similar to 160 Sm.Blocked BCS calculations in Table 3 support this assignment.However, the (6 − ) state in 162 Pm is strongly forbidden to decay into the (4 − ) isomeric state in 162 Sm due to the ΔI = 2 and parity change required.Therefore it is likely that the 162 Pm ground state decays into a level on top of the isomeric state.Indeed, a 146-keV γ ray is visible in a background subtracted 164-keV coincidence spectrum, shown in Fig. 7.This γ ray is tentatively placed as a transition from a (5 − ) state to the isomeric (4 − ) state in Fig. 6.
These Sm nuclei were also produced directly in the fission reaction at the start of BigRIPS.In order to study isomers in these nuclei a passive stopper was used in place of WAS3ABi, which allowed for a higher implantation rate.The experimental set-up is detailed in [8,19].The (4 − ) isomeric state in 162 Sm was also observed in this passive stopper part of the experiment, with a measured highprecision half-life of 1.7(2) μs [19], seen in Fig. 5.

Discussion
Blocked BCS calculations of the type in Ref. [20] were performed in order to better understand the spin-parities of the ground states in 160 Pm, 161 Pm, and 162 Pm, and to understand the spin-parity of the isomeric state in 162 Sm.The pairing strengths were fixed as G π = 21.0A•MeV and G ν = 20.0A•MeV, in accordance with Jain et al. [20], and the deformation parameters were taken from Möller et al [21].The results can be seen in Table 3 and Table 4. 2

160 Sm
The lowest energy configuration for the ground state of 160 Pm from blocked BCS calculations presented in Table 3 . This supports the assignment made in Section 3.1.The ground state of 160 Pm is assigned a (6 − ) spin-parity that β decays to the (6 − ) and (6 + ) states in 160 Sm.A 2 + ν 1 2 ration is also predicted by the calculations to have low energy.It is possible that a second state with 2 + spin-parity exists in 160 Pm that decays to the 2 + ground band state in 160 Sm, however, due to lack of experimental evidence the 2 + state in 160 Pm has not been placed in the level scheme.
The reduced hindrance of the 1128-keV transition depopulating the 5 − isomer is f ν ∼ 20.The reduced hindrances of the two known K isomers in 160 Sm are discussed in detail in reference [18].

161 Sm
Blocked BCS calculations display many possible ground state configurations of 161 Pm shown in Table 3.The calculations also reveal many possible low-lying states in 161 Sm.The two γ rays in the energy spectrum of 161 Sm are not in coincidence with each other.It is possible that they arise from the β decay of two different states in 161 Pm into a single state in 161 Sm.It is also possible that they are both populated from the β decay of one state in 161 Pm into two different states in 161 Sm.Therefore it is not possible to determine the decay pattern or to assign spin-parities to these possible states.

162 Sm
The blocked BCS calculations for the ground state of 162 Pm show a similar result to the calculations for 160   [521] that are only 43 keV apart.The isomeric state in 162 Sm is assigned a (4 − ) spin-parity based on the lack of observation of a transition from the isomeric state to the (6 + ) state.If such a transition existed it would be visible in the γ-ray spectrum.This assignment is also supported by the calculations presented in Table 4.
The reduced hindrance of the 775-keV transition depopulating the 4 − isomer is f ν ∼ 70.This is larger than in 160 Sm, but consistent with the limit found for the 4 − isomer in 154 Nd [17].

Conclusions
Low-lying states in 160 Sm, 161 Sm, and 162 Sm were populated via β decay for the first time.Isomeric states in 160 Sm and 162 Sm were also observed following β decay, assigned a (5 − ) π 5

Figure 2 .
Figure 2. Level scheme of 160 Sm populated by the β decay of 160 Pm.

Figure 5 .
Figure 5. β-delayed γ energy spectrum of 162 Sm with t ≥ 500 ns.A 789-keV γ ray from the self activity in the LaBr 3 (Ce) detectors added to EURICA is also visible.Inset: The exponential decay curve is from the isomeric decay of 162 Sm, found using the passive stopper part of the experiment.

Figure 6 .
Figure 6.Level scheme of 162 Sm populated by the β decay of 162 Pm.
Energy spectrum of prompt γ rays in 161 Sm.
+ → 2 + transition and the 257-keV γ ray is from the 6 + → 4 + transition.The 2 + → 0 + transition is expected to be around 70 keV from systematics.It was not observed due to the high internal conversion rate expected for this low energy transition.An isomeric state in Sm with − ) based on a lack of transitions to the (2 + ) and (6 + ) ground band states.This is supported by blocked BCS calculations presented in Table4.The level scheme of 162 Sm is shown in Fig.6.The intensities of the γ rays, shown in Table

Table 3 .
Low-lying quasiparticle states in 160 Pm,161Pm, and 162 Pm predicted by blocked-BCS calculations.Only K π values of favoured spin-couplings are shown.

Table 4 .
Low-lying quasiparticle states in162Sm predicted by blocked-BCS calculations.−)spin-parityduetopopulation of the (6 + ) ground band state in 162 Sm.The 257-keV transition from the (6 + ) state is weakly populated compared to the isomeric state, therefore it is determined to be a forbidden transition.The decay to the (5 − ) state on top of the isomeric state is allowed.It is possible that a second ground state in162Pm exists with a spin-partiy of 2 + as in160Pm, however experimental evidence is not present.If it exists it would decay into the (2 + ) ground band state in 162 Sm.The lowest energy quasiparticle configurations in 162 Sm predicted by blocked BCS calculations are a 5 −